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5 years ago ::
Jul 25, 2008 - 7:23AM
#1
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I'm attempting to construct a scenario where a player gets an actually infinite number of creatures in a game of magic. (Amazingly, in Mirrodin Block only). I understand that there are several methods of attaining an arbitrarily large number of creatures, but because of the loop rules of magic these only produce finite numbers of creatures. A caveat: It might take an infinite amount of time to physically generate these creatures, but the fact remains that with high probability an infinite number of creatures are created. Bob and Alice are playing a game of Magic. Bob has five life, a tapped Spikeshot Goblin  , a Summoning Station  , a Leonin Elder  , and some tapped Mountain  s. It's the Alice's turn (pre-combat main phase), and she has one life. She has a Wirefly Hive  , a Gilded Lotus  , a Voltaic Construct  , and a March of the Machines  . Alice can use her Gilded Lotus , Voltaic Construct , and March of the Machines to produce an arbitrary amount of mana. She wants to create enough Wirefly tokens to fly over Bob's defenses and deal lethal damage to him. If she is unable to produce enough Wirefly tokens, Bob will be able to untap and shoot her with the Spikeshot Goblin . If Alice gets lucky, she can win 5 flips in a row with her Wirefly Hive , which gives Bob 5 life from his Leonin Elder , and then fly over to kill him with her 5 2/2 Wirefly tokens. If Alice isn't quite as lucky and loses a flip after at least one Wirefly token is created, she gives Bob some life and then must be even more lucky to kill him. Every time a Wirefly token leaves play, Bob will use his Summoning Station to create a colorless (and non-artifact) Pincher token. Bob is wary of Alice's tricks and wants as many creatures as possible, just in case. With a high probability, no matter how many times Alice uses the Wirefly Hive , she will never create enough creatures to kill Bob. However, at any point in the process, she is not stalling, since she always has some (very small) chance of generating enough Wirefly tokens to win. Similarly, my understanding of magic loop rules leads me to believe that this scenario falls outside of them. Bob creates a Pincher Token every time a Wirefly token goes to the graveyard. With high probability, Alice will continue creating Wirefly tokens forever, and Bob will have an infinite number of Pincher tokens (again, with the caveat that it will take Bob an infinite amount of time to generate these tokens). I mentioned this loop in another post concerning infinity. Does this work?
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5 years ago ::
Jul 25, 2008 - 7:30AM
#2
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Date Joined:
Jan 19, 2003
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If you were to repeat that process indefinitely, alice would eventually get the tokens she needs. The probability of her getting enough wireflies is non-zero, and thus will eventually happen. Even if it takes so many iterations that Knuth's up-arrow notation becomes combersome, you are no closer to infinity than if she got it after only 5 activations. PS, you are correct that this scenario could not be shortened into a loop. And would need to be handled step by step.
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5 years ago ::
Jul 25, 2008 - 7:47AM
#3
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If you were to repeat that process indefinitely, alice would eventually get the tokens she needs. The probability of her getting enough wireflies is non-zero, and thus will eventually happen. Even if it takes so many iterations that Knuth's up-arrow notation becomes combersome, you are no closer to infinity than if she got it after only 5 activations.
PS, you are correct that this scenario could not be shortened into a loop. And would need to be handled step by step.
Some infinite series converge to infinity, and some infinite sequences of actions have a probability of 1 of converging. This is not one of them. That is to say, even though Alice has an infinite number of chances to win, the chance of winning drops so fast that the probability that Alice will eventually win is NOT 1.
To give an easier example, suppose Alice is going through a loop that has a 1/3 chance of winning after one iteration, a 1/9th chance after 2, a 1/27th chance after 3, etc.
The overall chance that Alice will win is 1/3 + 1/9 + 1/27... If we sum this infinite series, the answer is 0.5. Even after an infinite number of attempts, Alice will have a 50% chance of winning, despite always having a chance to win.
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5 years ago ::
Jul 25, 2008 - 7:58AM
#4
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Date Joined:
Jan 19, 2003
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Some infinite series converge to infinity, and some infinite sequences of actions have a probability of 1 of converging. This is not one of them. That is to say, even though Alice has an infinite number of chances to win, the chance of winning drops so fast that the probability that Alice will eventually win is NOT 1.
You're right, I take it back.
It would still require an infinite amount of time to get an infinite amount of tokens (which was your goal with creating a situation like this). In a practical game, you would be limited by the duration of the round (if you are in a tournament), or the attention spans of alice and bob (if playing casually with sane people), or the lifespans of alice and bob (if they are insane), or the duration until the universe ends (if you built self-replicating robots with the ability to flee from a dieing sun to finish out the game for you, and assuming of course that the universe actually has an end).
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5 years ago ::
Jul 25, 2008 - 8:41AM
#5
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Date Joined:
Mar 22, 2001
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I'm attempting to construct a scenario where a player gets an actually infinite number of creatures in a game of magic.
All you did was create a situation where you could claim it isn't pointless to endlessly repeat a sequence of actions. What you don't seem to realize is that no rule of Magic says you can't do that anyway.
All the so-called "loop rules" do, is define an ending point to such a sequence, that will always be the same for a given setup. When you finish one set, you could do it again within the rules of Magic. But if the ending point is the same (or: predictable in advance), a judge can cite you for wasting time, since you knew that the result would be the same (or: you knew how to get to that predictable result by "naming a number").
What you didn't do, was actually create the time in which to get all those tokens. Whether your attempts stop because a judge tells you to stop stalling, or the tournament ends, or your friends all go home, or the world comes to and end - the results are the same. You will not have achieved an infinity of tokens.
Does this work?
Depends on what you mean. Does it allow Alice to draw the game, instead of lose? Yes. Does it get her infinite tokens, or somehow "prove" that Magic needs to recognize the concept? No.
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5 years ago ::
Jul 25, 2008 - 4:26PM
#6
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How is a judge supposed to handle this? My understanding is that this example invokes neither the stalling nor the loop rules. This situation is unlike any other loop I've seen in magic. Consider: 1) Normal "arbitrarily large" loops, such as SquirrelCraft. These are well handled under the loop rules. You can't continue to create tokens. 2) Loops based on random conditions that will eventually be satisfied with probability 1. For example shuffling your deck and looking at the top three cards until you get the exact cards that you want. My understanding is that you must play out the scenario until the exact cards are found, and running the loop until that point is not stalling. Even in this case, the loop will eventually stop and you cannot get "infinite" iterations without stalling or breaking the loop rules. 3) This type of loop, which I contend is different than 1) or 2) Can you construct a different loop (say, without Wirefly Hive ) that with high probability will never stop, where neither player is stalling (and doesn't run afoul of the loop rules?).
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5 years ago ::
Jul 25, 2008 - 6:28PM
#7
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Date Joined:
Mar 22, 2001
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How is a judge supposed to handle this? My understanding is that this example invokes neither the stalling nor the loop rules.
Correct. Which is why I said it was a draw. But without infinite time, you do not get infinite itteration of the loop. You can only get a finite number.
1) Normal "arbitrarily large" loops, such as SquirrelCraft. These are well handled under the loop rules. You can't continue to create tokens.
It isn't the rules of Magic that accomplish that. It is the fact that you can get any finite number you want by simply "naming" the number. So not naming a number is stalling.
Your situation is different - there is a point, albeit an increasingly hopeless one, in continuing. Just liek there is a point in continuing a Gaea's Blessing loop. Since it is random, you can't invoke the loop rules. But it is still finite. Why are you assuming otherwise?
3) This type of loop, which I contend is different than 1) or 2)
It is no different than 2).
Can you construct a different loop (say, without Wirefly Hive) that with high probability will never stop, where neither player is stalling (and doesn't run afoul of the loop rules?).
What would be the point? YOU DON'T HAVE INFINITE TIME.
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5 years ago ::
Jul 25, 2008 - 7:59PM
#8
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Based upon your original post, what is giving the tokens Haste, so they could then fly over & hit Bob?
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5 years ago ::
Jul 25, 2008 - 11:45PM
#9
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Date Joined:
Dec 16, 2007
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Good point  Also Bob's Pincher tokens would have to have flying to block. I couldn't resist trying to figure it out... so assuming just for the sake of argument that Alice's tokens have haste and that Bob's tokens have flying, I think the odds are against Alice. The rough calculation I did shows Alice has less than a 4% chance of winning (although the operative word there is rough) . . . most of which comes from the 1/32 chance of winning the first 5 flips.
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5 years ago ::
Jul 27, 2008 - 1:21AM
#10
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First of all, I forgot to put Mass Hysteria (also in Mirrodin Block) in my example. That fixes the haste issue. The Pincher Tokens cannot block the Wirefly Tokens (as they don't have flying).
C
Your situation is different - there is a point, albeit an increasingly hopeless one, in continuing. Just liek there is a point in continuing a Gaea's Blessing loop. Since it is random, you can't invoke the loop rules. But it is still finite. Why are you assuming otherwise?
It is no different than 2).
What would be the point? YOU DON'T HAVE INFINITE TIME.
This loop I've described and any loop involving the ordering of cards are fundamentally different.
Suppose I have the ability to run a loop where I can (as many times as I wish) shuffle my cards and look at the top 3. I want to run this loop until I get the exact cards I want on top of my deck, in the exact order I wish.
After any shuffle, I have a low probability of getting the exact cards I wish. After enough shuffles, with probability approaching 1, I will get exactly the cards I wished. Suppose that some other card allowed me to generate a creature every time my deck was shuffled. At some point, I will get the exact cards I want and I will have a very large, but finite number of creatures. The probability that I will eventually get the exact cards is 1.
Now consider the situation described. In this case, the probability that the loop ends is not 1. It's actually around 1/30. [Anecdotally, I asked a (currently level 4) judge this problem and off-the-cuff he said he'd roll a 30-sided die to determine who would win... turns out he was pretty close].
Suppose a judge in the shuffle/look case let the player stack the three cards instead of actually simulating each shuffle (I know, this isn't the current rules, but members of this message board have stated that they felt that the rules should allow this). If the judge allowed a similar simulation to occur in the Wirefly Token case then Bob would have infinite creatures.
I stated in my original post that it would take an infinite amount of time to physically generate all the creatures. Almost every response has also pointed this out. However, this brings an element of "action time" to magic that I don't think exists in the rules of the game (except in the stalling rules, which only puts effective upper limits on how much time something can take)
We often speed up actions when we play magic. We pass priority until something interesting happens. If Squirrelcraft happens, we skip millions of decisions in the space of a single demonstration. We could calculate what will eventually happen in the shuffle/look case and skip a number of random actions because we know what will eventually happen. [I know, current rules say you have to actually simulate]. What's the difference in skipping a million breakpoints and skipping an infinite number?
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