infinite loops and stochastic states

[Eugene Hwang]

Warning: If you hate math or don't care about ridiculous corner-case rules questions, stop reading this post...

 

So there's this ridiculous thread on the EDH forums about unbounded loops in a stochastic state.  However, it's most likely way too tl;dr.  There are, however, three interesting rules scenarios to come out of it.  They are as follows:

1) Player 1 has an infinite mana combo and a Whetstone.  Player 2 has an Emrakul in their library.  The sum of the number of cards in player 2's graveyard and library is even.  Player 1 would like to mill player 2 "until the Emrakul and one other card are the only cards left."  Statistically speaking, the law of large numbers guarantees this state, but it is going to take a lot of shuffling.  How would you resolve this in a sanctioned match?  Does it matter whether player 1 cares what the second card in player 2's library is?  What if player 1 is up 1-0?

2) Player 1 is capable of generating an infinite storm count and has an Ignite Memories in hand.  Player 2 has, previously during this game, played out an infinite life combo, setting their life to some extremely large number X.  They no longer have this combo available to them.  Player 1 would like to generate some finite storm count Y and then cast Ignite Memories.  Statistically speaking, as Y->infinity, the probability of player 1 winning approaches 1, but there is no infinity in Magic.  How would you resolve the Ignite Memories in a sanctioned match?

3) Player 1 is has a Mass Hysteria, March of the Machines, Voltaic Construct, and Wirefly Hive, but is at 1 life.  Player 2 has a tapped Spikeshot Goblin and a Leonin Elder, and is at 5 life.  Player 1 can generate an arbitrary number of Wirefly Hive activations, but every time he loses a flip on Wirefly Hive, player 2 may gain some life, requiring player 1 to win even more consecutive flips in order to achieve victory.  If he fails to do so, obviously, he will lose next turn to the Spikeshot Elder.  Without going through the math on this one, if player 1 continues to flip coins until he has a number of wireflies equal to player 2's life total, there is a ~1/30 chance that he will achieve his desired game state, and a ~29/30 chance that he will flip indefinitely.  How would you resolve this in a sanctioned match?  What if player 1 is up 1-0?  Keep in mind that this is quite a non-trivial probability calculation, and chances are good that nobody in the room will be able or willing to solve it in a reasonable amount of time for the situation at hand.

[Gary Lynch]

Only one I can say for sure is number 2.

 

The rules state that  when doing an "infinate" combo you just have to demonstrate it 3 times and they you can just say " repeat 2 billion times".

So in Senario number 2 player 2 would have had to have chosen a number for his life total lets say 2 million. Player 1 can now do an infinate combo and choose 2 million and 1 or any number higher and win the game.

[Eugene Hwang]

Sorry, I neglected to mention an important detail in scenario number 2 - player 2 has both a spell of positive CMC and a land in his hand, so no matter what storm count is selected, there is a non-zero probability of sacking out like Nassif vs. Chapin.  The probability calculation is fairly easy in this binary case, but what if he has a full grip with a mixture of lands and spells across various CMCs?

[Daniel Royde]

No- because ignite doesn't do 1 damage each time it resolves.

If there's any zero costing card in their hand then there's a non zero chance of not doing enough damage, regardless of how high your storm count is.

 

These are all interesting situations.

1&2 have (to me at least) obvious "reasonable" solutions- player doing the loop gets what they want.

I don't think you should have to worry about the rate of damage dealing/ life gain either, since increasing the nubmer of iterations of your loop has no cost.

 

While 2) doesn't have some number of iterations which strictly garantees the kill, it doesn't seem unreasonable to use some threshold which you consider sufficient to be "certain". Then some number of iterations will garantee the kill.

 

Obviously reasonableness isn't always relevant since it's DCI rules.

 

3) is the most interesting one:

Even if you could calculate it within reasonable time, that doesn't garuantee that both your opponent and a judge can understand/believe your explanation.

 

On the other hand, as the wirefly player, you wouldn't lose that much chance of winning just by flipping a few coins- 10-15. So you could just iterate your loop here, I think that's what you'd do in practice.

 

I suppose that it's possible to create a similar situation where you need to do an unreasonable number of iterations to come close to having your correct chance at winning. Then... If calculating the correct answer takes more than a minute, it's slow play. You won't be able to do it as a loop. I don't see a practical solution.

 

Gary Lynch said:

Only one I can say for sure is number 2.

 

The rules state that  when doing an "infinate" combo you just have to demonstrate it 3 times and they you can just say " repeat 2 billion times".

So in Senario number 2 player 2 would have had to have chosen a number for his life total lets say 2 million. Player 1 can now do an infinate combo and choose 2 million and 1 or any number higher and win the game.

Gary Lynch said:

Only one I can say for sure is number 2.

 

The rules state that  when doing an "infinate" combo you just have to demonstrate it 3 times and they you can just say " repeat 2 billion times".

So in Senario number 2 player 2 would have had to have chosen a number for his life total lets say 2 million. Player 1 can now do an infinate combo and choose 2 million and 1 or any number higher and win the game.

[Alex Churchill]

Case 2, with Ignite Memories, was discussed on the DCIJUDGE-L and MTGRULES-L a few years back, talking about Gaea's Blessing. Here are the [O]fficial Wizards rulings:

 

Date:    Tue, 31 Jul 2007 12:22:59 -0700
From:    "Heckt, Andy" a href="mailto:[e-mail]">[e-mail]>
Subject: Re: Infinite life and Ignite Memories

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

 

Date:    Tue, 31 Jul 2007 19:08:44 -0600
From:    Scott Marshall a href="mailto:[e-mail]">[e-mail]>
Subject: Re: Infinite life and Ignite Memories

...
* 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).

[Thom Richardson]

So in a sanctioned match the answer would be play it out.

 

does anyone know if genreated pseudo random number sequences are acceptable to the DCI?

 

just generate one with wolfram on your phone and do a count of the sucesses.  pretty sure you could process it fast enough to get the win in the ignite memories example unless there wan't much time on the clock.

 

Alex Churchill said:

Case 2, with Ignite Memories, was discussed on the DCIJUDGE-L and MTGRULES-L a few years back, talking about Gaea's Blessing. Here are the [O]fficial Wizards rulings:

 

Date:    Tue, 31 Jul 2007 12:22:59 -0700
From:    "Heckt, Andy" a href="mailto:[e-mail]">[e-mail]>
Subject: Re: Infinite life and Ignite Memories

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

 

Date:    Tue, 31 Jul 2007 19:08:44 -0600
From:    Scott Marshall a href="mailto:[e-mail]">[e-mail]>
Subject: Re: Infinite life and Ignite Memories

...
* 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).

[Eugene Hwang]

So it appears that ruling is generalizable to all three situations.  AFAIK there's no prescribed way of picking a random card out of someone's hand, so presumably a PRNG is acceptable if both players agree to its use.  And a PRNG should be an acceptable substitute for flipping a coin, as any method of randomization that gives an equal likelihood of one result or the other is an acceptable substitute for a coin, if both players agree to its use.  However, that won't solve scenario 1, nor will it solve anything if the players can't agree.

 

So, if a player can't be forced to concede, and all of these situations involve everything happening in one turn (thus obviating the point of the five additional turns rule), what happens?  Just a game of chicken that holds up the tournament?  In scenarios 1 and 3, each iteration of some defined loop yields a nonzero chance for player 1 of moving the game state from losing to winning, so theoretically, they are well within their rights to continue looping, but is that "slow play" or something?  Or is this a case the rules just don't, won't, or can't cover?

[Thomas David Baker]

Practically speaking what will happen is that a bad judge will make a bad decision based on the wrong information and faulty reasoning.  Then you will appeal to the Head Judge who will be way, way better but still rule fairly arbitrarily.  Later when he's thought about it in more depth the Head Judge will probably come up to you and tell you they should have ruled the other way.

This happens a lot with a lot simpler situations than these.  They're only human.