The Impossible Loop - Brain Freeze vs. Gaea's Blessing [Archive]

Tacosnape

07-31-2007, 10:02 PM

Alright. I think I broke Magic. Here is the scenario.

1. I am playing Doomsday Combo, utilizing the kill that works with Second Sunrise, Conjurer's Bauble, Lion's Eye Diamond, and an infinitely large Brain Freeze. Once I commit to this Brain Freeze and to a specific number, due to the nature of my combo, I will not be able to cast any more spells whatsoever. It is my turn, the turn after I have cast Doomsday, and I am fully capable of executing the combo with no setbacks.

2. I have a Cephalid Looter in play. It is untapped and capable of using its activated ability to force my opponent to draw a card.

3. My opponent has no cards in hand and no relevant permanents on the board. He also has absolutely no way to disrupt my combo, and no way to harm the Cephalid Looter.

4. My opponent has exactly 48 cards in his library, exactly 3 of which are Gaea's Blessing. No other card in his library is relevant here.

Now, here's what I understand, so correct me if I have an error here:

I have to pick a number of times I'm going to repeat my LED/Second Sunrise/Conjurer's Bauble combo, in effect setting a Storm Count, then I cast my Brain Freeze. Let's say, for example, I cast Brain Freeze as the 10,000,000th spell for the turn. This should in effect end with 10,000,000 Brain Freezes on the stack, each milling the opponent at 3 cards a shot.

Now, the second I roll a Gaea's Blessing, the trigger from Gaea's Blessing will go on top of the stack, above all remaining Brain Freezes. As my opponent has no responses and neither do I, this will result in the graveyard as it stands at that moment being shuffled back into the opponent's library.

The key factor here, however, is that eventually, with 48 cards and 3 Gaea's Blessings in my opponent's library, his library is going to be randomly shuffled to this, from top to bottom:

45 Random Cards
Gaea's Blessing
Gaea's Blessing
Gaea's Blessing

The odds of this happening are, of course, astronomically low. However, should it happen, all three Gaea's Blessings would be milled at once, resulting with a stack of all three triggers at once.

I could then kill my opponent by tapping my Cephalid Looter before those triggers resolve.

The problem is this.

Since every shuffle is completely random and every shuffle will have an insanely low chance of arranging the library in that exact stack, but that chance does exist, how do you determine whether or not that stack actually happens in the span of 10,000,000 Brain Freezes?

Regardless of what number of Brain Freezes you decide to put on the stack, there's always a chance that the exact stack of 48 cards required for me to kill my opponent won't ever happen. And there's always a chance it will.

So given that it would be absolutely impossible to actually play through 10,000,000 Brain Freezes, and given that there's no mathematical way to prove whether I win or whether I lose, but I definitely either win or lose, what happens?

Machinus

07-31-2007, 10:07 PM

If it's game 3 and you are at time:

The judge probably decides to give you X minutes to try to resolve the combo. If your opponent doesn't concede the game before then, the round ends in a draw.

If it's not game 3, the judge will make some other ruling.

Bovinious

07-31-2007, 10:11 PM

Tacosnape

07-31-2007, 10:32 PM

I've asked the same exact question before, and basically the answer I got was that you cannot appeal to infinity or appeal that eventually the deck will be stacked that way. That could be wrong though, I think that with a way to get an arbitrarily large number of Brain Freezes you should be able to win, but Im not sure the rules allow for it.

That seems a bit ridiculous. If you declare your number high enough, say, 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, the chances of the deck not being stacked that way are virtually nonexistant, but still distantly existant enough to make it an uncertainty.

(EDIT: About 20 Zeroes were deleted from that figure due to the post going off the right side of the screen.)

Silverdragon

07-31-2007, 10:44 PM

I was able to find the following at StarcityGames Ask the Judge
http://www.starcitygames.com/pages/judgefinder.php?keywords=gaea%27s+blessing&Submit2=Ask+The+Judge%21

Q: I have Ambassador Laquatus in play and a method of generating arbitrary amounts of mana at will (and untapping creatures at will). My opponent has thirty-nine cards in his library, two of which are Gaea's Blessing and no cards in the grave. Since the milling and reshuffling could go on potentially forever, could I request that a certain three cards (two Blessings and an island) put left in his library and the rest in his graveyard? This would happen eventually anyway, right?

A: Just because it would eventually happen doesn't mean that you can just jump to that state. It's very different than repeating a set of identical actions with identical results (like mana with Rob Dougherty's Verdant Succession deck). This is one you'll have to play out, and take your actions in a timely fashion. I'd probably put a judge on the match to keep you moving along briskly and so your opponent feels confident that you're not stalling. If you run out of time and get to the five extra turns, I'd put you on the clock (five minutes), like we did in the days of TurboZvi.

So I guess in your example most judges will have you go through the motions until the very state you want is achieved or the time runs out. Personally I think that's not the perfect solution but I guess one has to deal with that.

Bovinious

07-31-2007, 11:10 PM

I guess sometimes playing that out might be good enough, like if you were up 1-0, you could play out the Brain Freezes for 25 min or whatever and take the 1-0 win, correct? Youre screwed though if you were down 1-0, I think that rule kneeds to be changed.

Tacosnape

08-01-2007, 12:23 AM

4 Lesbian Points* to Silverdragon for digging that up.

I guess sometimes playing that out might be good enough, like if you were up 1-0, you could play out the Brain Freezes for 25 min or whatever and take the 1-0 win, correct? Youre screwed though if you were down 1-0, I think that rule kneeds to be changed.

Wow. This gets more convoluted by the minute.

If you're up 1-0 and you're Doomsday, you pretty much win your match as a result. If you're down 0-1 and you're Doomsday, you pretty much lose your match as a result unless you can hit that Shuffle combination in however little time is left.

Going further along this path, it seems to me there could be a lot of potential for stalling for the Gaea's Blessing player by taking a little extra time to shuffle, flipping one card at a time into the graveyard, and so forth.

*(We had a fresh shipment of lesbians, but they all went to Pinder. So they're currently unredeemable.)

Bryant Cook

08-01-2007, 02:02 AM

Grapeshot > Brainfreeze.

Pinder

08-01-2007, 02:08 AM

*(We had a fresh shipment of lesbians, but they all went to Pinder. So they're currently unredeemable.)

My lesbians are on the way? Sweet.

And to actually post something useful, couldn't you just declare the number of copies of Brain Freeze you want to be the number of different ways that the 48 cards could be stacked? I mean, in a stack of 48 cards, you have 48 slots, which could be any one of 48 different cards, so the number of possible ways a stack of 48 cards could turn out is roughly 48^2 = 2304 possible ways (in truth it's a bit more complicated than that, but it's an accurate enough model for our purposes). Since it takes 16 copies of Brain Freeze to mill 1 complete set of 48, couldn't you declare 16x2304 = 36,864 copies of Brain Freeze and make the case that you've exhausted every possible combination of 48 cards? I suppose technically you could make the case that any number of those specific permutations of 48 (or a combination thereof) could appear a technically infinite number of times, but that's even more unlikely than the 1 specific stack of 48 with 3 Blessings on the bottom, don't you think?

In all honesty, I think it should be ruled with Murhpy's Law. If it can happen, it wil happen, eventually, and since that particular stack can happen, it's safe to say that it will happen within a potentially infinite number of copies of Brainstorm.

Then of course, there's the problem of not having infinite time to carry out an infinite number of cases, which is where the problem lies, IMO. To say that something will "eventually" happen is sort of a moot point because "eventually" might not happen before the end of the round.

cdr

08-01-2007, 09:03 AM

emidln

08-01-2007, 09:44 AM

Grapeshot > Brainfreeze.

WIN

RoddyVR

08-01-2007, 10:08 AM

Short answer:

No, you can't magically have your Brain Freeze copies leave your opponent's Gaea's Blessings on the bottom of his library. Loops only work with deterministic actions.

No, you can't try to play out 10,000 copies. Any more than a few would be Stalling.

So a judge's ruling will not take away the opponent's 10^(-1000000)% chance that the library never stacks the right way for the combo to kill him?

What if there was only one blessing in the deck? Would the fact that it being one of the bottom 3 cards is much more likely make any difference? although i guess at that point doing it manualy might almost be possible.

Actualy that's another question. Assuming that you wont allow the combo player to just say "10^1000000 brainfreezes, blessing will keep putting your yard in your lib, but if the blessing is one of last 3 cards, i will respond to blessing's triger by forcing you to draw with looter"
And then if it will have to be done manualy, how much can the opponent stall? The "loop" (i know that's not the right term here) then becomes:
"Resolve brainfreeze copies till blessing triggers and interupts the process. If there's no cards in lib at this point tap looter in response to blessing trigger , if blessing is earlier then one of last 3 cards, you shuffle your lib and we try again."

Would the judge allow the opponent to put the cards into yard 1 (or 3) at a time, or could it just be shortened to "shuffle, look at bottom 3 cards, shuffle again, look at bottom 3 cards....." and how much time could each shuffling take (lets assume there were fetches before, would it be ok for the opponent to start now shuffling more thoroughly then he did when he fetched earlier?)
In this scenario the fact that the opponent will get to a Blessing is prety deterministic, so is then the fact that he'll have to shuffle his library again, so would the shortcut of "forget the putting them in yard 3 at a time, just look at bottom 3 to see if it worked with this shuffle" be allowed?

chmoddity

08-01-2007, 10:14 AM

Thankfully, we have human beings as judges. And they can decide, based on their own perceptions, if you are stalling. Bottom line is that if the enormous amount of replication of actions isn't accomplishing anything reasonable, the judge should warn you, and eventually call you for stalling.

FoolofaTook

08-01-2007, 01:35 PM

My assumption, and it's just an assumption based on very long ago judge rulings, is that you actually have to defeat your opponent in the timeframe of the round. I have never had a game adjudicated for or against me based on a theoretical win condition that did not have a clearly finite and near conclusion. Actually thinking about it I've never had a game adjudicated anything other than a draw at time.

Caveats here would be that most of my match experience is in an untimed environment in which you won or lost with whatever you brought, and that once we went to the timed environment there was a concerted effort by the judges to crack down on U/W permission, particularly in U/W vs U/W scenarios, that saw a lot of drawn third games.

cdr

08-01-2007, 02:19 PM

Here is a statement by Andy Heckt, the Judge Manager (from today, interestingly enough):

"Probability of a result is not usuable to resolve loops. Either its 100%
certain, or impossible to do using a loop.

And yes, that's [O]fficial and resolved so several years ago.

Andy"

So a judge's ruling will not take away the opponent's 10^(-1000000)% chance that the library never stacks the right way for the combo to kill him?

It's not "a judge's ruling", it just how the rules work. The rules for loops cover only 100% certain (aka deterministic) actions, not uncertain (non-deterministic) actions, no matter how probable.

What if there was only one blessing in the deck? Would the fact that it being one of the bottom 3 cards is much more likely make any difference? although i guess at that point doing it manualy might almost be possible.

Actualy that's another question. Assuming that you wont allow the combo player to just say "10^1000000 brainfreezes, blessing will keep putting your yard in your lib, but if the blessing is one of last 3 cards, i will respond to blessing's triger by forcing you to draw with looter"
And then if it will have to be done manualy, how much can the opponent stall? The "loop" (i know that's not the right term here) then becomes:
"Resolve brainfreeze copies till blessing triggers and interupts the process. If there's no cards in lib at this point tap looter in response to blessing trigger , if blessing is earlier then one of last 3 cards, you shuffle your lib and we try again."

Would the judge allow the opponent to put the cards into yard 1 (or 3) at a time, or could it just be shortened to "shuffle, look at bottom 3 cards, shuffle again, look at bottom 3 cards....." and how much time could each shuffling take (lets assume there were fetches before, would it be ok for the opponent to start now shuffling more thoroughly then he did when he fetched earlier?)
In this scenario the fact that the opponent will get to a Blessing is prety deterministic, so is then the fact that he'll have to shuffle his library again, so would the shortcut of "forget the putting them in yard 3 at a time, just look at bottom 3 to see if it worked with this shuffle" be allowed?

Personally, I would allow no more than 30 seconds (a quick standard for slow play). The number of Blessings in the deck is irrelevant.

Nihil Credo

08-01-2007, 03:12 PM

Since Mind's Desire players are allowed to skip the shuffles altogether when they don't matter at all, might the Doomsday/Brain Freeze player be allowed to roll a d60 instead of doing a full shuffle when the only thing that matters is where the (assuming singleton) Gaea's Blessing ends up?

Edit: Writing this post made me realize the following: during the resolution of the g_64 Brain Freezes there is no way for the Doomsday player to know whether the opponent has the full four Blessings in the deck (and thus decking is impossible) or less than four, in which case he has a chance.

And since the Blessings player would have no reason to reveal that information, the whole issue ends up moot unless 1) the to-be-decked player previously "lost" at least one Blessing to discard/countermagic/Peek/etc.; 2) the Doomsday player got to look at the opponent's library (during which process it's highly likely the Blessings got RFGed); 3) it's the top 8 of a major tournament and decklists have been revealed.

Machinus

08-01-2007, 03:36 PM

Sanguine Voyeur

08-01-2007, 03:50 PM

I understand and agree with the rules policy, but mr heckt was not a math major in school. There is a 100% chance that it will happen, eventually...No there isn't, the chance of it never happening is almost neglegable, but each time it's shuffled there is a chance that it's not deck, Blessing, Blessing, Blessing.

Machinus

08-01-2007, 04:21 PM

No there isn't, the chance of it never happening is almost neglegable, but each time it's shuffled there is a chance that it's not deck, Blessing, Blessing, Blessing.

I could write out the equlity for you but it's not worth the effort. If there is no time limit the result is guaranteed.

Nihil Credo

08-01-2007, 04:32 PM

Machinus

08-01-2007, 05:08 PM

...which is what a "time limit" is, and why the judge's ruling is right.

However, the borrowing of "choose N" in the foundation of Magic prevents anyone, including judges, from being able to talk about things as 0% vs. 100%. By definition it's arbitrary.

This is one scenario where the practical limitations of magic, in this case time limits, contradict what is otherwise a natural conclusion, and that's just part of the game.

Pinder

08-01-2007, 05:18 PM

So I guess the moral here is that if you have a sorcery speed combo deck (and no way to continue comboing in response to a Blessing trigger like Solidarity), just kill with Tendrils or Grapeshot. I mean really, you're already supporting :b::b::b: for Doomsday, is it that hard to just use Tendrils?

Nihil Credo

08-01-2007, 05:18 PM

(Warning: the following is both academic and nitpicking)

Time limits and "choose N" are two entirely unrelated rules (to prove this, observe that only the latter applies in the finals of a Pro Tour).

The "choose N" rule was introduced to handle problems such as an infinite damage combo squaring off vs. an infinite pump combo, not to stop games from lasting until the end of the Universe.

Machinus

08-01-2007, 05:26 PM

I know that is why it was chosen, but the rule has many other implications. In this case, it directly prevents the storm player from winning specifically because of time limits.

He can choose any number of loops that he wants to, but he only gets the result out of as many as he gets to execute. Given unlimited time, the chance of him not getting it can be as arbitrarily close to zero as he wants, which academically is the definition of two things being equal.

Bovinious

08-01-2007, 07:55 PM

I agree with Machinus, if there was no time limit it should be allowed, because getting something arbitrarily close to 0 is the same as 0. It basically breaks down to the definition of distinct numbers (being that you need to be able to find a number in between for two numbers to be distinct). Its the same kinda thing that says Point 9 Repeating (PNR) is equal to 1, .00000000 (infinite) 00X equals 0 in the same sense, I think. But since judges dont accept this and there is a time limit, just use Grapeshot I guess.

Cait_Sith

08-01-2007, 08:19 PM

I just got an e-mail on an associated topic (I am an MtG Rules Advisor, so I get these sometimes):

Here is the question:

Suppose player A has somehow gained a lot of life and is currently at
> 1000000 life. Now player B plays the Reiterate + Seething Song + Cloud
> Key / Locket of Yesterday combo and decides to play Ignite Memories for
> *just* 1000000 copies.
>
> Consider if player A is holding
> 1. 5 spells
> 2. 5 lands
> 3. 5 high cmc spells and 1 land
> 4. something like 2 lands and a spell with cmc 3
>
> I think the answer is quite obvious for 1 and 2, but are there any rules
> for handling such cases?

To which Andy Heckt said:

Probability of a result is not usuable to resolve loops. Either its 100%
certain, or impossible to do using a loop.

In this case it definitely means that you MUST continue until either time runs out or someone wins.

Edit:

There is more:

Player A has won game one of a three game match. Game 2 is currently
in progress with 30 minutes remaining to complete the match. Player
A has 10,000 life. Player B performs the aforementioned Ignite
Memories combo 50,000 times. Player A is holding 3 cards with CMC 4
and one land and thus have a high probability of losing.

Since a loop cannot be used to resolve the stack, if Player A refuses
to concede, is he stalling? Can a judge issue a warning and simply
issue a game loss? What if he's holding five lands and one card with
CMC 4?

The answer:

The most common/infamous is the nearly-infinite milling vs. Gaea's Blessing
debate from the first week of July 2005 (and some number of other reruns
that have occurred since).

"What if he's holding five lands and..." - no change to the answer,
because it doesn't change the certainty. The addition of that "wrinkle"
also doesn't really add much to the things we need to learn from this
scenario, which are:

* Judges can not force players to make a specific sort of play, neither
to break a loop nor to win a game (or lose it). Judges can maintain the
pace of play, and progressing through this loop can go quickly - but
probably not quickly enough to resolve 50,000 copies of Ignite Memories.

* If a series of repeated actions contains only certainties, it can be
handled via the loop rules; if there's any chance of a different
outcome, then the loop rules do not apply.

* Oddball scenarios like this rarely happen in real life; they usually
only exist in the minds of devious judges (like me).

Oh, and: no, this is not a topic for debate; the decision has long since
been stated - and now repeated, above.

The emphasis is mine.

T is for TOOL

08-01-2007, 09:02 PM

Given unlimited time, the chance of him not getting it can be as arbitrarily close to zero as he wants, which academically is the definition of two things being equal. This scenario is meaningless to Magic and not worth discussing. Time limits will always exist because the players could end up dying before the desired gamestate is reached. Suppose your opponent is a terminally ill cancer patient and the doctors say that he has less than six months to live but could pass away at any time. Are you going to call a judge over and argue that, given an unlimited amount of time (or even just six months), your opponent will be unable to continue the match and thus we should 'jump in time' to that gamestate and declare you the winner? Just because the odds of him being dead increase over time toward 100%, the judge isn't going to rule that your opponent is a corpse until it actually happens. He'll sit and make you play your match out and occasionally check to see if your opponent has kicked the bucket.

Machinus

08-01-2007, 10:02 PM

I already stated that the judges ruling is correct. You would see exactly why that point is important if you read this thread more carefully.

TheInfamousBearAssassin

08-01-2007, 11:40 PM

No, you can't try to play out 10,000 copies. Any more than a few would be Stalling.

This is flagrantly bullshit. It's not stalling when you're playing as fast as reasonably possible to a clear goal (the right stack that lets you kill your opponent). You might as well say it's stalling to attack an opponent with a hundred+ life. How the Hell do you justify calling the action that lets a person win the game stalling? I'm boggled by this and alarmed that it's coming from a judge.

cdr

08-02-2007, 12:08 AM

I understand and agree with the rules policy, but mr heckt was not a math major in school. There is a 100% chance that it will happen, eventually...

Suffice to say that people much better at math than you had input into the ruling. I've seen more than enough about it over the years, I don't argue about it.

This is flagrantly bullshit. It's not stalling when you're playing as fast as reasonably possible to a clear goal (the right stack that lets you kill your opponent). You might as well say it's stalling to attack an opponent with a hundred+ life. How the Hell do you justify calling the action that lets a person win the game stalling? I'm boggled by this and alarmed that it's coming from a judge.

You are not advancing the state of the game in any manner - you are likely to be repeating the same things over and over, with little to no difference in the game after 30 seconds. Your goals are irrelevent. Attacking advances the state of the game - a life total is changing, phases are changing, turns are being taken, etc. You will hear this from every informed judge - it's fairly basic application of policy.

Machinus

08-02-2007, 12:09 AM

Suffice to say that people much better at math than you had input into the ruling. I've seen more than enough about it over the years, I don't argue about it.

I'd be very surprised if this were true. Regardless, I'm still correct.

TheInfamousBearAssassin

08-02-2007, 01:44 AM

You are not advancing the state of the game in any manner - you are likely to be repeating the same things over and over, with little to no difference in the game after 30 seconds. Your goals are irrelevent. Attacking advances the state of the game - a life total is changing, phases are changing, turns are being taken, etc. You will hear this from every informed judge - it's fairly basic application of policy.

I call bullshit yet again. It is not certain that you will be able to kill an opponent with this action, just like it is not certain that attacking will do me any good against an opponent with four hundred life, but it's still part of my plan for winning.

When I let Brain Freeze stack after Brain Freeze stack resolve, I am working towards a clear and definable goal of getting the random shuffle that will cause my opponent to fucking die. And given the nature of the deck, that's pretty much my only way left of winning anyhow. How the Hell can you argue with a straight face that trying to kill the opponent is stalling?

APriestOfGix

08-02-2007, 02:59 AM

No it isn't. The Doomsday player is not allowed to perform anything but a finite number of shuffles. Limits to infinity do not enter the picture.

To put it another way: the Doomsday player is allowed to choose a natural number for the storm count, which is associated to the chance of him managing to deck his opponent. But no number he can choose is associated to a chance of 1.

he is correct, you are basically fighting Xeno's paradox. Given an infinite number of recursive steps, you approach the asymptote of 100% and buy Newton's law, it becomes 100% (thats why we can walk). So therefor there is a 100% chance that is will happen over a infinite storm count.

The problem is that we do NOT have infinite storm. Also each shuffle is an independent action. This means that the previous results play no effect of future effects (in the math world, where you are venturing to try and make your case). This is because each action, does not change the possible outcomes of the future events.

This means that over time, (not infinite time) there is only the given % chance of it happening, which is (deck #)/3^(deck #).

This means you have no way to make sure this event will happen, and thus you must play it out, and there for lose, since the likly hood of it happening in the allotted time are very slim.

and BTW, i play doomsday, and Wasted Life is right...

Grapeshot > Brain Freeze

Nihil Credo

08-02-2007, 06:24 AM

Nightmare

08-02-2007, 08:01 AM

Quoting myself since the question seems to have been ignored. To Akki and other judges: would you allow this shortcut in your games?

No. A) You don't know how many Blessings are in the deck, and your opponent is not obliged (nor should he be) to tell you. B) There are never (or at least, very rarely) 60 cards in a library. C) Brain Freeze does not say "Roll a D60. If the result is 1, 2, or 3, win the game."

cdr

08-02-2007, 01:05 PM

Since Mind's Desire players are allowed to skip the shuffles altogether when they don't matter at all, might the Doomsday/Brain Freeze player be allowed to roll a d60 instead of doing a full shuffle when the only thing that matters is where the (assuming singleton) Gaea's Blessing ends up?

With the number of posts made, I think you can forgive one being overlooked.

That would not be acceptable. Rolling dice is done for actual random effects (like choosing a random card in hand), not for situations that might seem effectively random like yours. The other cards in the deck do matter, even if they don't to you. Policy is not to try to "model" any situation like this.

Skipping shuffles on cards like Mind's Desire is completely different and unrelated - if the deck is randomized, you don't need to keep re-shuffling it.

troopatroop

08-02-2007, 01:56 PM

Personally, I would allow no more than 30 seconds (a quick standard for slow play). The number of Blessings in the deck is irrelevant.

If I chose to make 10,000 copies of Brainfreeze, I have that right as a player. You can't as a judge tell me that the number I chose is too large because it's a judgement call for however much I think I need. Just because it intervenes with the amount of time you have allotted me to take during this round does not mean that I have to let it affect my decisions in game. That is an intelligence check on a player, and thusly, you can't make it. I may not know the number of cards in his library, or that it is in my right to ask. I could possibly not know that there are 60 cards in a library by being a newer player, or what if I actually had dimentia and thought there were 6,000 cards in my opponents library? You could go so far as to say so many things based on a lack of playskill.

You shouldn't being able to infer to a player what the correct number on a loop may be, so if I actually think that I need 10,000 Brainfreezes, you can't tell me I don't.

Basically, I'm putting 10,000 brainfreezes on the stack. So now, don't I have to play them all out? And being that the result could possibly win or lose me the game if I get lucky (Or unlucky) enough, isn't it my right to continue doing so? Wouldn't you stopping me from resolving the affects on the stack be benefitting my opponent in an unfair way, so unfair in fact that it could be stopping me from winning after only one more shuffle?

Nightmare

08-02-2007, 02:16 PM

If I chose to make 10,000 copies of Brainfreeze, I have that right as a player. You can't as a judge tell me that the number I chose is too large because it's a judgement call for however much I think I need. Just because it intervenes with the amount of time you have allotted me to take during this round does not mean that I have to let it affect my decisions in game. That is an intelligence check on a player, and thusly, you can't make it. I may not know the number of cards in his library, or that it is in my right to ask. I could possibly not know that there are 60 cards in a library by being a newer player, or what if I actually had dimentia and thought there were 6,000 cards in my opponents library? You could go so far as to say so many things based on a lack of playskill.

You shouldn't being able to infer to a player what the correct number on a loop may be, so if I actually think that I need 10,000 Brainfreezes, you can't tell me I don't.

Basically, I'm putting 10,000 brainfreezes on the stack. So now, don't I have to play them all out? And being that the result could possibly win or lose me the game if I get lucky (Or unlucky) enough, isn't it my right to continue doing so? Wouldn't you stopping me from resolving the affects on the stack be benefitting my opponent in an unfair way, so unfair in fact that it could be stopping me from winning after only one more shuffle?

You're complicating the situation needlessly. If you mill for 30 secs, even in a deck with Battle of Wits (the largest reasonable deck size in a tournament, which is the only scenario where this matters), you have plenty of time to see if they have Gaea's Blessing or not. If not, they will have milled the library. If so, then the situation becomes more complex, and the "loop" fails in the eyes of the rules. It absolutely is at the judge's discretion as to how long you're allowed to eat clock time with this combo.

RoddyVR

08-02-2007, 02:29 PM

so a judge can come over and rule (to the doomsday player)
"those 99999980 (the first 20 or so were used to go through lib once and find a blessing) brainfreezes you have on the stack only give you a very small chance of winning before time runs out, but they will waste a lot of time, so we're just gonna take them off the stack and assume that you never got his library to stack the perfect way"

but a judge can NOT come over and rule (to the opponent)
"those 999999980 brainfreezes give you a very small chance of surviving this game, and it would be a waste of time to try to resolve them one at a time, so lets just take them off the stack and assume that one of them stacked your deck the right way for you to lose."

what's the difference?
in both cases the judge is saying to the players that this small chance of achieving something (win or loss) is not worth the time it will waste to actualy get to it.

as for advancing the game state, ofcourse resolving the stacked brainfreezes is advancing the game state, its taking spells off the stack. there isnt some rule somewhere that sais a player isnt allowed to take more then X minutes for a single phase (cause if there was solidarity as a deck would be banned).

rufus

08-02-2007, 02:46 PM

Appealing to math when you say 'in an infinite number of actions' is not a good way to make an argument.

The probability of getting three particular cards at the bottom of an n-card deck in a particular shuffle is:
6/(n*(n-1)*(n-2))
For a 48 card deck, that works out to 1/17,296 chance that it will happen per shuffle, so a few million brainfreezes should be sufficient.

However, it's very unlikely to occur within the amount of time allowed for a game. In addition physical shuffling has issues.

Skipping shuffles on cards like Mind's Desire is completely different and unrelated - if the deck is randomized, you don't need to keep re-shuffling it.

Actually, there are in-game events triggered by shuffles (Psychogenic Probe), or something like Lantern of Insight which reveals the top card of the library could be in play and would force the shuffle.

Of course, the structure of shuffling in the rules does allow both players to just tap the deck, and doing anything else (barring conditions) might qualify as stalling.

Nightmare

08-02-2007, 02:50 PM

cdr

08-02-2007, 02:54 PM

troopatroop / RoddyVR
I wasn't completely clear. If you as the Brain Freeze player (or even your opponent) wants to continue with a game that is not advancing within a reasonable amount of time, as in this situation, you would be stalling.

You are not going to be allowed to take up the entire round shuffling and re-shuffling a deck.

At that point, if there are copies left on the stack, you have two options that avoid stalling: both players can agree to draw, or one can conceed.

Actually, there are in-game events triggered by shuffles (Psychogenic Probe), or something like Lantern of Insight which reveals the top card of the library could be in play and would force the shuffle.

Of course, the structure of shuffling in the rules does allow both players to just tap the deck, and doing anything else (barring conditions) might qualify as stalling.

Skipping shuffles is an established shortcut - game situations can modify whether shortcuts are appropriate to use. Neither Psychogenic Probe nor Latern of Insight would force you to shuffle, either - you can just take the damage / reveal the card as appropriate, without actually shuffling. That's a different topic, though.

rufus

08-02-2007, 05:13 PM

Neither Psychogenic Probe nor Lantern of Insight would force you to shuffle, either - you can just take the damage / reveal the card as appropriate, without actually shuffling. That's a different topic, though.

Ruling that way vis-a-vis Lantern of Insight is incorrect. After each copy of Mind's Desire resolves, the players get priority, and the top cards of each library is revealed. As soon as players can make decisions based on what the top card of the library is, the library ceases to be random because the Mind's Desire player might, for example, have cantrips that he or she can play to pull dead cards out of his or her own deck

Tacosnape

08-02-2007, 05:40 PM

I fail to see how doing this with Ambassador Laquatus and doing this with Brain Freeze are the same thing.

With Brain Freeze, you have to pick a number, and that number isn't guaranteed to get there.

With Laquatus, assuming you can continue your mana engine while it's in play, you don't have to pick a number, because you can continue to redo it. Therefore there is absolutely no chance the deck won't eventually be stacked the way you want it.

I feel that should be a different case.

TheInfamousBearAssassin

08-02-2007, 05:56 PM

I wasn't completely clear. If you as the Brain Freeze player (or even your opponent) wants to continue with a game that is not advancing within a reasonable amount of time, as in this situation, you would be stalling.

You keep using that word. I do not think it means what you think it means.

intransitive verb
: to play for time : delay
transitive verb
: to hold off, divert, or delay by evasion or deception

Cheating includes, but is not limited to, the following intentional activities:
...Stalling the length of a turn to take advantage of a time limit...
Slow Play
Players must take their turns in a timely fashion regardless of the complexity of the play situation. Playing too slowly or stalling for time is not acceptable. If a Judge determines that a player is playing excessively slowly at any point during the tournament, the responsible player will be subject to the appropriate provisions of the DCI Penalty Guidelines.

Under Stalin's leadership, the Soviet Union played a decisive role in the defeat of Nazi Germany in the Second World War (1941-45) and went on to achieve the status of superpower. The social effects and human cost resulting from the crash programs of industrialization and collectivization in the 1930s, along with the USSR's ongoing campaigns of political repression have been the subject of much study and debate as well whether the Holodomor famine was induced or deliberate. Scholars estimate deaths under his regime to be from between under 2[4] to over 20[5][6][7][8] million people.

The situation described is not someone delaying for time. It is not someone playing slowly. It is someone approaching their one remaining path to victory with all due speed as is their right as a player. Can you grasp that? They are doing the one thing that enables them to win, and which clearly has a real, tangible chance of success. You cannot logically maintain that the rules won't let you determine that after declaring a googolplex iterations of the action, that it would eventually happen and so you can move the game state along; but then in the reverse situation, determine that because someone's chance of immediate success with the strategy isn't very large, you can just skip it. Your stance is inconsistent and illogical.

Fred Bear

08-02-2007, 06:13 PM

It really seems like the 'infinity rule' assumes that the action is degenerate or the sum of the actions does nothing to the game state outside of the loop, in which case it would make sense to pick a number and execute the action that many times.

In this case, though, you can show mathematically that repeating this action (milling to Blessing and re-shuffling) infinite times will contain a case where the deck stacks in the way you want it to (all Blessings on the bottom), meaning the sum of actions converges to a real result. It's a fairly easy math proof, too.

It seems like the rules should be modified to take these types of situations into account.

Fred Bear...

cdr

08-02-2007, 07:21 PM

TheInfamousBearAssassinI don't argue about it. I am relaying rules and policy. Feel free to go harass #mtgjudge or judges elsewhere.

I fail to see how doing this with Ambassador Laquatus and doing this with Brain Freeze are the same thing.

With Brain Freeze, you have to pick a number, and that number isn't guaranteed to get there.

With Laquatus, assuming you can continue your mana engine while it's in play, you don't have to pick a number, because you can continue to redo it. Therefore there is absolutely no chance the deck won't eventually be stacked the way you want it.

I feel that should be a different case.

They're actually mostly the same - you can create an arbitrary number of 3-card mills with Brain Freeze copies, or an arbitrary number of 3-card mills with Laquatus activations. By the rules, they're the same - neither is a loop.

The difference tournament-wise is that you can force a draw or concession with enough Brain Freeze copies, whereas with Laquatas you are directly controlling the milling and would have to stop activating him or face stalling penalties.

It seems like the rules should be modified to take these types of situations into account.

You could try writing to someone on the rules team. They're pretty sick of this (largely inconsequential) topic, though.

As Andy Heckt wrote:
"Realize the likelyhood of these situations is very very low and the
debates about them (which rise up about every 2 years) occur more often
than actual situations. In fact a table collapsing during a match occurs
more often"

Illissius

08-02-2007, 08:49 PM

The difference tournament-wise is that you can force a draw or concession with enough Brain Freeze copies, whereas with Laquatas you are directly controlling the milling and would have to stop activating him or face stalling penalties.

As Laquatus can be activated at instant speed, what about getting an arbitrarily large amount of mana, and using all of it to activate Laquatus in response to itself? This seems logically equivalent to the Brain Freeze version. Could you force a draw or concession that way?

And what if the players can't agree on either drawing or one of them conceding?

cdr

08-02-2007, 09:10 PM

You are choosing to activate Laquatas, so you are intentionally wasting time. Past a reasonable amount of time, you have to continue the game (stop activating Laquatus) or you are stalling. I sort of see what you're saying, and I guess it's pretty much equivalent.

I would tell the players that drawing is the only reasonable option, if one of them doesn't want to conceed. Continuing the game is not an option. I would think that the players would be reasonable.

RoddyVR

08-02-2007, 10:22 PM

I would think that the players would be reasonable.
lol. i think that right there is the problem. players =! resonable in any situation where a game loss depends on it.

Bane of the Living

08-03-2007, 09:34 PM

Id just play through the ten million copies of freeze letting my opponent agonize over never getting a play again. If you explain to them your milling with 10 million copies on the stack I cant see this as stalling. You comboed. If your opponent doesnt like it they can concede. You just need to be up one game obviously.

I could see a judge ruling against your probable mill but he cant tell you to stop the gamestate when you have millions of copies of a spell on the stack. Mill away, let your opponent shuffle their deck till their hands bleed.

cdr

08-03-2007, 11:33 PM

APriestOfGix

08-04-2007, 01:42 PM

lol. i think that right there is the problem. players =! resonable in any situation where a game loss depends on it.

Syntax error: =! unknown operator.

(!= btw)

Tacosnape

08-04-2007, 02:46 PM

cdr

08-04-2007, 04:13 PM

As I said earlier, the player not agreeing to draw would face stalling penalties. I don't want to speculate about neither player wanting to take the draw; I don't think it's ever happened and I certainly hope it never does.

In fact, I've never even seen this type of situation actually occur in a tournament, and have heard about it happening maybe once.

freakish777

08-04-2007, 04:38 PM

How is Ambassador Laquatus entering the equation here? If you have him and a way to make your opponent draw a card and infinite mana, you win the game, Blessings or not.

Opponent reveals a milled Blessing, trigger goes on the stack, you respond by activating Laquatus again, repeat at next Blessing trigger, etc, your opponent eventually has zero cards left you force them to draw.

If you have infinite mana, Laquatus and no way to make them draw a card, and they have Blessing, you lose. They have a 100% chance of having a library after your arbitrarily large number of shuffles after Blessing triggers.

That simple.

Other thoughs on this:

This topic isn't really worth anyone's time. Why would you use Brain Freeze over Grapeshot? What's the probability of this specific interaction coming up in tournament? Why are people deciding that their own view of the game is more important than the rules of the game?

The rules are pretty clear that you have to advance the state of the game, or that you're stalling for time.

State =

Cards in hand,
Phase,
Turn,
Life,
Permanents in play,
number of cards left in library

Nowhere in the state of the game does order of the library come up because that information is hidden. Some of you may be thinking that "you've got # of cards left in library, wtf?", however, the number of cards left in the library isn't changing after the action you took (action = playing a spell, attacking, making some other decision). You played a spell (took an action), their library isn't going away (state isn't changing).

It's really irrelevant if it's your only avenue to victory. Maybe you shouldn't play a crappy deck...

Cait_Sith

08-05-2007, 08:37 AM

I'll say this once more: the judge will not let you play through more than a few copies. He can and will "tell you to stop". You can agree to draw the game, or you can likely get disqualified for stalling.

The problem is, THIS IS FLAGRANTLY WRONG.

* Judges can not force players to make a specific sort of play, neither to break a loop nor to win a game (or lose it). Judges can maintain the pace of play, and progressing through this loop can go quickly.

The judges MUST let you play through as many copies as there are. The judge can make sure you don't take forever for each copy, but you cannot force someone to concede or be punished.

Lego

08-05-2007, 07:58 PM

Finally, someone makes some sense on this thread. I didn't expect it to be Cait_Sith, but seriously... I can't believe Akki actually counsels telling a player they can't perform an action that will very probably win the game just because it'll take some time. Remind me to check which tournaments Akki is judging before I go. "Hi, we're going to let you play as much Magic as you want today, but we reserve the right to force players to draw rather than play out their games. Thanks!"

MattH

08-05-2007, 10:14 PM

They're actually mostly the same - you can create an arbitrary number of 3-card mills with Brain Freeze copies, or an arbitrary number of 3-card mills with Laquatus activations. By the rules, they're the same - neither is a loop.

Woah there pardner. They are NOT the same. For example, consider Power Artifact on Grim Monolith + Ambassador Laquatus + Cephalid Looter in play. That combo is truly INFINITE - if I ever run out of mana, I can just make more. I can make a million copies and if it isn't enough I can always make a million more. In this situation, if the opponent tries to stop me from winning, their argument will always rely on their not being enough time in the round to win by my chosen method. In that case the OPPONENT is trying to use the time limit against ME.

By contrast, the posted Doomsday combo is merely "arbitrarily large" (you pick a natural number N, and that is a large but finite [and shrinking as the copies resolve] number of copies).

It would be different if you didn't have the way to force a card draw, because then even if you get the perfect shuffle, the library will be reshuffled. In that case, resolving more copies of the ability will not do anything meaningful, and that would indeed be stalling.

You are choosing to activate Laquatas, so you are intentionally wasting time.
It is not a waste of time to try and win the game by the only means at your disposal!

State =

Cards in hand,
Phase,
Turn,
Life,
Permanents in play,
number of cards left in library
Wrong. You left out "objects on the stack." A critical error.

Angelfire

08-06-2007, 10:10 AM

Ambassador Laquatas is no where near comparable to Brain Freeze. If you have an infinite mana engine + Laquatas + a way to make your opponent draw at instant speed it wouldn't matter if your opponent's deck was 300 Gaea's Blessings, you could just mill them in response to each trigger and then make them draw a card with no cards in library and 300 Gaea's Blessing trigger on the stack.

However, if someone says that 999,999,999,999,999,999 copies of Brainfreeze doesn't beat 3 Gaea's Blessings doesn't understand logic. The chances of the 3 Gaea's Blessings not showing up on the bottom in any of the near infinite cases is essentially 0. If you are handed a loss and disagree, why are you running 3? Either run 4 or 1, 3 is probably the worst number to run.

4eak

08-06-2007, 01:01 PM

Woah there pardner. They are NOT the same. For example, consider Power Artifact on Grim Monolith + Ambassador Laquatus + Cephalid Looter in play. That combo is truly INFINITE - if I ever run out of mana, I can just make more. I can make a million copies and if it isn't enough I can always make a million more. In this situation, if the opponent tries to stop me from winning, their argument will always rely on their not being enough time in the round to win by my chosen method. In that case the OPPONENT is trying to use the time limit against ME.

By contrast, the posted Doomsday combo is merely "arbitrarily large" (you pick a natural number N, and that is a large but finite [and shrinking as the copies resolve] number of copies).

If one is not infinite, then the other is not infinite as well. At any point you 'Power-out' another set of Laquatus triggers you are forced to pick a natural number N as well. Laquatus triggers are not infinite, they remain arbitrarily large.

Clearly, the difference between the Doomsday and Power-Laquatus scenarios would be that the latter could continue milling in response to Gaea's Blessing triggers. This does not make Laquatus "infinite" if you believe that arbitrarily large numbers must be named.

It boils down to this:

Doomsday=A single set of some arbitrarily large number of triggers.
Power-Laquatus=An arbitrarily large number of sets of some arbitrarily large number of triggers.

Power-Laquatus is not infinitely larger in a relevant sense, it is the arbitrarily larger number of sets that is relevant.

More importantly, if you used a different "infinite" mana engine, one that could not generate mana on the stack, we could run into a likely scenario in which Laquatus=Brainfreeze. If, for some reason, you spent all your mana milling, and saved none (perhaps you didn't anticipate Gaea's Blessing), then you are stuck in the same position (at least on the stack). Of course, as long as you floated an arbitrarily large amount of mana, and you didn't use it all, then Laquatus can obviously do something Doomsday cannot.

-----------------------

As for the problem at hand, it would seem reasonable, as a matter of logical requirement, for a judge to force the players to enter the state in which the 3 Gaea's are on the bottom of the library as along as neither player can state they have a possible play to make on the stack (Time Stop?).

If 2+2=4, then why can't we follow the logical flow and intent of the scenario in which an infinite (or even arbitrarily large enough, such as what mathematicians tend to do) set of Brainfreezes must deterministically arrive at the 3 Gaea's Blessing eventually being the last three cards in the library?

Gaming is about fairness--people deserve the consequences of their actions. They should be rewarded properly for their actions. Assuming the laws of logic and mathematics, it is evident that the Doomsday player in fact deserves to win this game.

If anything is the problem it is that the rules of magic are too lacking to handle the obvious. The judges who create/interpret the rule system fail to realize the improper risk/reward ratios formed by their illogical rules and rulings. Rule-creators have simply not been smart enough (or too lazy) to deal with an obvious problem: people who are rationally using more complex ideas of mathematics (dealing with infinity and loops) are not receiving due reward (or consequences) for their choices. This is a limitation on skill and justice in gaming.

The solution requires more work on the creators and interpretors of the rules, not the players. Eventually, WotC will continue to define and clarify the rules to better allow fairness this game, including better rules to deal with infinite numbers and loops. For now, they just consider it too much of a 'nightmare' to fix, perhaps at the expense of game itself.

peace,
4eak

troopatroop

08-06-2007, 01:28 PM

Lukas Preuss

08-06-2007, 02:52 PM

Let me say that I find this thread highly interesting, but most of you approach the problem wrong:

However, if someone says that 999,999,999,999,999,999 copies of Brainfreeze doesn't beat 3 Gaea's Blessings doesn't understand logic. The chances of the 3 Gaea's Blessings not showing up on the bottom in any of the near infinite cases is essentially 0.

I have read many comments like this... the problem is that people of this opinion don't understand Analysis, which is the mathematical branch that deals with limits.
Right, the chances of the 3 Gaea's Blessing not showing up are close to zero. If there were actually infinite copies, the chance would actually be zero, but this is were you have to take a closer look. And were MtG's policy of picking a number smaller than infinite makes all the difference.

http://en.wikipedia.org/wiki/Limit_%28mathematics%29

As you see from that link (actually I haven't read it, if it doesn't tell you the difference that infinity makes, try to google for an explanaition), even if something is getting as close to zero as possible, it will never actually be zero, but if it goes on infinitely, you can assume that it is zero (zero is the limit). For every other case and everything that goes on for less than infinite times, it doesn't reach zero. It gets close, yes, but it is not zero.

With other words, the chance of it the three Gaea's Blessings not being the last three cards is getting smaller and smaller with each try, and it gets closer to zero everytime, but it never reaches zero, unless you actually have infinite copies. Which is not the case because you have to choose a number (thanks to the rules).
If the chances are larger than zero for this case to happen (which they are, even if you have "999,999,999,999,999,999" Brain Freeze copies), no judge should ever let you allow to jump to a gamestate that might never be reached, just because it is "most likely (and not definitely) possible if you have enough time". Since you can't choose infinty as a number, there is always the chance that you are just unlucky and you will not put the three Gaea's Blessings on the bottom of your library (by the way, the average possibility for this to happen with a 48 card library is 0.0001206%, if I'm not mistaken), no matter how hard and how often you try.

I hope this made some sense... If not, maybe someone else who knows his (or her) mathematics can try to explain it a little better.

4eak

08-06-2007, 04:30 PM

I have read many comments like this... the problem is that people of this opinion don't understand Analysis, which is the mathematical branch that deals with limits.

We know (or I assumed most of us did) that a finite number of triggers would still leave open the "technical" possibility that having 3's Gaea's on the bottom would not happen. However, if you look even closer into the field of mathematics (and physics), you'll find that many of those scholars say at some point that it reaches zero (even when we can show it doesn't). For example, many draw the line of impossibility at 1 out of "more particles than there are in the universe". Perhaps we are coming to terms with what probability means inside this universe (theory meets RL), and we'll need to make a few assumptions to have any answer at all.

Personally, I don't buy the argument. I think there are other arguments to consider.

Firstly, we could just say that the Doomsday player, in all likelihood, deserved to win. Not just probably, but that it would even be next to impossible that he didn't deserve to win. If we are going to remove the reality of infinite loops from a game that really does form them all the time, forcing us to pick an arbitrary number unfairly, then it would not be unreasonable to say that the Doomsday player won.

Also, there is an obvious intent to what was played in the game. It is clear that the Doomsday player deserved a true infinite set of Brainfreezes on the stack, and thus he always deserved the outcomes of it. The only reason he didn't get the true infinite set of triggers is because WotC is just never learned to deal with the concept in the game. Lazy rule-makers and bad rules create unjust outcomes.

I won't deny it. There is a technical possibility that even the largest finite number you can think of does not reduce the chances of not having "3's gaea's at the bottom" to zero. Whether that possibility is a reality...I don't know. This, again, is actually debated (or arbitrarily judged) by scholars even today.

I'm perfectly happy assuming it WOULD happen because it is so probable. It reminds me of the idea that you can't build a -true- working model of something that isn't as big or larger than what you are model after...With that in mind, probability concerns that are that improbable, where the very math variables in a universe might not even take them into account due to the size of the number, would certainly be difficult to justify as even possible.

All in all; desert is desert. Let's keep that in mind.

peace,
4eak

Tacosnape

08-06-2007, 08:01 PM

If one is not infinite, then the other is not infinite as well. At any point you 'Power-out' another set of Laquatus triggers you are forced to pick a natural number N as well. Laquatus triggers are not infinite, they remain arbitrarily large.

Clearly, the difference between the Doomsday and Power-Laquatus scenarios would be that the latter could continue milling in response to Gaea's Blessing triggers. This does not make Laquatus "infinite" if you believe that arbitrarily large numbers must be named.

It boils down to this:

Doomsday=A single set of some arbitrarily large number of triggers.
Power-Laquatus=An arbitrarily large number of sets of some arbitrarily large number of triggers.

Power-Laquatus is not infinitely larger in a relevant sense, it is the arbitrarily larger number of sets that is relevant.

You are dead wrong.

First of all, let's assume that for some reason you can't just respond to the Blessing Triggers with more Laquatus activations. Like, there being some bizarre enchantment that says "You can't play activated abilities while an opponent has triggered abilities on the stack."

What we have here, by logic, is not an arbitrarily large number of loops. It is a loop that the player can repeat, over and over, infinitely, until he or she wins. Period. No number has to be chosen, ever. The player can say "Do the loop one time," and then decide whether to do it again based on whether or not he won on that given execution of the loop. The Laquatus player will always win eventually here.

This is different from the situation with the Brain Freeze where any number you name has a distant chance of not winning. The Laquatus loop, mathematically, always wins.

Here's the loop in simple terms. Assume that the player has 48 cards in their library (16 Laquatus Activations.)

Step 1. Set a Variable, "X" = 1.

Step 2. Generate 3 mana and activate Laquatus.

Step 3. Check if there's a Gaea's Blessing in opponent's graveyard. If there is, wait for Reshuffle, then choose to go back to Step 1. If not, increase variable "X" by 1.

Step 4. Check to see if X = 15. (If it does, there's 3 cards left and they're all Gaea's Blessing.) If it does, end the loop and win. If not, go back to Step 2.

MattH

08-06-2007, 08:22 PM

If one is not infinite, then the other is not infinite as well. At any point you 'Power-out' another set of Laquatus triggers you are forced to pick a natural number N as well. Laquatus triggers are not infinite, they remain arbitrarily large.
No. Dead wrong. The difference is this: with Doomsday/Freeze, I pick my number of copies N and resolve them. Even with N copies (where is N is any natural number), there is a chance the perfect shuffle never happens in that number of tries. If the perfect shuffle doesn't show up in that number of tries, Doomsday loses, game over.

If Power-Ambassador makes N copies and they all fail to produce the perfect shuffle, it can just make ANOTHER N copies. And if those fail, ANOTHER N copies. And another, and another. There is never a point where it has to stop. It can ALWAYS try again. It has an infinite supply of arbitrarily large triggers. That is why it is truly infinite, which is much larger (infinitely so!) than merely "arbitarily large." Even if you use a sorcery-speed mana engine (replace Power-Monolith with Salvagers-LED, say), it still is infinite.

The fact that infinite > arbitrarily large is why Aluren beats Life. The Life combo can gain any number of life, but Aluren's combo can always deal that much plus more.

Given no time limit, Ambassador+Salvagers+LED beats 3 Gaea's Blessings. Doomsday-Brain Freeze probably will, but might not. The only way the former does not beat 3 Blessings is if the judge, not understanding higher math, rules that the A-S-L player has to play the loop manually and they run into time constraints. The DoomFreeze player might lose legitimately to random chance, because he merely names a large number and has to live with what he named; the A-S-L player does not have to live with it. If he didn't name big enough, he can just name bigger.

If 2+2=4, then why can't we follow the logical flow and intent of the scenario in which an infinite (or even arbitrarily large enough, such as what mathematicians tend to do)
Total misunderstanding of math right there.

With other words, the chance of it the three Gaea's Blessings not being the last three cards is getting smaller and smaller with each try
And another one, but I know you're from Europe and this is probably due to English not being your native tongue. It's only true if each try involves larger and larger N.

It is clear that the Doomsday player deserved a true infinite set of Brainfreezes on the stack
No he did not deserve that. The cards themselves demand a single natural number, and if his winning scenario doesn't come up in that number of tries, then he deserves to lose. It's the same as if I am at 20 life and you are at 1 and I play Mana Clash and I lose 20 flips in a row. Did I "deserve" to win just because it was extremely likely for me to win? No.

Whereas with a truly infinite milling combo, there is NO WAY for the Blessing player to win EXCEPT by running out of time on the clock.

Lego

08-06-2007, 08:33 PM

The fact that infinite > arbitrarily large is why Aluren beats Life. The Life combo can gain any number of life, but Aluren's combo can always deal that much plus more.

Well, not really... Aluren just gets to name a larger arbitrarily large number. They still don't "go infinite" because Magic rules don't allow that. If Aluren goes off and just gains "infinite" life, black splash Life can do infinite damage to kill Aluren the same way. They both choose arbitrarily large numbers, so whoever chooses second chooses a bigger one.

Tacosnape

08-06-2007, 10:35 PM

Well, not really... Aluren just gets to name a larger arbitrarily large number. They still don't "go infinite" because Magic rules don't allow that. If Aluren goes off and just gains "infinite" life, black splash Life can do infinite damage to kill Aluren the same way. They both choose arbitrarily large numbers, so whoever chooses second chooses a bigger one.

You're missing the point.

The point is that the loop can be repeated at its controller's discretion rather than building into one final climactic spell or ability.

This means the loop truly is infinite. This has nothing to do with not "going infinite" per magic rules and selecting a number of times to repeat the loop. It works like this.

1. I Declare my loop.
2. I choose number of times I go through it as "1."
3. If this loop doesn't result in me winning the game, I declare my loop again and choose "1."

This is by definition an infinite loop, because there's nothing to stop me from repeating it. Therefore, eventually, I am guaranteed to get my win.

Think of it like this:

Let's say to win a coin flip, the coin must come up "Heads" exactly once.

If you make ten flips of a coin, there's a chance (1 in 1024) that all ten flips will be Tails and you'll lose.

If you make just one flip, however, but get to redo the flip as often as you want if it doesn't come up Heads, you will -always- get Heads eventually.

This is what you're doing with Laquatus. Redoing the loop until it ends up the way you want it. This has an absolute 100% rate of success.

Slay

08-06-2007, 10:41 PM

No he did not deserve that. The cards themselves demand a single natural number, and if his winning scenario doesn't come up in that number of tries, then he deserves to lose. It's the same as if I am at 20 life and you are at 1 and I play Mana Clash and I lose 20 flips in a row. Did I "deserve" to win just because it was extremely likely for me to win? No.

For this analogy to be valid you have to have an arbitrarily large amount of life, and the other person has to have about 200,000,000 life.

troopatroop

08-06-2007, 10:50 PM

You're missing the point.

The point is that the loop can be repeated at its controller's discretion rather than building into one final climactic spell or ability.

This means the loop truly is infinite. This has nothing to do with not "going infinite" per magic rules and selecting a number of times to repeat the loop. It works like this.

1. I Declare my loop.
2. I choose number of times I go through it as "1."
3. If this loop doesn't result in me winning the game, I declare my loop again and choose "1."

This is by definition an infinite loop, because there's nothing to stop me from repeating it. Therefore, eventually, I am guaranteed to get my win.

Think of it like this:

Let's say to win a coin flip, the coin must come up "Heads" exactly once.

If you make ten flips of a coin, there's a chance (1 in 1024) that all ten flips will be Tails and you'll lose.

If you make just one flip, however, but get to redo the flip as often as you want if it doesn't come up Heads, you will -always- get Heads eventually.

This is what you're doing with Laquatus. Redoing the loop until it ends up the way you want it. This has an absolute 100% rate of success.

Yes, but you won't have a 100% chance of winning in the time limit.

Cait_Sith

08-06-2007, 11:03 PM

Tacosnape, you are wrong on two levels.

First, there is NOTHING that says given infinite time and infinite mana you MUST eventually reach a specific result. The odds of hitting the result can go up 99.9(repeating)%, but it cannot reach 100% because, as long as there is at least ONE other option, it is possible to hit that option, even infinite times.

Second, I turn to another's words:

Probability of a result is not usuable to resolve loops. Either its 100%
certain, or impossible to do using a loop.

And yes, that's [O]fficial and resolved so several years ago.

Ridiculous Hat

08-06-2007, 11:19 PM

Yes, but you won't have a 100% chance of winning in the time limit.Yeah, um, isn't this obvious? Probability plays second fiddle to logistics when it comes to actually running a magic tournament. The ruling has very little to do with actual math.

MattH

08-06-2007, 11:35 PM

The odds of hitting the result can go up 99.9(repeating)%, but it cannot reach 100% because
0.999... is exactly equal to 1.000.... If you don't understand why, take a real analysis class. Until you do, you're wrong and don't even know why.

For this analogy to be valid you have to have an arbitrarily large amount of life, and the other person has to have about 200,000,000 life.

You're just drawing an arbitrary line. Why is letting the person with less life have 1/(2^20) chance of winning too much to round to zero, but your situation (which is still a nonzero chance) is not, and can be safely rounded to zero?

Here's a hint people: whenever you say "arbitrarily large," remember that you ought to be saying "arbitrarily large, but finite." The infinitude of the Aluren or Laquatus kills comes not from being able to choose larger-than-arbitrarily-large numbers of activations, but from being able to try an infinite number of times. They still have to choose finite numbers, but they can make an infinity of such choices.

If a player has a nonzero chance of winning the game, it is wrong for the judge to force him to lose (or even draw). An arbitrary but finite number of Brain Freeze copies still gives the Blessing player a chance to win, but an infinity of Laquatus activations (powered by the sorcery-speed LED/Salvagers engine) does not.

Andy Heckt is right: it is either 100% certain (Laquatus kill) or impossible to do with a loop - which means that while creating the Doomsday copies of Brain Freeze can be done with a loop, resolving them cannot be done with a loop and must be played out until the game is won or a player concedes or time is called. It is wrong IMO for the judge to shut the resolution of copies down before the round is over, because either player could end it immediately by conceding, yet they don't, indicating that both are fine with taking up the entire round time doing this.

Naturally, a judge can't let this hold up the next round of play, but that's a different call altogether.

Bovinious

08-06-2007, 11:40 PM

Yea, point 9 repeating equals 1, heres a quick little proof:

1/3 = .3333....

3(1/3) = 3(.3333.....)

1 = .9999......

pretty simple stuff actually.

Cait_Sith

08-07-2007, 07:43 AM

0.999... is exactly equal to 1.000.... If you don't understand why, take a real analysis class. Until you do, you're wrong and don't even know why.

Wow, you are acting like a brat. Seriously. I KNOW THE PROOF. I take Calculus for the fun of it; math is not foreign to me. The problem is you are, as most adepts in this thread, wrong.

Let us examine why:

I decided to take a short cut, assuming that people would be smart enough to understand it. Forgive me for overestimating you. In order to reach .9999... in this example, you need infinite time, otherwise you will only end up dealing with an arbitrarily large finite decimal, but never a repeating one. However, in the context of the example there is a tournament limit, making a very real and very finite time limit, forcing you to use a very real and very finite probability, ensuring nothing.

Also, you are both beings idiots for bothering with the Laquatus example anyway. Watch:

Mill X, flip a Blessing. In response Mill X, flip a Blessing. In response Mill X, flip a Blessing. In response Mill them down to 0. In response to the third Blessing trigger play any draw spell or ability that makes them draw too. Congrats, you won the game.

Arguing over an example irrelevant to the OP (and also a situation EASILY dealt with) does not contribute to e-penis points.

Tacosnape

08-07-2007, 03:03 PM

First, there is NOTHING that says given infinite time and infinite mana you MUST eventually reach a specific result. The odds of hitting the result can go up 99.9(repeating)%, but it cannot reach 100% because, as long as there is at least ONE other option, it is possible to hit that option, even infinite times.

First of all, outside of the world of Magic, this is wrong, because in both mathematic and logistics, "forever" is thought of as an absolute infinite. Meaning therefore, no, it can't go on forever, because forever never ends. It could theoretically span eons, but if you assume that the loop is repeated until the coin flip hits Heads, then eventually the coin flip -has- to hit Heads. There is no other possible eventuality.

Slay

08-07-2007, 06:06 PM

Edit: nvm, not going to contribute to more flaming. someone lock this thread.
-Slay

Tacosnape

08-07-2007, 07:10 PM

Er, before this is locked, what was the final ruling? Did we ever get that figured out?

Bovinious

08-07-2007, 11:34 PM

The impression I got from reading what the judges posted was that game will be a draw, basically b/c the DCI doesnt incorporate higher level math/theory into their policies.

MattH

08-08-2007, 12:53 AM

Also, you are both beings idiots for bothering with the Laquatus example anyway. Watch:...
I've said multiple times since this was originally pointed out that we're assuming a sorcery-speed mana engine, and I named LED-Salvagers as a specific one.

I KNOW THE PROOF. I take Calculus for the fun of it
The sloppy or untrue mathematical statements you've made in this thread do suggest that you're an amateur at it, yes. For example:

"First, there is NOTHING that says given infinite time and infinite mana you MUST eventually reach a specific result."
Which you directly contradict in your next post:

"In order to reach .9999... in this example, you need infinite time"
:D! Happily, the latter post is correct, but in a more interesting way than I first realized:

otherwise you will only end up dealing with an arbitrarily large finite decimal, but never a repeating one. However, in the context of the example there is a tournament limit, making a very real and very finite time limit, forcing you to use a very real and very finite probability, ensuring nothing.
Upon further reflection I suppose the LED-Salvagers-Laquatus-Cephalid Looter can't be used as an infinite kill.

I think I see your point: though you can make an infinity of activations, you can only make them finitely many at a time, and you need to know if the last one worked before moving on to the next, and the only way to tell that is by actually resolving it.

It isn't a guaranteed kill, because you have to pick a specific copy in a specific arbitrarily large loop of Freeze copies to respond to with the forced-draw effect. Because the draw effect requires a player's action, a player cannot declare an infinitude of activations and then say "oh and if it ever comes up, I respond with a draw effect" because if he ever stops looping to activate the ability, he hasn't got an infinitude of activations. Because the kill requires a player's action that is not part of the loop and does not come at the end of the loop (because there is no end), it can't be declared infinite.

However, this begs the question: could you make a combo, using currently-available cards, that COULD be declared an infinite-mill loop in a finite amount of time? It would be interesting to investigate if this is possible. What about this: using the same Auriok-LED mana engine, but instead place either Pemmin's Aura or Freed from the Real on Cephalid Looter, and declare your loop as:

(assuming 45 cards between opponent's library and graveyard, which have already been shuffled together once)
1. Make 48 mana (45 to mill with, 2 to return the LED if you need to try again, 1 to untap in step four).
2. Put 15 copies of Laquatus' ability on the stack.
3. Resolve them all.
4. Activate Cephalid Looter and untap it.

With that loop, the Looter is part of the loop, and therefore you don't need to "monitor" your loops for the proper circumstances; the kill will come as a loop-able action. If the shuffle wasn't perfect, the Looter effect does effectively nothing (the card they discard will be reshuffled on the next unsuccessful pass, even if it was a Blessing); if it was one of the 3-GB-on-bottom shuffles, it's lethal.

The obvious problem is that if you have infinite Looter activations, why not just use that and ignore Laquatus? Even if you switch to a sorcery-speed untap effect like Threaten (plus a way to constantly reuse the Threaten; Future Sight+Soldevi Digger comes to mind), you could still bypass Laquatus entirely and just go for infinite untaps on the Looter. Is there a set of cards such that it makes the Looter only able to activate during that part of the loop and no other? I don't think so, but maybe someone can figure it out.

Incidentally, I saw someone above say words to the effect that if a player is using 4 Blessings, he is not under obligation to inform the opponent of that. And while that is true, if a player has 4 Blessings in his deck against the OP's Doomsday combo, is there any reason he wouldn't make this information known, at least to a judge? Wouldn't that prove/couldn't he argue that any number of resolved Brain Freeze copies will not deck him, and there's no point in resolving even one, and any attempts to do so constitute stalling because there would be zero chance of actually decking the Blessing player?

the DCI doesn't incorporate higher level math/theory into their policies.
Surely a mistake! Look how great this thread has been!

Lukas Preuss

08-08-2007, 04:40 AM

The impression I got from reading what the judges posted was that game will be a draw, basically b/c the DCI doesnt incorporate higher level math/theory into their policies.

Wrong. The game will be a draw, basically because the DCI does incorporate higher level math/theory into their policies... they do this by creating the ruling that forces you to choose a number smaller than infinite.

Peter_Rotten

08-08-2007, 09:50 AM

Are we enjoying this thread in a friendly manner, or is it time for lock-down?

Bovinious

08-08-2007, 11:55 AM

Wrong. The game will be a draw, basically because the DCI does incorporate higher level math/theory into their policies... they do this by creating the ruling that forces you to choose a number smaller than infinite.

This is true, infinity is a direction not a value and couldnt be chosen as a number for a loop even if the DCI didnt have this rule. I still think there should be a way that you can achieve the same results as infinite copies without actually having to choose infinity, for example if you named the storm as the number of particles in the universe, its 100% safe to say that that will win you game eventually in this scenario. This kind of defeats the point of having to choose a natural number though, if a number big enough is treated the same as infinity, so maybe this is inpractical and counter-intuitive to do. This situation is so rare (and now obsolete with the printing of Grapeshot) and inconsequential, so I dont forsee any change in this rule.

Are we enjoying this thread in a friendly manner, or is it time for lock-down?

I think its going okay and doesnt need to be locked, hasnt gotten to flames or anything. Sorry for answering if that was rhetorical, the intarwebs isnt very good at rhetorical questions.

Ridiculous Hat

08-09-2007, 03:59 AM

Are we enjoying this thread in a friendly manner, or is it time for lock-down?I guess that depends on how much you like internet pissing contests.

Bryant Cook

08-09-2007, 10:20 AM

I guess that depends on how much you like internet pissing contests.

I can piss farther than you.

DeathwingZERO

08-09-2007, 11:31 AM

Thanks for making me need to piss. And picturing 8 billion copies of Brain Freeze trying to resolve in one's lifetime.

I spent the entire time while reading this thread (about an hour), trying to actually figure out how to pull off a number of instances that 1) wouldn't get you thrown out of the tournament (or banned) and 2) actually was relevant enough to let the judge know that your option is possible.

Unfortunately it's looking to come down to the exact ruling most of the judges have given. Since "infinite" is not an option, and 10,000,000,000,000+ copies still has that margin (even if it's one trillionth of a percent) of possible bad luck, there's nothing that can be done.

To be honest, I think that's complete BS, but it looks like it'll never change, because even if 99.9 repeating is 100 for all intents and purposes when examining it in the infinite grasp, that minute chance that it wouldn't happen when "Infinite" turns to "X", is enough to have us stuck with their decision.

EDIT: Oh, and to agree with most, Grapeshot >>>>>>> Brain Freeze if you can successfully target your opponent in the first place.

Nightmare

08-09-2007, 01:51 PM

Just because it was bugging me, the real proof:

Define the variable "X":
-_
.9 = .9 repeating = x

Multiply through by 10:
-_
.9 * (10) = 10x
--_
9.9 = 10x

Subtract x:
--_---_
9.9 - .9 = 10x - x

Simplify:

(10x - x) => x(10-1) => 9x

9 = 9x

1=X

But by definition,
-_
.9 = x

So,
-_
.9 = x = 1

Therefore, mathematically, 99.9999....% is the same as 100%.

Tacosnape

08-10-2007, 01:20 AM

Bovinious

08-10-2007, 01:37 AM

There are multiple proofs of it, the one I posted earlier is the simplest one, I figured the brevity would make it easiest to understand, but Nightmare's is cooler I gotta say.

Ridiculous Hat

08-10-2007, 02:39 AM

I can piss farther than you.That may be true, but I can piss in your eye. And the odds of that are 100%, so I can do it over and over again-- but I'll only announce it once.

Angelfire

08-14-2007, 12:29 PM

Ok assume they printed this new card:

Sorcery

Flip a coin, if heads target opponent takes 1 damage, if tails does nothing.

Storm
_______________________________________________

Ok so my opponent is playing life and is at 500 billion life. I have some infinite combo like topx2 and helm of awakening. I choose to do 500 google storm, then cast that coin flip spell. Does my opponent die or do you have to do it out? The chance that even 51% of the 500 google coming up heads or tails is so freakin low that it is retarded that it wouldn't just be a guranteed win. Now with the brain freeze, blessing example it is virtually the same thing.

Anusien

08-14-2007, 12:53 PM