Infinite questions

[Gabethebabe]

1) My opponent plays Life and has 6.37 googolplex life. I set up an infinite loop with Walk, Timetwister and Regrowth and have an Elvish Spirit Guide in play. Do I win even though I will not be able to attack my opponent to 0 in this lifetime?

2) Same question, but now I set up this loop when we are in turns and I´m not able to kill him in the 5 turns that remain. E.g. my opponent is at 21 life. This is a draw I suppose.

3) My opponent has capped my win conditions out of my deck and is one turn away from killing me with his Mountain Goat. I set up infinite turns again. Is it a draw or am I obliged to give my opponent a turn so he can kill me ?

[Harlequin]

It depends on if the game can ever change.  Here is an easier example:

I have a mountian goat in play, and two squee's in my yard,  and I have a possessed portal in play.  My opponent has infinite life.  After several turns of me discarding squee, discarding squee, return two squees ... all the while my opponent is lossing board and hand, and not drawing cards ... my opponent has no board and no cards in hand.  At this point I can declare that the board possition will never change, and that I intend to attack "infinitely" with Mountain Goat.  No players will draw any cards, and my opponent cannot possibly change the game.  And I will always be able to feed the portal infintely with my two squees.

So if I understand your loop... you have:
with 4UUG availible every turn.
All other cards are removed from game or in play all but these 9 cards....
Timetwister - in the yard.
Regrowth - in hand
Timewalk - in hand
card
card
card
card
card

So you play time walk, regrowth --> timetwister.  Cast it.  Now you have Draw 7 cards (creating a one card library) and Timetwister starts a new yard. Pass the turn.  Now you go to walk turn and draw your 8th card and start the combo again.

I'm fairly sure this would NOT constitute a hard lock, because at some point your opponent might have a response to something, your opponent draws 7 cards each turn as well.  This is grey area.  It would require knowledge that your opponent has NO Alternate casting cost spells and NO elivish spirit guids in the entire deck.

[Godder]

It's rare that infinite turns can be proven, while not allowing the opponent play – Isochron Scepter + Final Fortune + Platinum Angel is a well-known "infinite" combo that would work in the Life scenario. I don't think that a combo with Timetwister would work, though, because the opponent could potentially disrupt things with their 7 cards.

[Norm4eva]

The thing of it is, in Magic there's no uncontrolled 'infinities' - or at least, none that end favorably for either player.  So if you can set it up to where you can attack with a Mountain Goat over 2134982134234234 turns - t3h 5VG, btw - then you can declare that you will do so 2134982134234234 times.  Even if the number is arbitrarily high, if the action requires one or more choices on behalf of the player controlling the effect, it must ultimately be a finite loop.

421. Handling "Infinite" Loops

421.1. Occasionally the game can get into a state in which a set of actions could be repeated forever. These rules (sometimes called the "infinity rules") govern how to break such loops.

421.2. If the loop contains one or more optional actions and one player controls them all, that player chooses a number. The loop is treated as repeating that many times or until another player intervenes, whichever comes first.

421.3. If a loop contains optional actions controlled by two players and actions by both of those players are required to continue the loop, the first player (or the first involved player after the active player in turn order) chooses a number. The other player then has two choices. He or she can choose a lower number, in which case the loop continues that number of times plus whatever fraction is necessary for the active player to "have the last word." Or he or she can agree to the number the first player chose, in which case the loop continues that number of times plus whatever fraction is necessary for the second player to "have the last word." (Note that either fraction may be zero.) This sequence of choices is extended to all applicable players if there are more than two players involved.
Example: In a two-player game, one player controls a creature with the ability ": [This creature] gains flying," and another player controls a permanent with the ability ": Target creature loses flying." The "infinity rule" ensures that regardless of which player initiated the gain/lose flying ability, the nonactive player will always have the final choice and therefore be able to determine whether the creature has flying. (Note that this assumes that the first player attempted to give the creature flying at least once.)

421.4. If the loop contains only mandatory actions, the game ends in a draw. (See rule 102.4b.)

421.5. If the loop contains optional actions controlled by different players and these actions don't depend on one another, the active player chooses a number. In APNAP order, the nonactive players can each either agree to that number or choose a higher number. Note that this rule applies even if the actions could exist in separate loops rather than in a single loop.

[Scoops666]

1) You couldn't prove infinity here because the game state is always changing w/ the cards you, and especially your opponent, are drawing. Unless, however, you have seen the contents of his deck this game(say duress and cap in 1 turn) and know that he doesn't have an out. Then you could call a judge and state your case. However, if you don't have this knowledge, then it's always possible to find some sort of out that you may not know about.

2) Yeah, this is a draw. Sorry man.

3) You have to give him a turn. There are basically 2 kinds of loops(1 of the many ways to view loops): breakable and unbreakable. Unbreakable is something like Dragon. It's loop is triggering off triggered abilities, which is something you can't simply choose to "not trigger," meaning if you don't have another animate target, the game draws because the Dragoon will just keep coming in and out of play. This loop involves you casting a series of spells to constantly repeat itself. At any point in this chain, you can stop it by simply not casting one of the spells. This is a breakable loop. And the rules state that if you can break it, you eventually have to.

[Harlequin]

Well in Mathematics and Probability, there is a concept of "countably infinite" Which is defined in laymans terms as: "An Event governed by logic that will happen at an indetermined time. In Theory, could continue infinitely, but it has eventuality."  An Example of such an event is: Flipping a coin UNTIL you flip 5 tails in a row.  Could you flip infinitely with this never happening? well that depends on how you define infinite.  But at some point this will happen.  So saying "I attack UNTIL you have 0 life" is not nessisarily saying the same thing as "I attack you infintely."
The fact that your opponent has a Finite total of life makes picking a finite number of attacks very easy.. just pick a number that is equal to thier life total.



Fun Time:  WARNING -- BELOW IS HIGHLY MATHMATICAL, IF YOU HATE MATH PLEASE AVERT YOUR EYES!
Magic and Probability - This was something I did for an extra credit project in my "Probability and Statstics Using Simulations" Class.

Thank God I don't have to go over the back story of what magic is.

Here is the Story:
You are playing Dragon, You only have Abasador Laquatus as your only win condition, and you have enough life to cast 2 Deep Analysis from your graveyard.  Your opponent plays Oath and has 2 Gaea's Blessings in thier Library.  Use "Comperable Probability" to simplify your odds of winning.

Your plan is to float sufficent mana from the dragon combo, then grab laquatis from your library.  Mill your opponent X times where X is the number of mill that will leave 2, 3, or 4 cards left in your opponents library (remeber that laquatus must mill 3 cards in a single activation).  Then look at the grave yard.  If no Geae's Blessings are in the yard, then you cast Deep analisis twice targeting them.  If you hit blessing, then allow the deck to reshuffle and repeat.

The remainder cards is the number left after a "complete" mill.  So if your opponent has 60 cards left in the deck then the number of mills required for a "complete" mill would be 57 (or 19 activations) and the remainder will be 3.  In other words L = cards in library and R = Remainder.  R = [(L - 2) MOD 3 ] + 2.
Given R, there is a Probability of a Successful Mill.  

>The Event S will define a Mill in wich both Gaea's Blessing are left in the R card remaining in the library.  After a "complete Mill"

R=r,  Prob(S = True)| R=r
-------------------------
4,  0.003391881
3,  0.001724138
2,  0.000564872

Comperable Probability:
Suppose we pick an arbitrary event with simple probabilty.  If we can declare that the probabilty of failure of One Complex event, is smaller than the probabilty of failure on another event... then we can perform the simiple event instead of the complex event.  
Simple Event.  Roll "20" on a 20 sided dice N times in a Row.  
N = n,   Prob( "20" N times and a number <"20" 0 times)|N=n
---------------------------------------------------------------------------------------
5,    3.125 E -07
100  7.8886 E -131
200  6.223 E -261

So above says, the probabilty of rolling 200 "20"'s in a row is 0.[260 "0"'s]6223.  If I can float enough mana to prove that the probabilty of me NOT accomplishing the event above S is smaller than the probabilty of Rolling 200 "20"s in a row, then I can say ... "start rolling, If you can roll 200 "20"s in a row, then I fizzle, otherwise I successfully mill you until your Blessings are the only cards left, and Deep Analysis you to death."

R, Number of "Complete" Mills, Prob( Event S = False every time)
-----------------------------------------------------------------------------------
4, 4 409, 3.121 E -07
3, 8 681, 3.120 E -07
2, 26 505, 3.124 E -07

4, 88 171,  7.8832 E -131
3, 173 603, 7.8837 E -131
2, 530 095, 7.8877 E -131

4, 176 342,  6.2145 E -261
3, 347 206,  6.21533 E -261
2, 1 060 190,  6.22169 E -261

What does all that mean.  That means... Suppose you have a 3,002 card library with 2 Gaea's Blessings in it.  that would mean if I float 3000 x 1,060,190 = 3,180,570,000 Mana (oh + 4 for the two Deep analysis activations).  Then I spend 3000 mana to mill 3000 cards... 1.06 million times the probabilty that I NEVER am able to successfully get your 2 Geae's Blessing as the bottome two cards is SMALLER than the probabilty that you can roll 200 "20"s in a row...  Math is fun.

[vartemis]

Here is the Story....

Thanks for almost giving me an anurism.  I have talked with a couple of judges and even pm'd  DicemanX regarding the Laquatus problem.  Many judges still wont accept this and will make you play it out, obviously running the game to time.  It can also be stated that given an infinite amount of mana, your opponents library could be stacked in any order you wanted. While the math is sound, judges are human.  You should just post your full report as a .doc in a Dragon primer to be printed and brought to tournaments.  I would love to see a dragon player pull that out on a judge and explain it.

j

[Moxlotus]

Your opponent has every right to continue to take his turn if he is alive.  Even if there is no way he can win you still have to reduce his life total to 0 or run him out of cards.  Hell, his deck could be 40 Mountains remaining and he would still be able to take his turn.  Its the same reason life decks couldn't just declare victory when they combo'd--they still needed to actually win the game in a fashion they can prove by playing it out, even if they couldn't lose.

Magic rules don't use statistics in the rules--the rules affect what happens while being played out.

[Harlequin]

Here is the Story....

Thanks for almost giving me an anurism.  I have talked with a couple of judges and even pm'd  DicemanX regarding the Laquatus problem.  Many judges still wont accept this and will make you play it out, obviously running the game to time.  It can also be stated that given an infinite amount of mana, your opponents library could be stacked in any order you wanted. While the math is sound, judges are human.  You should just post your full report as a .doc in a Dragon primer to be printed and brought to tournaments.  I would love to see a dragon player pull that out on a judge and explain it.

j

Yeah, I never expected this arguement hold water in a tournement.  It was more of a fun "how much would it take." I showed it to Ray before a waterbury one time, and he liked it.  If figgured if there was anyone who could appriciate it, it would be ray.

I left out a ton of math, for the reason ... it doesn't really matter.  I have the math to back each number, but it is rather irrelevant.  I used Excel VBApps to write a script that incrimented the "Number of Full Mills" until Prob(1) was less than Prob(2).  I also have that.  I however do not have the actually report that I handed in for the class becasue I wrote up that on a school computer.  I did all the code at home though.

I wanted to do roll 1,000 "20"s in a row, but (1/20)^1000 is far too much for Excel to handle.  so 200 was pritty much the limit.

If you end up playing it out, you would spend SIGNIFIGANTLY less mana, because the method is rather in-efficent on mana.  Because technincally you could let each mill resolve and see if Blessing is hit... then let the deck reset, and save the rest of the mana, but that is WAY too much work to calc that probabilty.  Permutation suck!  This way you stack the appropraite number of mills then let them resolve and THEN evaluate whats left in the deck. 

I also fail to see how you can stack their deck...

[Toad]

1) My opponent plays Life and has 6.37 googolplex life. I set up an infinite loop with Walk, Timetwister and Regrowth and have an Elvish Spirit Guide in play. Do I win even though I will not be able to attack my opponent to 0 in this lifetime?

If you can prove this is a real loop (cf. the Final Fortune example above), you win this game.

2) Same question, but now I set up this loop when we are in turns and I´m not able to kill him in the 5 turns that remain. E.g. my opponent is at 21 life. This is a draw I suppose.

Draw.

3) My opponent has capped my win conditions out of my deck and is one turn away from killing me with his Mountain Goat. I set up infinite turns again. Is it a draw or am I obliged to give my opponent a turn so he can kill me ?

If you don't pass the turn, expect a Warning for Slow Play soon, and a DQ for Stalling soon after.

[warble]

Here is the Story....

Unfortunately, sound mathematics and a good theorem has never won a tournament.  Maybe if the game was called Mathick Theorem Gathering and we played on blackboards with chalk...if it's not something you can play out by hand it's not something you can use to win the game.

It is obvious that with infinite arrangements of your opponent's library, you can reach any configuration of those cards, but hey...that's only because we understand infinity and very large alpha.

[vartemis]

I also fail to see how you can stack their deck...

Given -  a deck of 60 cards has a finite number of ways in which the cards can be found in a specific order.
Given - with infinite mana you could mill your opponent's entire library and have it shuffled untill a desired outcome on the order of cards is received.

I assume that no judge would let you set up your opponent's entire deck, but I once was let to remove the blessing, shuffle the library and mill a set multiple of 3 until a number of cards in the library <3 was left, then place the blessing on top, then cause them to draw it using an instant.

j

[Harlequin]

I also fail to see how you can stack their deck...

Given -  a deck of 60 cards has a finite number of ways in which the cards can be found in a specific order.
Given - with infinite mana you could mill your opponent's entire library and have it shuffled untill a desired outcome on the order of cards is received.

I assume that no judge would let you set up your opponent's entire deck, but I once was let to remove the blessing, shuffle the library and mill a set multiple of 3 until a number of cards in the library <3 was left, then place the blessing on top, then cause them to draw it using an instant.

j

That's very very shady.  But that is "Countable infinity" for ya.  The idea that you could do this takes the randomness out of the problem.  Lets say you shuffle a deck 100 million times.  There is a random chance (be it almost immessurably small) that you will "shuffle" the deck into an aphabetically sorted pile on EVERY shuffle.  My point being that even if you have an insanely huge amount of tries to accomplish a task it cannot be assumed that you have automatic sucess, if there is even a sliver of probabilty that you will fail.  This is why the "comparably probabilty" is such a good method.  If you say, you have a greater chance to roll 200 "20"s in a row than i have a chance of failing to set the deck up the way I want... then at least you are still factoring in that sliver of probabilty by wich your chance of failure is greater than zero.

To word the same argument differently, there is no number of shuffles that will ENSURE that you get every combination of cards, as you stated in the original part of the post.  True, as the number of shuffles increases the probabilty of not getting one of each combination decreases.  If you were to plot this curve it would be tangential to the line f(x) = 0.  So it would in fact require and "Infinite" ammount of mana to accomplish a true 0% failure chance.

[vartemis]

That's very very shady.  But that is "Countable infinity" for ya.  The idea that you could do this takes the randomness out of the problem.  Lets say you shuffle a deck 100 million times.  There is a random chance (be it almost immessurably small) that you will "shuffle" the deck into an aphabetically sorted pile on EVERY shuffle.  My point being that even if you have an insanely huge amount of tries to accomplish a task it cannot be assumed that you have automatic success, if there is even a sliver of probabilty that you will fail.  This is why the "comparably probabilty" is such a good method.  If you say, you have a greater chance to roll 200 "20"s in a row than i have a chance of failing to set the deck up the way I want... then at least you are still factoring in that sliver of probabilty by wich your chance of failure is greater than zero.

To word the same argument differently, there is no number of shuffles that will ENSURE that you get every combination of cards, as you stated in the original part of the post.  True, as the number of shuffles increases the probabilty of not getting one of each combination decreases.  If you were to plot this curve it would be tangential to the line f(x) = 0.  So it would in fact require and "Infinite" ammount of mana to accomplish a true 0% failure chance.

I didnt have a problem with it because the whole deck ends up random, except for the placement of the blessing.  If you really wanted to, you could just keep milling and shuffling till the blessing ended up being in the remaining 1-3 cards, but that would take forever.  As for setting up the actual order of your opponents deck, I don't think any judge would actually let you, but it is theoretically possible.

j

Edit: Mind you this was done when dragon was in its infancy stage and judges didnt know how to deal with the infinite loops and whatnot.

[Harlequin]

As for setting up the actual order of your opponents deck, I don't think any judge would actually let you, but it is theoretically possible.

I disagree.  As far as Theory goes, it is theoretically Possible for you to never .. even given 10^(10^9) ... thats 1 with 1 million zeros after it ... it is theoretically possible for you to FAIL EVERY time to shuffle both blessings to the bottom 3 cards.  Unless you intend to say that in any given itteration of process that the placement of Gaea's blessing is not random.  Each time you ittereate the cycle, you have independant probabilty.  Its like the question: If you flip Heads, Tails, Heads, Tails... that pattern for 1 million times in a row, then you flip tails, whats the probabilty of flipping heads .. the answer is still onlt 50% because each trial is independant.  The same goes for Gaea's Blessing, the independance means that you can never be sure that you infact will certainly get one result given X number finite trys.

However if you have the ability to add more mana, and thus add more trys, then you have a countabily infinte loop... and that means you could infact stack your opponents deck.  Because you can continue to retry as many times as you wish until you hit that perfect 1 stack.  in a deck of 60 unique cards there are roughly 8.3 E +81 number of unque piles... wich is large but finite.  So given a countably infinite number of trys, you can arrive at any pile you choose.  But in the story above you must choose a set amount of mana before you choose to animate laquatus.  So you have X mana for Y number of full mills... and no more.

[Toad]

About the Dragon stuff, you will not be allowed to assume you get the 2 Blessings at the very bottom of the opponent's deck. There is indeed no guarantee that you can reach that stage in a finite amount of shuffles. So you would just have to try to get in that situation on your own, and in a timely manner. If you can't do it in a timely way, warning for slow play. If you keep going for too long, stalling may kick in.

[PucktheCat]

Stalling?  You are changing the game state in a potentially meaningful way each time you run through the cycle.  Each time you mill you have a chance to win the game.  How is that appreciably different from the Gifts player who Brainstorm, Fetches, Brainstorms, Cycles a card, etc. to find his one out spell.  In both cases the players are using lots of time consuming spells and shuffle effects with a low chance of success.  What distinguishes those situations in your mind?  Is it just the chances of success that are different or is there something else that I'm missing.

Another question, Toad.  Would you rule differently if the Ambassador was in play during the Dragon cycle?  Then you would have infinate mana available to mill until you put the Blessing in the bottom 3.

[Godder]

I personally don't think Stalling comes into it – Stalling implies that a player is deliberately playing slowly with a view to manipulating the time limit to their advantage. In the classic Laquatus example, the player is actively trying to win, and it's actually in his/her best interests to go through the motions of each iteration as fast as possible.

[jro]

3) My opponent has capped my win conditions out of my deck and is one turn away from killing me with his Mountain Goat. I set up infinite turns again. Is it a draw or am I obliged to give my opponent a turn so he can kill me ?

If you don't pass the turn, expect a Warning for Slow Play soon, and a DQ for Stalling soon after.

I'd like to ask you a followup to this, Toad.  Let's suppose that this same scenario happens, but time has been called on my opponent's last turn.  It is now my turn, the first of the final five turns.  Could I now perform the "infinite" turn combo to draw the game, or would I have to give one of the next 5 turns to my opponent?

[Jacob Orlove]

You are free to take all five turns, if you can do so in a timely manner.

[Toad]

Stalling?  You are changing the game state in a potentially meaningful way each time you run through the cycle.  Each time you mill you have a chance to win the game.  How is that appreciably different from the Gifts player who Brainstorm, Fetches, Brainstorms, Cycles a card, etc. to find his one out spell.  In both cases the players are using lots of time consuming spells and shuffle effects with a low chance of success.  What distinguishes those situations in your mind?  Is it just the chances of success that are different or is there something else that I'm missing.

The Gifts situation is different. Players are requested to play in a timely manner, and do stuff that are changing the game state in a meaningful way. The Brainstorm chain is real action, because It will lead to a clear situation, where the Gifts player either has no more plays, or no more mana available. This will be achieved in a limited amount of time. Repeatedly milling / shuffling a deck hoping to get 2 given cards into the bottom of the library is not changing the game state in a meaningful way, because you have no guarantee in succeeding. I can see you trying to do the trick once or twice in a game, but considering the time It takes, you'd better have a serious backup plan.

Another question, Toad.  Would you rule differently if the Ambassador was in play during the Dragon cycle?  Then you would have infinate mana available to mill until you put the Blessing in the bottom 3.

No, I won't rule this differently. Nothing guarantees that you will have the Blessing in the bottom 3 after a fixed amount of tries. Probabilities tell you that the Blessing *will* necesarily end up there after an infinite amount of tries, but that infinite notion doesnt exist at Magic. Even if you try 1000 times, you can still have bad luck. So you would have to play It for real, and once again, in a timely way.

I personally don't think Stalling comes into it – Stalling implies that a player is deliberately playing slowly with a view to manipulating the time limit to their advantage. In the classic Laquatus example, the player is actively trying to win, and it's actually in his/her best interests to go through the motions of each iteration as fast as possible.

In the Laquatus situation, the player playing Dragon has no direct solution to the double Blessing trap. Considering that he is unlikely able to get into a situation where he can get the 2 Blessings at the bottom of the deck, It's also unlikely that he can actually win this game. Hence, doing repeated shufflings will only consume time for nothing, which is why this can be assimilated with Stalling, even if you are trying to win. The notion of "tries" and "probabilities" doesnt exist at Magic, and shuffling a deck is not doing relevant stuff.

Jacob is correct for the question from jro.

[Matt]

If you don't pass the turn, expect a Warning for Slow Play soon, and a DQ for Stalling soon after.

I find this answer very unsatisfying. If I know that giving my opponent a turn will lose me the game, and my deck has within it the capability to deny my opponent ever getting another turn, why can't I play for the draw? Let me construct what I feel is a similar situation:

I have no library, no hand, four lands, Soldevi Digger, and Fountain of Youth. The only card in my graveyard is Tormod's Crypt. My opponent has Mountain Goat and also no hand or library, also no graveyard due to my Crypt, and he has a Platinum Angel with Pacifism on it, and no other permanents. I am at 2 life.

Every turn he can attack me for 1 with the Goat, and do nothing else. Every turn I can gain that 1 life back and Digger my Crypt to keep from decking myself, then draw the crypt, and use it on my opponent. I have the capability to not lose this game, but it depends on me performing certain voluntary actions. Should I be forced to NOT use my Fountain/Crypt in order to give my opponent the chance to kill me? Of course not. It's labeled a loop after demonstrating it 3 times, and the game is declared a draw.

And now I say, how is that different from: 1 life, four lands, Soldevi Digger, and Time Walk are my only in-game cards and permanents, opponent has the damn Goat again. I don't think it is any different - my same voluntary actions keep my from dying. Again, loop.

And now replace the simple Digger recursion with whatever Twister recursion you like - after casting Timetwister I have Regrowth, Time Walk, five random cards in hand, no library, and Sensei's Top and like a full of set of dual lands in play. I can Walk, Regrowth the Timetwister, and cast Twister, then take another turn, etc. If the Walk is ever the one card I didn't draw, I use Top to get it and keep going. This is essentially the situation he was asking about. How is this not a "loop demonstrated 3 times" and thus a draw?

Yes, the opponent is seeing new cards. But you can't say that I'm "wasting time and stalling" because nothing I do is changing the situation, yet claim that the opponent seeing new cards makes this not a true "demonstrate 3 times and call it a draw" loop. Letting my opponent see new cards either IS changing the situation (in which case my actions are not stalling) or it's NOT (in which case I can claim a draw).

[PucktheCat]

This will be achieved in a limited amount of time.

Well, the milling scenario will end in a limited amount of time too, at least in the scenario where Laquatus enters play after the Dragon loop.  In that situation the Dragon player has a fixed amount of mana (say, 3,000,000) and can therefore activate the Ambassador a fixed number of times (1,000,000).  That process will end in a limited amount of time if each player is diligent about shuffling, etc.  It may be a very long amount of time, but it is not unlimited.

Repeatedly milling / shuffling a deck hoping to get 2 given cards into the bottom of the library is not changing the game state in a meaningful way, because you have no guarantee in succeeding.

The Gifts player has no guarantee of success either.  In my last tournament I came to a situation where I had Thirst for Knowledge in hand and needed to draw a non-fetch blue source, a Mox, and Echoing Truth with the Thirst to win the game, otherwise I lose when I pass the turn.  My chances of success on that play were probably lower than the Dragon players chances of getting the 2 Blessings in the bottom 3 cards.  But no one would claim that by casting Thirst I was stalling.

(for the record, the three cards I drew were Polluted Delta, Mox Pearl, and Echoing Truth.  I was at 1 life, so I couldn't use the Delta.)

[Toad]

@ Matt.

The situation you describe is different. In the original situation, the loop is just there to prevent the opponent from winning by not passing him the turn. Basically, even if you are doing actions, you are just doing actions who are completely irrelevant to the game state considering you can't kill your opponent, just in order to reach the time limit. Here is a more extreme situation. You are playing ReapLace and have a Reap in hand, one in the graveyard with the Black Lotus. Opponent has 2 Black permanents so you can loop. Nevertheless, he already Crypted your Ancestral Recall and your other win conditions, so all you do is to do Reap on Reap and Lotus followed by Reap on Reap and Duress. At some point the opponent has no cards in hand and yet you keep Duressing him. All you do is doing completely irrelevant stuff from that point, and It's pretty obvious here. The first example is similar, and that's the reason why the player should not be allowed to play for the draw. His opponent, knowing he has no win conditions left, will likely call the judge here.

@ PucktheCat

Time is the important information here. Playing 2 Brainstorms as a Gifts player will take at most 2 minutes (30 if you are Smmenen) before resolution ends and opponent can play. Shuffling / milling can be done for hours without a clear result.

[Gabethebabe]

OK.

I though that since the loop was not in one turn, I could be legal.

In situation one. I have a proven infinite turns, something like Walk, Regrowth, Timetwister, Lotus, 5 other cards between library, graveyard and hand and enough mana on the table to play: Walk, Timetwister. Take the new turn, draw the last card from my lib, walk, regrow Timetwister and play it etc.

What happens if my opponent at 6.37 googolplex life doesn´t accept that I win the game and wants me to play it out? He could have a card in his deck that foils my combo (a single Chant e.g. and mana to play it). Of course I can´t win if we play it out, so will a judge go through his deck and see if he actually has a way to stop me?

[warble]

if we play it out

This is not a good assumption, the "default action" you will be taking is to play cards.  Any demands like "concede the game" or "let me see if you're lying by checking your deck" is completely unsportsmanlike.  You play the game for the joy of playing, some cool prizes, for the awesome people you meet, and other such wonderfullness.  The thing about your combo is it relies on your opponent combo-ing with you.  If you really want to resolve this the only sportsmanlike thing would be to allow your opponent to choose his 7-card hand (imho).  Otherwise you have to play enjoy playing the game with him, and enjoy the fun of flipping cards.

Odds are the best you get out of this game is a draw...because you really didn't win the game man...you just proved you "could" win the game.  Your combo is infinitely different than life's combo...haha "I made a funny" - Master Splinter

[Norm4eva]

This all sounds very similar to that grumble in Extended a little while back, in regards to that Confinement deck that was built without a win condition, but it was quite good at simply 'not losing' until time was called.  I'm not sure that I necessarily like the idea of playing with or against such a deck, but I'm sure we can all recall a situation where people have 'won', or at least obtained a stalemate, by simply not losing in the alloted time.  It happens frequently, especially in Limited; sometimes players take their 5 remaining turns and nothing of import happens.  This is not zero-sum game theory we're dealing with here, sometimes nobody actually wins.
Look, this talk of higher math and countable infinity is reeeeeally interesting, but in the end it has to be tantamount to actual gameplay.  The game generally comes down to a single moment when you end up asking the opponent, in one way or another, "Can you deal with XYZ?" If you put 234 Storm triggers on the stack from Tendrils, and I have the means to deal, then the least I can say is you don't win this turn.  If you can swing for lethal and for whatever reason I never let you untap, I think I built a better mousetrap.  If you're playing Neo.dec and I'm running Smith.pile, and we stalemate, isn't that just another potential contingency that we face?  Why work so hard to edit that out of the game?

[LordHomerCat]

if we play it out

This is not a good assumption, the "default action" you will be taking is to play cards.  Any demands like "concede the game" or "let me see if you're lying by checking your deck" is completely unsportsmanlike.  You play the game for the joy of playing, some cool prizes, for the awesome people you meet, and other such wonderfullness.  The thing about your combo is it relies on your opponent combo-ing with you.  If you really want to resolve this the only sportsmanlike thing would be to allow your opponent to choose his 7-card hand (imho).  Otherwise you have to play enjoy playing the game with him, and enjoy the fun of flipping cards.

Odds are the best you get out of this game is a draw...because you really didn't win the game man...you just proved you "could" win the game.  Your combo is infinitely different than life's combo...haha "I made a funny" - Master Splinter

Not to be mean or anything, but the question is not "is it more fun to play it out or scoop?" but rather, are the situations suggested legal means of drawing or winning the game, or is it slow play.

Toad, why is it Slow Play if you continue to take turns (say, the twister-walk-6 other cards loop) in normal match time, but if I do the loop when we are in the last 5 turns in order to deny my opponent a chance at one, its perfectly alright?  I mean, if my 8 cards contain no possible way to win, or deck him, or cause anything but a draw at best, why is it alright for me to take all 5 of the extra turns (as I read your answer, you said this was alright), but its Slow Play and Stalling if I take extra turns in the regular game?  The only difference is that in one situation, the draw is going to happen sooner than the other.

[Gabethebabe]

if we play it out

This is not a good assumption, the "default action" you will be taking is to play cards.  Any demands like "concede the game" or "let me see if you're lying by checking your deck" is completely unsportsmanlike.  You play the game for the joy of playing, some cool prizes, for the awesome people you meet, and other such wonderfullness.  The thing about your combo is it relies on your opponent combo-ing with you.  If you really want to resolve this the only sportsmanlike thing would be to allow your opponent to choose his 7-card hand (imho).  Otherwise you have to play enjoy playing the game with him, and enjoy the fun of flipping cards.

Odds are the best you get out of this game is a draw...because you really didn't win the game man...you just proved you "could" win the game.  Your combo is infinitely different than life's combo...haha "I made a funny" - Master Splinter

I don´t agree with you. I have a proven loop that slowly eats his life. The infinite rule gives me the possibility to choose a number of times that I want to repeat my loop. With which I would kill my opponent (and subsequently go and drink a beer with him and discuss our awesome decks). There is only a way out of this loop if the deck of my opponent can provide it. If he knows he can´t, then yes, I expect him to concede.

[Toad]

What happens if my opponent at 6.37 googolplex life doesn´t accept that I win the game and wants me to play it out? He could have a card in his deck that foils my combo (a single Chant e.g. and mana to play it). Of course I can´t win if we play it out, so will a judge go through his deck and see if he actually has a way to stop me?

If you have proven a loop that only involves actions from your side, you'll decide how many times you want to loop, your opponent will decide how many times he wants you to loop, and you will loop an amount of times equal to the minimum of the two. If your opponent wants you to play everything entierely, you are in the right to call a judge and tell him that your opponent claims he has a solution for your plays that he could draw off Timetwister, for example. Judge will likely pick the player off the table and have a quick talk with him to analyse his options. If no Orims Chant or similar, he would have been caught trying to abuse the time limit by telling you he has a solution to your plays, which is bad news for him.

Toad, why is it Slow Play if you continue to take turns (say, the twister-walk-6 other cards loop) in normal match time, but if I do the loop when we are in the last 5 turns in order to deny my opponent a chance at one, its perfectly alright?  I mean, if my 8 cards contain no possible way to win, or deck him, or cause anything but a draw at best, why is it alright for me to take all 5 of the extra turns (as I read your answer, you said this was alright), but its Slow Play and Stalling if I take extra turns in the regular game?  The only difference is that in one situation, the draw is going to happen sooner than the other.

Well I was assuming you could perform a loop rather fast, which means you could have done 5 Time Walk recursions in a very timely manner. Thats why there is a difference between doing lots of loops for nothing in 30mn to get a draw off the clock, and playing It out in a timely way to just get 5 Time Walks. Even out of the additionnal turn, the player is allowed to loop and accumulate Time Walks. But at some point, he will have to do something relevant, or else judge would force him to pass the turn.