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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-16 10:01 am 
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I think if you're having problems with this, you really need to ask yourself a fundamental question - "Are you OK with combo decks at your EDH table?". If the answer is no, then the problem here is not the combo itself. If you ARE, then put aside the rules restriction that disallows a conditional stop point and ask yourself if what they propose makes clear logical sense? If it does, then ask yourself if there's any reason to not allow it compared to the myriad of other instant-win combos out there? Tooth and Nail into Mike & Trike is just as effective, probably more so.

Carthain wrote:
So you put a cap on how many times you can do something if you can prove it's actually infinite. I've heard X ranging from 5-6 up to 100 or so.

This is the sort of house rule you enact to make people never play combo decks, because some loops require more than X iterations to reliably do what you're trying to do.

Carthain wrote:
using social pressure.

Is probably the way to go if you really don't like it, but it still feels a bit rules-lawyery to me to enforce that restriction. Can anyone tell me WHY you aren't allowed a conditional stop point? There's got to be a better reason than preventing infinite shuffle combos.

Here's another one that technically doesn't work - I enchant myself with Wheel of Sun and Moon. I play Azami, Lady of Scrolls and Mind Over Matter. I would like to craft a perfect hand of X cards, where X is the number of cards I currently have in hand. Technically I can do this - I discard cards I don't want until I draw all the cards I do. But I have no idea how many cycles that will take. Would anyone oppose me just picking X cards and shuffling?

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-16 11:09 am 
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Sid the Chicken wrote:
This is the sort of house rule you enact to make people never play combo decks, because some loops require more than X iterations to reliably do what you're trying to do.
Depends on the value of X. And depending on the values of X required by the combo ... not sure I'd want to encourage that kind of combo. IMO if you can't figure out how to kill people in 100 iterations (probably where I'd put it were I implementing it) of your combo, then it's likely not a combo that I want to encourage people to play.

Sid the Chicken wrote:
Can anyone tell me WHY you aren't allowed a conditional stop point? There's got to be a better reason than preventing infinite shuffle combos.

Far as I can tell, because saying "Just pick a number for how many times you do it" is easier and significantly easier to understand and judge than trying to figure out how many times it would take for something to occur.

Also, Magic (outside of Un- rules) doesn't recognize "infinite" ... so if something would be infinite, then you get to just pick whatever number you like. So while the odds of you getting the deck order of your preference may come to pass if you can do it an infinite # of times, Magic rules reject the concept of infinite, therefore that logic just doesn't work out.

Finally - I think someone did mention above that, unless you have a way to confirm those conditions -- then how do you expect to know if you should stop or if you continue the combo when you should stop?


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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-16 2:05 pm 
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Carthain wrote:
IMO if you can't figure out how to kill people in 100 iterations (probably where I'd put it were I implementing it) of your combo, then it's likely not a combo that I want to encourage people to play.

Any combo that deals 1 damage at a time cannot win a 4-man table without help, for example, if you set a limit at 100. I feel like it would be better to simply ban infinite combos if you're doing house rules, rather than allow them but not really.

Carthain wrote:
I think someone did mention above that, unless you have a way to confirm those conditions -- then how do you expect to know if you should stop or if you continue the combo when you should stop?

Pretty sure I mentioned that, among others...
Sid the Chicken wrote:
As such I'm fine with such shortcuts so long as they can be verified. It's not kosher to assume you reach a state without being able to KNOW that you've reached the desired state.

But as I said, if the condition CAN be verified, I see no reason to disallow it as a stopping point.
Carthain wrote:
Also, Magic (outside of Un- rules) doesn't recognize "infinite" ... so if something would be infinite, then you get to just pick whatever number you like. So while the odds of you getting the deck order of your preference may come to pass if you can do it an infinite # of times, Magic rules reject the concept of infinite, therefore that logic just doesn't work out.

Except it really does. If you choose a high enough value of X, it is functionally the same as infinity. The rules let you pick ANY WHOLE NUMBER, so 10^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100 is a valid choice. We're talking number larger than the estimated number of atoms in the universe type numbers. In this case, the "rare event" you're looking for is essentially guaranteed to happen. I assume magic doesn't do infinity because it's not a defined value, which makes it hard to define the numeric values of things.

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-16 3:10 pm 
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Sid the Chicken wrote:
If you choose a high enough value of X, it is functionally the same as infinity. The rules let you pick ANY WHOLE NUMBER, so 10^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100 is a valid choice. We're talking number larger than the estimated number of atoms in the universe type numbers. In this case, the "rare event" you're looking for is essentially guaranteed to happen. I assume magic doesn't do infinity because it's not a defined value, which makes it hard to define the numeric values of things.
Yes, but when you pick a number your shortcut is to do whatever it is you're shortcutting that many times not that many times or until I get the result I want. That's why you can't shortcut the Four Horseman combo and why you can't shortcut whatever this combo is the OP is talking about.

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-16 11:12 pm 
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To summarise, a shortcut involves proposing a series of distinct actions we will all take. It may be repeated some number of times or not. We may nest these series of actions in our proposal. There may not be conditions in there.

A player can either accept the shortcut, or decline it by proposing a point during the shortcut during which they do something different to what the shortcut proposes.

An everyday example is that if I start my turn, untap, draw, then say "your turn," I am proposing a shortcut in which we both just pass priority until my turn ends. You can either accept, or decline by suggesting something you will do other than pass priority during my turn, such as proposing you hold priority during my second main phase. The shortcut now ends there.

Kemev wrote:
spacemonaut is technically correct that the rules governing shortcuts are in the Magic Comprehensive rules (CR); unfortunately, those rules also refer you back to the Magic tournament rules (MTR) and infraction procedure guide (IPG) for appropriate remedy. So, the Four Horsemen combo cannot be legally shortcut as described in the CR... but the CR provides no insight on what to do when the combo is assembled.

We don't really need the MTR for a remedy—the thing simply isn't following the rules of the game, and we remedy that the same way any other time someone isn't following the rules, like when they try to attack with a creature that can't attack. You can't do it. If you insist on doing it anyway, at that point the game is kinda over because you're unwilling to continue playing it by the rules.

Sid the Chicken wrote:
Can anyone tell me WHY you aren't allowed a conditional stop point? There's got to be a better reason than preventing infinite shuffle combos.

A classic example though of something that can't be shortcut because it's conditional is Wirefly Hive. You can't propose “Using this infinite mana & untap combo, I flip until I get a million Wireflies.” (Aside, if someone has Okaun, Eye of Chaos out, we also don't know how big Okaun will be at the end of that combo, though we do know that Flinging him will almost certainly kill someone.) You could, in theory, propose “I flip coins 100 times” but we have no idea how many wireflies you will wind up with at that point; it's indeterminate. You might have one, none, or a hundred from a hundred perfect flips.

But, also consider this: you have Future Sight out. You propose a shortcut where you shuffle until Card X is on top, which we'll both know because it's visible. I am sure (but don't know for certain) that a different card, Card Y, is in your deck and I want it gone. I respond to that shortcut by saying I'll wait until Card Y is on top, then mill that card and exile your graveyard. (Your combo only lets you shuffle at sorcery speed, so I'll be able to do that if it shows up.)

The thing with shortcuts is they are completely deterministic: we can always know exactly what state the game is in after every single step, and always know exactly when we might want to respond to the shortcut. But in this scenario, at the end of the shortcut, is Card Y milled and your graveyard exiled, or not? We don't know. Card X could be the very next card shuffled on top or it may never show up for ten thousand shuffles. Maybe we'll roll a dice to see which one's more likely to happen sooner, but that requires calculating probability: I don't know your deck composition and you aren't obliged to reveal how many of Card X or Card Y exist in there to me, and even with that knowledge I also have to know some college-grade probability mathematics in order to come to an accurate answer about how likely it is Card Y will show up on top before Card X. Magic: the Gathering doesn't require beyond elementary school knowledge and shouldn't require completing a college-level mathematics course to play accurately.

So... this whole scenario's a mess. It's easier just to prevent it from ever happening by saying shortcuts must be deterministic.

Related reading is these two articles talking about the Four Horseman combo which relies on random outcomes: Deck Tech: Four Horseman with Jeff Liu, and also Horsemyths - Policy Perspectives on MagicJudge which talks about how the combo can wind up not advancing the game state meaningfully resulting in a tournament play warning.

Sid the Chicken wrote:
Carthain wrote:
Also, Magic (outside of Un- rules) doesn't recognize "infinite" ... so if something would be infinite, then you get to just pick whatever number you like. So while the odds of you getting the deck order of your preference may come to pass if you can do it an infinite # of times, Magic rules reject the concept of infinite, therefore that logic just doesn't work out.

Except it really does. If you choose a high enough value of X, it is functionally the same as infinity. The rules let you pick ANY WHOLE NUMBER, so 10^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100 is a valid choice. We're talking number larger than the estimated number of atoms in the universe type numbers. In this case, the "rare event" you're looking for is essentially guaranteed to happen. I assume magic doesn't do infinity because it's not a defined value, which makes it hard to define the numeric values of things.

That isn't infinite, just an enormous number of times, like Viperion is pointing out. You can absolutely pick arbitrarily high numbers.

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Last edited by spacemonaut on 2019-Jan-17 4:59 am, edited 5 times in total.

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-17 1:41 am 
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Sid the Chicken wrote:
Any combo that deals 1 damage at a time cannot win a 4-man table without help, for example, if you set a limit at 100. I feel like it would be better to simply ban infinite combos if you're doing house rules, rather than allow them but not really.
Fair. That's your opinion vs my hypothetical one. :)

Sid the Chicken wrote:
Except it really does. If you choose a high enough value of X, it is functionally the same as infinity. The rules let you pick ANY WHOLE NUMBER, so 10^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100 is a valid choice. We're talking number larger than the estimated number of atoms in the universe type numbers. In this case, the "rare event" you're looking for is essentially guaranteed to happen. I assume magic doesn't do infinity because it's not a defined value, which makes it hard to define the numeric values of things.

I notice you say "essentially" guaranteed, not actually guaranteed. Which means you admit that there is a chance that will not work out. I have a 50% chance of flipping Heads on a coin, but after 20 flips I am "essentially guaranteed" to have flipped a heads ... but not actually guaranteed. All 20 flips could be tails.

Also, what Viperion said about picking a number and the rules saying you do it that many times, not up to.


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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-17 9:43 am 
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Carthain wrote:
I notice you say "essentially" guaranteed, not actually guaranteed. Which means you admit that there is a chance that will not work out. I have a 50% chance of flipping Heads on a coin, but after 20 flips I am "essentially guaranteed" to have flipped a heads ... but not actually guaranteed. All 20 flips could be tails.

20 flips is not essentially guaranteed. A number of loops so great that the chance of failure is a million times less than the chances of winning Powerball IS essentially guaranteed. Frankly, the only reason I say "essentially" is to acknowledge the 0.000000000000000000000000000000000000000000000000000000000000000000000000000000001% chance of failure so it cannot be nitpicked that I didn't.

Carthain wrote:
Also, what Viperion said about picking a number and the rules saying you do it that many times, not up to.

I am quite aware of how the rules are worded and what they mean. I merely find it unsporting to strictly enforce the "no conditional end point" clause, as I have yet to see a realistic explanation as to why it is necessary, and thus it seems like more of a "gotcha" for people that want to rain on others' parades. The closest I've seen thus far for an explanation boils down to "math can be complicated", which is a pretty frustrating reason IMO.

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-17 9:48 am 
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spacemonaut wrote:
That isn't infinite, just an enormous number of times, like Viperion is pointing out. You can absolutely pick arbitrarily high numbers.

Again, I GET THIS. But pointing out that an arbitrarily high number technically isn't infinity is true but also IRRELEVANT. Because they are functionally the same thing.

Here's another case (one I'm pretty sure is a legal play as well) to highlight why understanding how math works saves time; I control Chance Encounter and Frenetic Efreet. During my last opponent's end step I activate the Efreet's ability an astronomic number of times. Assuming no enchantment hate, does anyone really want to argue that I don't win on my upkeep? Does anyone really want to watch me flip coins until the inevitable happens?

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-17 10:23 am 
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Sid the Chicken wrote:
Here's another case (one I'm pretty sure is a legal play as well) to highlight why understanding how math works saves time; I control Chance Encounter and Frenetic Efreet. During my last opponent's end step I activate the Efreet's ability an astronomic number of times. Assuming no enchantment hate, does anyone really want to argue that I don't win on my upkeep? Does anyone really want to watch me flip coins until the inevitable happens?

I'd probably concede the win there.

I still wouldn't concede that we get to use the shortcut rules to shuffle our deck to an arbitrary state. We don't have to, and our opponent can find another infinite combo way to win that doesn't expect us to let them violate game rules. If deck stacking is the issue we can just use infinite scry 2+, that already canonically lets you stack your deck however you wish; in a tournament setting you're not even expected to understand why it works.

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-17 10:41 am 
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Sid the Chicken wrote:
20 flips is not essentially guaranteed.
Remember, I'm talking about getting a single heads result. The 20 flips is around 99.99999% chance of that happening. And it demonstrates my point sufficiently. You say you said "essentially" to avoid someone nitpicking that really low percentage that it might not happen -- but aren't you now just using that to nitpick that my example isn't a valid simplification? If you could do the 20 coin flips within a minute (about 3 seconds per flip); Then you'd be flipping coins for... approximately over 300 years in order to "essentially" guarantee that you'd get a set of flips within 1 minute that contains no results of 'heads'.

I'd say that fits your example -- we're both talking about doing something a stupid amount of times in order for the odds to to say that if you could go through every possible combination and with the outcome we want at the end -- we'd be there for an exceedingly long time. The actual length of time doesn't really matter.

So to dismiss my example simply because yours has more decimal points seems like you are arguing without actually looking at what others are saying.

Sid the Chicken wrote:
I am quite aware of how the rules are worded and what they mean. I merely find it unsporting to strictly enforce the "no conditional end point" clause, as I have yet to see a realistic explanation as to why it is necessary, and thus it seems like more of a "gotcha" for people that want to rain on others' parades.

Careful -- "unsporting" is a very loaded and subjective term. Some people may consider your switching to large math, and saying things like "essentially guaranteed" to be unsporting. Some people may say that if you can't actually demonstrate it happening, then shortcutting it is unsporting.

... Some people call Counterspell "unsporting."

So what is unsporting to one person can be perfectly fine for another. So to simply say that sticking to the rules as written is unsporting seems.... very counter-productive in the end.


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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-18 3:02 am 
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Maybe I'm not as well versed in probability as I think I am, but I'm still missing how the example in OP's description can happen without a quadruple Future Sight effect or something of that nature. Yes, if you shuffle the deck an infinite amount of times you'll eventually get a shuffle that has cards A, B, and C on the top. However, in order for the player to be able to pull that off, they would have to have some way of knowing which specific shuffle did it.

I also seem to remember that at least once in the past it's been ruled that performing an action multiple times in a way that has no clear and tangible effect on the game is indistinguishable from performing it once. For example, forcing your opponent to shuffle their library several times in a row with no change to the library, known information, or board state is treated as doing it once, as shuffling is a randomizing effect.

Sid's Chance Encounter scenario isn't comparable for a couple reasons. The first is that unlike the infinite shuffling mechanic, the result of the infinite coin toss is not dependent on the last one. You are theoretically guaranteed to sculpt the deck exactly the way you want it to be if you shuffle infinitely, but it's completely irrelevant unless you have some way to ensure that the final shuffle has that result. Compare it to the infinite coin toss, where it doesn't matter which individual results end up as heads, only that 10+ of them do. And again unlike infinite shuffling, each individual action of flipping the coin does have a potential impact on the board state, that impact being adding another chance counter.


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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-18 6:23 am 

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Sid the Chicken wrote:
I am quite aware of how the rules are worded and what they mean. I merely find it unsporting to strictly enforce the "no conditional end point" clause, as I have yet to see a realistic explanation as to why it is necessary, and thus it seems like more of a "gotcha" for people that want to rain on others' parades. The closest I've seen thus far for an explanation boils down to "math can be complicated", which is a pretty frustrating reason IMO.

Because you cannot say what the game state is at any point for sure. Because while you are explaining that *someday* you will win with Gitrog Horseman, i am not required to tell you i have Faerie Macabre and Extirpate in my hand. I can say "Okay, proceed with your combo".

And no one has to wait 45 minutes for you to shuffle through it, regardless of opinions.

Another problem is if i do have the grave hate, and the Horsemen player says "shortcut until i get i combo pieces and win" (or that effect), they need to perform the actions until my grave hate is relevant. We do not and can not shortcut to "find those cards i want to exile and put them in your yard".

At least with Efreet and coin flipping it's an action that doesn't require cards. You either have enchant hate in hand or you do not, but with something much more tedious like Gitrog (and especially with something like Macabre that nabs 2 cards) i can't really say when in the actions i will respond.


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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-19 11:45 am 
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Sovarius wrote:
Because you cannot say what the game state is at any point for sure. Because while you are explaining that *someday* you will win with Gitrog Horseman, i am not required to tell you i have Faerie Macabre and Extirpate in my hand. I can say "Okay, proceed with your combo".

Yes you can, and you can proceed to screw me over as soon as the intended state is reached... I'm not seeing the issue there.

Sovarius wrote:
At least with Efreet and coin flipping it's an action that doesn't require cards.

It is, however, just as indeterminate as infinite shuffle. It is just as likely that I will not win due to the infinite flips as it is that I will not achieve the desired state post-shuffle - that is to say, extremely unlikely. So really, what is the difference? If I have the demonstrated ability to perform the same action as many times as I desire, and there's no outside influence restricting that, then I still don't see what the issue is. If you, say, have a Psychogenic Probe in play, then there's a clear reason I can't just shortcut it, because in all likelihood I'd be dead long before achieving the goal.

Sovarius wrote:
Another problem is if i do have the grave hate, and the Horsemen player says "shortcut until i get i combo pieces and win" (or that effect), they need to perform the actions until my grave hate is relevant. We do not and can not shortcut to "find those cards i want to exile and put them in your yard".

Sure, but do remember that when a player proposes a shortcut, another player may modify that shortcut - for instance the classic case of shortcutting phases - I say "Go" or "Pass turn", and you say "on end step, I do X", thus modifying my proposed shortcut of passing priority until it's your turn with passing priority until my end step, when you do your thing. There is no reason you shouldn't be allowed to modify "I shuffle until X state" in a similar fashion.

Uktabi_Kong wrote:
Yes, if you shuffle the deck an infinite amount of times you'll eventually get a shuffle that has cards A, B, and C on the top. However, in order for the player to be able to pull that off, they would have to have some way of knowing which specific shuffle did it.

I wouldn't dispute that, nor would I permit someone to shortcut it if they didn't have the ability to know.

Carthain wrote:
Remember, I'm talking about getting a single heads result. The 20 flips is around 99.99999% chance of that happening. And it demonstrates my point sufficiently. You say you said "essentially" to avoid someone nitpicking that really low percentage that it might not happen -- but aren't you now just using that to nitpick that my example isn't a valid simplification? If you could do the 20 coin flips within a minute (about 3 seconds per flip); Then you'd be flipping coins for... approximately over 300 years in order to "essentially" guarantee that you'd get a set of flips within 1 minute that contains no results of 'heads'.

I'd say that fits your example -- we're both talking about doing something a stupid amount of times in order for the odds to to say that if you could go through every possible combination and with the outcome we want at the end -- we'd be there for an exceedingly long time. The actual length of time doesn't really matter.

So to dismiss my example simply because yours has more decimal points seems like you are arguing without actually looking at what others are saying.

Point conceded about 20 flips - I didn't take the time to realize that it was already that high a percentage. However, I don't think you're really looking at what I'm saying either when you take the time to make that "AHA, but there IS a chance that heads doesn't come up!" argument. Plus I still have people saying "THE RULES TELL US THIS" as if I haven't already acknowledged that.

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-19 9:12 pm 
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Sid the Chicken wrote:
There is no reason you shouldn't be allowed to modify "I shuffle until X state" in a similar fashion. [...] Plus I still have people saying "THE RULES TELL US THIS" as if I haven't already acknowledged that.

I did provide a couple of examples here of ways nondeterministic or conditional shortcuts break down.

Basically though: I expect my fellow players to play by the rules of the game. If someone is capable of going infinite they can do so within what the rules let them do. The fact is "shuffle infinitely until my deck is in a certain state" is not an action available within the game rules. If they wanted to stack any part of their deck they picked the wrong thing to do infinitely: infinite scry 2+ would do that. Shuffling infinitely is functionally not much different from shuffling once; handy sometimes but won't win the game. I'm not inclined to waive the rules and say this thing that can't win goes straight to this nigh game-winning state, and I'm under no obligation to do so, not even socially.

If you're willing to let the player shuffle to a certain stacked deck state, sure, go for it, that's your game.

If someone could attack infinitely with a 0/1, would you accept them saying "but let's pretend this does damage and I win"?
If someone could draw infinitely, would you accept them saying "but let's pretend I have Laboratory Maniac and I win"?
Probably for the same reason I wouldn't accept someone saying "but let's pretend the shortcut rules let me do things I can't so I reach a state where I'll win".

Uktabi_Kong wrote:
I also seem to remember that at least once in the past it's been ruled that performing an action multiple times in a way that has no clear and tangible effect on the game is indistinguishable from performing it once. For example, forcing your opponent to shuffle their library several times in a row with no change to the library, known information, or board state is treated as doing it once, as shuffling is a randomizing effect.

They mention that in Horsemyths, a judge article on the Four Horsemen deck. A player is meant to perform actions that meaningfully advance game state and gets a slow play warning if they're not doing that.

The Four Horseman pilot self-mills with an infinite combo for certain cards, but might hit ROE Emrakul, in which case they have to shuffle their deck back into their library. It the pilot hits ROE Emrakul again a second time in the turn then they've gone back to an identical game state they had earlier this turn: now they have performed a ton of actions that did not meaningfully advance game state and get a slow play warning. (The article clarifies this warning is only issued once this happens, if it happens, because if it does not happen there is no problem.)

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 Post subject: Re: Theoretical Probability as Win Condition
AgePosted: 2019-Jan-20 9:51 am 
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spacemonaut wrote:
I did provide a couple of examples here of ways nondeterministic or conditional shortcuts break down.

You've provided a few instances where you can throw something else into the mix to make it impractical. That's fair - I can't see shortcutting two opposing indeterminite loops. And I suppose it is easier from a rules perspective to just say no to all cases rather than try to determine which ones could function smoothly and which could not.

spacemonaut wrote:
If they wanted to stack any part of their deck they picked the wrong thing to do infinitely: infinite scry 2+ would do that.

Except it's impossible to know the exact number of scry instances necessary, so by your appeal to strict rules enforcement, that doesn't work either.

Which kind of gets to the heart of what I'm trying to say - there's rules, and then there's common sense and being reasonable. It's reasonable to say "OK, you'd get there eventually" and just go with it, because we can see logically how it would happen, even if it would take forever to play out step-by-step, unlike your 0/1 creature and invisible Labman examples.

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