Re: 61 or more cards in toolbox decks
Ok, let me start by saying that this thread really can't "prove" anything. Yes, mathematics shows us that your probability of drawing a "better" card in a 61 card deck is lower than 60. What this *doesn't* consider is how cards interact with one another, or, for that matter, the game of Magic at all.
My *opinion* is this. Start by saying that obviously (to most people) a 70 card deck is non-optimal. I'd even argue that 65 cards is also non-optimal. For me personally, I'm either playing 60 or 61 cards. Why do I even allow 61 cards? Because, like it or not, there are games that run to someone being decked. And there are people playing Solidarity out there. Yes, the odds of you being helped by having 61 cards vs. 60 is fairly miniscule, but then again, so are the increases in probability of drawing a certain card.
I'd be willing to allow up to 63 cards. Why 63? Because I feel after that, that you can remove a full set of 4 cards from the deck and probably increase the power level, or meet some ratio you're trying to achieve in some other way (lands, to creatures, to removal, for instance). However, I really feel that *either* 60 or 61 are optimal. But once again, that's just my opinion.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
SpencerForHire
Then that card should have been in the main over another card. That comes back to optimal deck building.
No, it isn't always true.
A simple example is when every card in my 60 allows me to win 0,7% of my matches, the 61 card wins me an addition 0,6% of my matches while playing 60 cards allows me to win 0,5% more of my matches. Looks weird indeed, but maybe the added flexibility of the additional card allows me to win more matches than the slighltly optimization offered by 60.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
Rico Suave
I challenge anybody in this thread to post a list that is optimal with 61 cards, and I will show you a way to improve it by cutting down to 60.
Question: does the deck have to be good, or merely a legal decklist?
I'm assuming that if someone posts a vintage-legal Boros deck that you aren't planning on responding with, "Cut 61 cards, add a 60-card Tezzeret deck." Claiming that you can find a better decklist is not the same as claiming that you can find a better decklist which is a strict subset of the original. As quoted above, your challenge is the latter.
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I would like to untie two issues being discussed in this thread which some people have conflated.
Statement One: Every 61 card deck can be improved by cutting one card.
Question Two: Assume Statement One is true. Choose a card to cut. Can it be proved that the chosen card was the correct one to cut?
These are NOT the same question, and should not be treated as such. Also, it seems like some people (looking at you, Rico Suave, although you're far from alone on this) need a refresher on the definition of proof. "A convincing demonstration" is not proof. 'Evidence' is not proof.
Re: 61 or more cards in toolbox decks
"60 cards is optimal" is a theory in the way that gravity is a theory. We can't prove that 60 card lists are always optimal, just like we can't prove "gravity" is what's keeping us from floating off the planet. However, both ideas are the best and most realistic approximations of reality we can come up with right now. As such, the burden of proof is on those who say 61 cards is optimal in Deck X.
I believe that we can all agree on the following statements:
Some cards in your deck are better in more situations than others, i.e. stronger. Force of Will is generally better than Spell Snare, etc.
You want to draw the strongest cards in your deck as often as possible. In a Survival deck, this means drawing Survival of the Fittest. In Goblins --- Goblin Lackey, In CounterTop --- Counterbalance, Tarmogoyf, or Force of Will.
If you don't need the strongest card in your deck, then you need to draw the strongest card for the situation. This could be drawing a Trygon Predator against Stax, or a Tormod's Crypt against Ichorid.
Running a 60 card deck maximizes your chances of drawing both your strongest cards, both for most specific situations and overall.
The difference between a 60 card deck and a 61 card deck is minimal, but real.
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Given the above statements, how can it be beneficial to run 61 cards? Yes, it doesn't make much of a difference if you run 61 cards instead of 60, but why would you want to dilute the quality of your draws at all? What benefit do you gain from reducing the power of your average draw? Sure, if you run a Faerie Macabre in your Survival deck as the 61st card because there is a lot of Loam and Ichorid in your meta, you're improving your chances of winning. But by running 61 cards, you're reducing your chances of drawing that awesome Faerie Macabre. You could make the matchup even better by going to 60 cards. Maybe cut that fourth Thoughtseize or Cabal Therapy that you're always sideboarding out.
Every deck I've played has always had a weakest card or couple of cards. Do you find yourself siding out a certain card or cards more often than the rest of your deck? Consider cutting one and going to 60 cards. Obviously the card isn't needed in the first place.
A very excellent Patrick Chapin article was linked early in the thread and ignored. I would like to see some in the 61 card camp issue a rebuttal to the article's points. Here it is again:
http://www.starcitygames.com/magic/s..._Roulette.html
I don't really care if 12 Mountain/48 Shock.dec is optimal at 61 cards, because real Magic decks don't look like that. Sure, it's an optimal 61 card list, but how is that relevant to Legacy?
DISCLAIMER: I'm not saying it's impossible in Legacy for a 61 card deck to be optimal in theory. I'm just saying that we have nothing to suggest that it is, and everything we know suggests that 60 cards is optimal in most, if not all situations.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
Kuma
"60 cards is optimal" is a theory in the way that gravity is a theory. We can't prove that 60 card lists are always optimal, just like we can't prove "gravity" is what's keeping us from floating off the planet. However, both ideas are the best and most realistic approximations of reality we can come up with right now.
That's not the point. The problem isn't that it's only a theory, the problem is that the theory isn't powerful enough. To take the gravity analogy, what we have with 60 card superiority at this point isn't general relativity, it's not even Newton, it's more like saying "things fall down because look around! things fall down", while trying very hard to ignore helium balloons. Nobody is going to doubt the fact that things fall down. That doesn't mean everyone has to be in perfect satisfaction with the theory.
(As an aside, while in the physical sciences it's not possible to prove anything, only to disprove, the same isn't true of mathematics and logic. You have plenty of proofs in math. And because Magic is a strictly artificial/logical construct rather than a physical phenomenon I'd say it falls into the latter camp. But again, this is besides the point, because I don't even expect a strictly rigorous mathematical proof here -- that would be foolish and more or less impossible.)
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As such, the burden of proof is on those who say 61 cards is optimal in Deck X.
Indeed. However, the burden of proof is also on those who insist that 60 cards is optimal in 100.000000% of cases with no possible exceptions whatsoever.
Quote:
DISCLAIMER: I'm not saying it's impossible in Legacy for a 61 card deck to be optimal in theory. I'm just saying that we have nothing to suggest that it is, and everything we know suggests that 60 cards is optimal in most, if not all situations.
Great! Then we're in perfect agreement and have nothing to argue about.
All I'm really for, I guess, is for people to have a greater awareness of how things work rather than just relying blindly on dogma. To the best of our knowledge, playing 60 cards is best, but the best of our knowledge isn't terribly advanced.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
MattH
Question: does the deck have to be good, or merely a legal decklist?
I'm assuming that if someone posts a vintage-legal Boros deck that you aren't planning on responding with, "Cut 61 cards, add a 60-card Tezzeret deck." Claiming that you can find a better decklist is not the same as claiming that you can find a better decklist which is a strict subset of the original. As quoted above, your challenge is the latter.
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I would like to untie two issues being discussed in this thread which some people have conflated.
Statement One: Every 61 card deck can be improved by cutting one card.
Question Two: Assume Statement One is true. Choose a card to cut. Can it be proved that the chosen card was the correct one to cut?
These are NOT the same question, and should not be treated as such. Also, it seems like some people (looking at you, Rico Suave, although you're far from alone on this) need a refresher on the definition of proof. "A convincing demonstration" is not proof. 'Evidence' is not proof.
Of course, the correct card to cut depends on a lot of factors. Nevertheless, the deck can be improved by cutting a card (the correct card).
Is this true beyond the shadow of a doubt, with no possibility now or in the future that 61 cards may perhaps be optimal? No. It's quite possible a mechanic can be printed that will change things. One has already been printed in the form of Battle of Wits.
However, 60 cards being optimal is a fact. A rule. Facts and rules have been known to change in time. However, a fact by definition is known through experience and observation, much like scientists collect facts through the same methods.
As such, I don't feel wrong calling it a fact or a rule.
Rule of thumb, however, is very rough and approximate, and I disagree with the color in that term because there is a lot more to support 60 cards than a rough unscientific method.
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You still aren't catching some of the complexities of this issue, but whatever. That's fine; even if you understood the reality of this issue, it would not amount to any difference in how you play magic at this point in time. (Perhaps it would change how you study magic though)
I understand everything you are saying.
You claim that it cannot be proven that 60 cards is always optimal, but I am saying it is irrelevant when building a deck because we cannot ever prove that 61 cards is optimal either. It's just a silly argument.
We can, however, concede to the overwhelming evidence in favor of 60 cards and apply a little common sense.
Re: 61 or more cards in toolbox decks
@ MattH
Quote:
does the deck have to be good, or merely a legal decklist?
I'm assuming that if someone posts a vintage-legal Boros deck that you aren't planning on responding with, "Cut 61 cards, add a 60-card Tezzeret deck." Claiming that you can find a better decklist is not the same as claiming that you can find a better decklist which is a strict subset of the original. As quoted above, your challenge is the latter.
I think its quite possible to consider both pretty easily. And, for clarification, Rico's series of arguments could certainly include the former. One of his problems with my shock/mountain example was the poor quality of cards chosen for the deck in (what he presumed to be) a format with much better cards. The idea was "why consider shock.dec when we have Tarmogoyf?" and so on.
This quote strikes me as questioning what we mean by the word "optimal". I should have been more specific a while back about it.
Optimal = Highest chance to win given the format's cardpool and the targeted metagame.
You'll probably think this is a severe definition in some ways. Also, please note that this allows for possible "ties" between 2 or more decks sharing the top spot. I'll be brief in my discussion of the terms.
You can artificially limit cardpools. If you only have certain cards to work with, then that is a limit on your cardpool. If you are only interested in playing Landstill or Survival as your pet deck, then you'll have a limited cardpool. Of course, we must distinguish your cardpool and the cardpool of your metagame (as your opponent's may not have the same artificial limits). One might argue that the metagame shapes the cardpool, but at this point, I'm not going to explain what that isn't true enough to abolish the distinction between these two things.
There is the mathematically perfect metagame (which we'll never arrive at), the average world metagame (which our DTB tries to emulate, and what most people call "Legacy"), and what I usually call "specific" metagames which are basically local to any particular tournament ("specific" despite the fact that all of these are theoretically specifiable, not just the local tournament). Metagame information will also include odd things like tournament structure (they can vary), and perhaps other game mechanics. It is important to note that defining metagames is necessary to define deck optimality--there is no way to discuss a deck's optimality without reference to the other expected decks and players in whatever environment they are to be compared and tested.
You appear to dislike your former claim. I'm guessing it would amount to disliking some aspects of how one would define optimal. In that case, I'd initially want to ask then, if "optimal" is so restrictive in meaning, then why would you even want to consider developing tier 2 decks?
I see 3 reasons to develop the so called "tier 2" decks:
- It is possible that the current "tier 1" isn't the optimal deck in a format, and perhaps a currently recognized "tier 2 deck" could be optimized into what is actually the optimal deck in a format/metagame.
- A player has artificially imposed a cardpool limit (for whatever personal/financial/"for the challenge" reason you could think of)
- What is considered a "tier 2" deck, which may in fact be suboptimal in the perfectly mathematical and the average world metagames, may actually be optimal in more specific metagames.
Optimality is not easy to calculate. Defining the cardpools and metagames are preconditions to testing for optimality, and that ain't easy. Even if you could create a simple vacuum (as I did in the very restrictive burn.format), you'll still see how difficult it can be to truly distinguish optimality.
Quote:
I would like to untie two issues being discussed in this thread which some people have conflated.
Statement One: Every 61 card deck can be improved by cutting one card.
Question Two: Assume Statement One is true. Choose a card to cut. Can it be proved that the chosen card was the correct one to cut?
These are NOT the same question, and should not be treated as such.
Instead of just begging the question in statement one, automagically limiting the scope of this discussion, let's restate that as an open question. "Can every 61+ card deck can be improved by cutting one card?"
I don't think this explication is true to the spirit of the discussion though. I think we want to know if any 61+ card decks can possibly be called optimal (in whatever cardpool and metagame).
Yes, some people have simplified the 60-card rule debate into "improvement through the cutting of one card". That is not, however, the overall point in question. The "cutting one card" concept is a gross oversimplification of the optimization process which would be used to move from 61 to 60 cards.
To give a brief example, a 61-card toolbox deck might run:
1x Circle of Protection: Red
1x Circle of Protection: Green
It might be the case that the correct optimization of the deck within the context of the cardpool and metagame would not amount to removing just 1 of these CoPs, but perhaps the the replacement of both of these cards with:
1x Story Circle
Even this is far from showcasing the complexity of optimizing. Clearly, we aren't 'just' talking about cutting one card though, even if that is how it was phrased. I think its difficult to talk about the issue (Ill's "handwaving" perhaps). This is, after all, a less-than-perfectly explored topic without a great deal of shared terminology. Surely you will admit that the larger question in the discussion, "Are all 61+ card decks supoptimal?", to be the heart of the matter.
Question one: "Are all 61+ card decks supoptimal?"
Before anyone can honestly say they know the question, before we even try to answer that question,, we need to ask whether or not it is physically possible for us to answer that question. The second question I've tried to answer then is:
"Can it be proven that all 61+ card decks are suboptimal?"
If the answer to this second question is "No", then we will need to answer question one with "I don't know". That's a lot of metagames and cardpools to consider.
Now, you remind us of what "proof" means. I'm willing to discuss epistemology with you, but I doubt you have the patience or interest in it. Let's be charitable. If we have very good reason to believe that the answer to the second question is "No", then likewise we have a very good reason to answer question one with "I know don't".
Because we lack the mathematics and computation power, we inevitably must answer question one with "I don't know".
We may even want to qualify that and say, "In the vast majority of cases, 61+ card decks are very likely suboptimal." However, we will still need to leave room for exception.
@ Rico Suave
Quote:
You claim that it cannot be proven that 60 cards is always optimal, but I am saying it is irrelevant when building a deck because we cannot ever prove that 61 cards is optimal either. It's just a silly argument.
As I said, for someone who isn't concerned about magic theory or progress, this is good enough. This isn't a silly argument for anyone who might believe that progress is possible. One day enough progress could be made that this discussion will be relevant to how you build decks. The route I'm taking (computerizing the game) has a long-standing tradition in general game theory of "solving" games and optimizing strategy.
peace,
4eak
Re: 61 or more cards in toolbox decks
I will admit I have not read this thread in its entirety but I think there is a very obvious example to prove that 61 card decks can be better than a 60 card deck mathematicaly at least.
Let us assume for simplicity sake that magic does not limit us to 4 copies of a card. thus if your deck was 20 Mountains and 40 Lightning Bolts each card in your deck would deal on average 2 points per card ((40 bolts X 3 damage per bolt)/60 cards). Then lets say you add a 61 card thus increasing the average damage per card to 2.02, a small increase per card but an increase none the less. On the other hand one can argue to merely cut a mountain instead of going to 61 to make the average damage per card 2.05, better yet correct? Sort of.
In the above example the 41 bolt deck with 60 cards deals more damage per card on average but runs less mana then the 40 card bolt deck with a 61 card deck. The other aspect of this then becomes the change in the odds of drawing the needed land for your spells. With the 61 card, 20 mountain deck your odds are about 32.79% of drawing a land as opposed to 31.67%. While this change is not very noticeable on such a small scale imagine this on a larger scale to see the eventual magnitude because a 1.1% change does not SEEM large on paper.
While I think most people would cut the 20th Mountain that may not always be right. It seems much better in this example since Bolt only costs one but imagine using some really bad burn spell that costs like 3 mana... Eventually you will begin to see that there are so many variables to account for that such a determination of wether or not a 61st card is better than a simple 60 is nearly impossible. To help explain the 3 mana burn spell argument note that land 1,2,4,5,7, and 8 do nothing. The only lands that count are multiples of 3 so until a multiple of 3 land is in play those lands are dead draws. You would want to hit the exact right mix to maximize your odds of winning.
Re: 61 or more cards in toolbox decks
That's basically the example 4eak was using, I think, only he did it with Shocks.
Clearly the best way to optimize a 41 Shock, 20 Mountain deck is to replace them with 40 Lightning Bolt, 20 Mountain. QED.
Re: 61 or more cards in toolbox decks
@ nodahero
I see where you are coming from. I'd love to see a purely mathematical demonstration of the value of lightning bolt in that deck. Unfortunately, the problem may be too complex for us to feasibly apply a purely mathematical treatment. Brute-forcing on a computer might be necessary.
As Nihil explained, variance from running more cards is a factor (which I mistakenly assumed to be somewhat insignificant until I ran the simulation).
Mulligan rules make it even more difficult to consider.
Conditions and choices in the game are pretty modular, and "averaging" is difficult. Each card in the deck isn't 1/3 part Mountain and 2/3 part Bolt, and that really makes the deck play out differently.
The best way I know to realistically understand the value of those cards, at this point, is to grind it out on a computer.
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I will admit I have not read this thread in its entirety
You probably should read the thread then.
@ Illissius
I actually tested Lightning Bolts and 4 damage for 1cc (Uberbolts?) to see what would happen. I didn't post the results though.
It was useful, I just forgot to talk about it because I was busy frying other fish.
Having looked at the differences in Shock/Bolt/Uberbolt, for example, I know that as the damage of your 1cc burn card rises (moving from Shock to Bolt, etc), the more mountains you will want to run (which seems obvious in hindsight). It wouldn't be difficult to imagine a 30 Mountain, 30 1cc for 20 damage Burn Spells showing this to be true. That was interesting to me because I sometimes mistakenly think of "curving out" without regard to the value of the spells I'm casting (assuming the same mana costs).
There are implications to this. One might, for example, make a formula which analyzes the average CC of cards in the deck and try to create the appropriate mana-base for it. But, clearly, that wouldn't be effective. The values of land are in complete feedback with the values of the other cards in the deck; it was nice to see "proof" of that so clearly before my eyes.
In fact, this also led to a change in the mulligan-rules. And, even if I didn't adjust the mulligan rules, because I should/could run more land in higher damage burn decks, as the damage increased on my burn spells, and the numbers of mountains played increased, the less i needed to mulligan, which only made each card all the more valuable on average (because I was more likely to open with a keepable 5, 6 or 7 hand and win even earlier).
peace,
4eak
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by Rico Suave
Of course, the correct card to cut depends on a lot of factors. Nevertheless, the deck can be improved by cutting a card (the correct card).
Is this true beyond the shadow of a doubt, with no possibility now or in the future that 61 cards may perhaps be optimal? No. It's quite possible a mechanic can be printed that will change things. One has already been printed in the form of Battle of Wits.
However, 60 cards being optimal is a fact. A rule. Facts and rules have been known to change in time. However, a fact by definition is known through experience and observation, much like scientists collect facts through the same methods.
As such, I don't feel wrong calling it a fact or a rule.
Rule of thumb, however, is very rough and approximate, and I disagree with the color in that term because there is a lot more to support 60 cards than a rough unscientific method.
You made a specific challenge, one that I would like to answer. You said, "I challenge anybody in this thread to post a list that is optimal with 61 cards, and I will show you a way to improve it by cutting down to 60." Now, I love a good challenge. But my answer hinges on two things you've left vague: what you mean by "optimal" and what you mean by "show". I would like you to define these before I give my answer so there's no weaseling out of it later with, "But that's not what I meant!"
1. Does the deck need to be good, or just a legal decklist? As stated, your challenge says that you are simply going to make a single cut to a decklist I provide, but you include that fuzzy word, 'optimal', which looks like a secret escape pod for you. I don't want to come up with a 61-card Survival deck only to see you try to get out of it by saying, "Survival isn't a good deck anymore, therefore it isn't optimal. Cut the Survivals and utility guys for Brainstorms and Counterbalances and FoW and then it's optimal."
To avoid this, are you willing to claim that you can improve any 61-card list by finding a 60-card proper subset of that list? Your original boast sounds like this, but I want to be sure.
2. I also don't want to waste time coming up with a 61-list only to have your definition of "show" turn out to mean, "I will show you that 60 cards is better by cutting a card and then claiming that the deck is obviously better because it's now 60 cards." That would be circular reasoning.
However, you don't have to show that the card you're cutting is the best possible cut; it's certainly possible that there are several possible cuts to a 61-list, any of which would be an improvement! You only have to find one such, but you DO have to show, without a doubt, that your cut has made the deck stronger.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
MattH
You made a specific challenge, one that I would like to answer. You said, "I challenge anybody in this thread to post a list that is optimal with 61 cards, and I will show you a way to improve it by cutting down to 60." Now, I love a good challenge. But my answer hinges on two things you've left vague: what you mean by "optimal" and what you mean by "show". I would like you to define these before I give my answer so there's no weaseling out of it later with, "But that's not what I meant!"
1. Does the deck need to be good, or just a legal decklist? As stated, your challenge says that you are simply going to make a single cut to a decklist I provide, but you include that fuzzy word, 'optimal', which looks like a secret escape pod for you. I don't want to come up with a 61-card Survival deck only to see you try to get out of it by saying, "Survival isn't a good deck anymore, therefore it isn't optimal. Cut the Survivals and utility guys for Brainstorms and Counterbalances and FoW and then it's optimal."
To avoid this, are you willing to claim that you can improve any 61-card list by finding a 60-card proper subset of that list? Your original boast sounds like this, but I want to be sure.
I'm not looking to tell people to play a different deck entirely. For the sake of this, let's just go with something that could reasonably win a match in a Legacy tournament. Survival has a legitimate chance to win the entire tournament, let alone a single match, and is actually a great example considering the original question was asking about 61 cards in a toolbox deck.
I used the word optimal, meaning that the person who presented it feels that there is no way to improve the list at 61 cards, or maybe they just aren't sure.
With the list, the following would help:
1) An expected metagame
2) A SB
3) Any concerns about mana, specific choices, or any other important information.
I will mention maybe 1-5 possibilities for a card that could be cut, why they can be safely cut, and how it impacts the rest of the deck and its strength in certain matches. If other issues come up, like mana issues, I may recommend 2-5 changes max.
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2. I also don't want to waste time coming up with a 61-list only to have your definition of "show" turn out to mean, "I will show you that 60 cards is better by cutting a card and then claiming that the deck is obviously better because it's now 60 cards." That would be circular reasoning.
However, you don't have to show that the card you're cutting is the best possible cut; it's certainly possible that there are several possible cuts to a 61-list, any of which would be an improvement! You only have to find one such, but you DO have to show, without a doubt, that your cut has made the deck stronger.
I would certainly explain why. In fact it might become a very lengthy reasoning because it would involve how the deck would play out against several decks.
@4eak
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As I said, for someone who isn't concerned about magic theory
Do not assume I am not concerned about magic theory.
You are discussing math and computer theory, which is different.
Re: 61 or more cards in toolbox decks
@ Rico Suave
Quote:
Do not assume I am not concerned about magic theory. You are discussing math and computer theory, which is different.
Perhaps you are concerned with magic theory to a small extent, but by and large, you have me convinced otherwise. Just because a theory doesn't have immediate impact on your choices doesn't make it silly (or pointless). You seem to think the argument I've provided you (which uses a computer and is theoretical) is not useful because it doesn't directly impact your deckbuilding at this very moment. As I've said, sometimes it takes a while for a theory to be cultivated and developed or for a breakthrough to occur which is applicable. If I thought you were more fully concerned about the topic, you wouldn't continue to hold your position.
It looks like you haven't quite received the message yet because you keep walking into the trap (for example, MattH is setting one up for you) in this thread and boasting about a capacity we know you don't have.
Lastly, you realize that mathematics and computers are languages and observation tools in which we can objectively consider this topic, right? They are quite appropriate to magic theory discussions.
peace,
4eak
Re: 61 or more cards in toolbox decks
About computer simulations, I built one to know which one between Ponder and Serum Visions was the best to have 2 lands by turn 2 and less than 4 lands by turn 10. I was considering that I was playing 4 braintorms, 8 fetches, 10 other lands (all fetchable). Even in this simple case, I had to cope with situations where it was not clear what the best strategy was (2 BS + Ponder in hand, what do you play first?, do you mulligan with a hand with ). My solution to this was first to ask these questions on forums, but the debates it created were definitely not productive. Then I planned to use reinforcement learning (which is somehow my PhD thesis subject), but, since ponder was obviously better, I've never done it.
I'd be very interested to deal with this kind of stuff later.
Ps: even the shock/mountain metagame is very interesting in the way that you can't ignore your right to mulligan and this mulligan decision makes this a reinforcement learning problem too.
PPs: Mulligan choices is probably the first topic on which simulation might help.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
Rico Suave
However, 60 cards being optimal is a fact. A rule. Facts and rules have been known to change in time. However, a fact by definition is known through experience and observation, much like scientists collect facts through the same methods.
...
You claim that it cannot be proven that 60 cards is always optimal, but I am saying it is irrelevant when building a deck because we cannot ever prove that 61 cards is optimal either. It's just a silly argument.
This is just... wow... 60 cards being optimal (all of the time) is not a fact/rule/proven. Something that is known through experience and observation (without the rigour of proof) is a theorem. That's all there is to it. Anybody who says otherwise is just plain wrong. Do I really need to explain this? In order to prove that 60 cards is optimal, you need to show it's optimal for all possible decks. Good luck with that...
Anyways, can we stop stating things as fact? This thread is all people giving there opinion, and that's it. I will agree that 60 cards is better than 61 cards in a majority of cases (though I won't dare to say I could prove that either).
P.S. As percentages show us, in order to show a difference in 0.5% probability, one would need to play a minimum of 200 games. Actually, it's more than this due to random fluctuation. In addition, since the chance of winning over any one deck varies, you'd have to play all these games against the same deck (to have a controlled experiment). Then you'd have to do that against every deck in the field.
P.P.S. No automated deck builder/game player will *ever* be able to prove 60 cards is better than 61, not even with any reasonable error margin. Do you know the compute time for this!? So let's not even suggest that.
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
tivadar
P.P.S. No automated deck builder/game player will *ever* be able to prove 60 cards is better than 61, not even with any reasonable error margin. Do you know the compute time for this!? So let's not even suggest that.
Computer time? 10 minutes at most for the simple shock/mountain problem. Computer time is not the problem, developer's time or player/game models is the issue.
Re: 61 or more cards in toolbox decks
I more meant the compute time to test a deck against "every deck" in the field. Not to mention trying to determine what the best 60 vs. 61 card list is itself. The number of possibilities are endless. But you're correct, building an oracle would probably be even harder.
Re: 61 or more cards in toolbox decks
I thought about that CoP example and it shows the problem with the value of a card. While in some matchups CoP:Red has a value of 100 (against burn) its useless against other decks (value 0 against Merfolk)
Therefore you should only pack cards in your deck which have the highest average value. Now you can come to the point that you should pack those cards as often as allowed in your deck (4ofs)
If you think this further, mathematically you shouldnt build a deck with cards you only want to have 1,2 or 3 times.
In the end you shouldnt play toolbox-decks at all, because statistically they are less consistent than piles of quadruples (aka Canadian ***** f.e.)
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
Rico Suave
For the sake of this, let's just go with something that could reasonably win a match in a Legacy tournament.
Ahh there you go, hedging your bet! (And still leaving yourself outs, with that fuzzy word, "reasonably".) That was not part of the original challenge. ;D
How about we start small. I claim that the following deck is optimal:
26 Swamp
35 Relentless Rats
and by "optimal" I mean that removing either a swamp or a rat will result in a worse deck. I claim that if you remove a rat, you will draw too many lands, and if you remove a land, you will not draw enough land. According to you, one of those two claims MUST be wrong, and the other right. Find out which one, and prove that you chose the right one.
This should be super-easy, right? There's only two possible choices, so you've got 50% odds if you just blindly guess! Tell me, which card should be cut from this? And remember, you do have to justify why the cut is better than not making the cut without resorting to "it must be better because now it's 60".
This is just the easiest example. I have others. P.S. This challenge is open to anyone who cares to try it!
Re: 61 or more cards in toolbox decks
Quote:
Originally Posted by
4eak
@ Rico Suave
It looks like you haven't quite received the message yet because you keep walking into the trap (for example, MattH is setting one up for you) in this thread and boasting about a capacity we know you don't have.
I have been on friendly terms with Matt for years. He has seen every Legacy list I've played since the B/R list was revamped to be more than just a shadow of T1.
I would hardly call it a trap.
Quote:
Originally Posted by
MattH
Ahh there you go, hedging your bet! (And still leaving yourself outs, with that fuzzy word, "reasonably".) That was not part of the original challenge. ;D
How about we start small. I claim that the following deck is optimal:
26 Swamp
35 Relentless Rats
and by "optimal" I mean that removing either a swamp or a rat will result in a worse deck. I claim that if you remove a rat, you will draw too many lands, and if you remove a land, you will not draw enough land. According to you, one of those two claims MUST be wrong, and the other right. Find out which one, and prove that you chose the right one.
This should be super-easy, right? There's only two possible choices, so you've got 50% odds if you just blindly guess! Tell me, which card should be cut from this? And remember, you do have to justify why the cut is better than not making the cut without resorting to "it must be better because now it's 60".
This is just the easiest example. I have others. P.S. This challenge is open to anyone who cares to try it!
I was hoping you would have gone through the efforts to make a Legacy Battle of Wits deck, as I didn't rule that out either. :D
Let's assume this deck could reasonably win a Legacy match-up.
The only change to be made is to change it from 61 cards to 300+ cards. Now your match-up against High Tide is nearly impossible to lose, and to boot you can achieve a more precise mana:spell ratio.
None of this takes away from the power of the deck or its strategy or how it plays out either.
For the sake of the argument, yes, Relentless Rats and Battle of Wits are 2 exceptions to the rule. This was also pretty evident in Pat Chapin's article too.
