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Thread: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

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

    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?

    Quote Originally Posted by majikal View Post
    Damn it, Taco, that exactly sums up my opinion on the matter. I need to buy you a beer for that post.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Quote Originally Posted by Bovinious View Post
    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.)

    Quote Originally Posted by majikal View Post
    Damn it, Taco, that exactly sums up my opinion on the matter. I need to buy you a beer for that post.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    I was able to find the following at StarcityGames Ask the Judge
    http://www.starcitygames.com/pages/j...k+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.
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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    4 Lesbian Points* to Silverdragon for digging that up.

    Quote Originally Posted by Bovinious View Post
    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.)

    Quote Originally Posted by majikal View Post
    Damn it, Taco, that exactly sums up my opinion on the matter. I need to buy you a beer for that post.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Grapeshot > Brainfreeze.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Quote Originally Posted by Tacosnape View Post
    *(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.
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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.
    “It's possible. But it involves... {checks archives} Nature's Revolt, Opalescence, two Unstable Shapeshifters (one of which started as a Doppelganger), a Tide, an animated land, a creature with Fading, a Silver Wyvern, some way to get a creature into play in response to stuff, some way to get a land into play in response to stuff (a different land from the animated land), and one heck of a Rube Goldberg timing diagram.
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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Quote Originally Posted by wastedlife View Post
    Grapeshot > Brainfreeze.
    WIN
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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Quote Originally Posted by Akki View Post
    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?
    Last edited by RoddyVR; 08-01-2007 at 10:13 AM. Reason: bit of grammar/spelling mistakes

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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"

    Quote Originally Posted by RoddyVR View Post
    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.
    “It's possible. But it involves... {checks archives} Nature's Revolt, Opalescence, two Unstable Shapeshifters (one of which started as a Doppelganger), a Tide, an animated land, a creature with Fading, a Silver Wyvern, some way to get a creature into play in response to stuff, some way to get a land into play in response to stuff (a different land from the animated land), and one heck of a Rube Goldberg timing diagram.
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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.
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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Quote Originally Posted by Akki View Post
    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"
    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...

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Quote Originally Posted by Machinus View Post
    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.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    Quote Originally Posted by Sacul Kamadaka View Post
    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.

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    Re: The Impossible Loop - Brain Freeze vs. Gaea's Blessing

    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.
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