David J Prokopetz

Okay so this is taken from the Three Card Blind discord server from an acquaintance of mine, Quag.

It’s Alice’s turn and she controls Zimone and has a Fling, an Awaken the Woods, and a fragmentize in hand. She controls 2 Forests (green mana), a Plains (white mana), a mountain (red mana), as well as two lands that are here because they can be sacrificed.

Both Alice and Bob have infinite mana colorless mana made via an artifact that can untap itself for more mana.

Bob has 10 life and controls a Wasteland and two Forests. He has a Nourishing Shoal in hand. He also controls a Battle of Wits and has 250 cards in his library.

To win before Bob does next turn, Alice needs to create a large creature token with Zimone by casting Awaken the Woods, and at end step Fling the token. However, Bob with his infinite mana can cast an arbitrarily large Nourishing Shoal, gaining 10^100 life for example. Alice will try to Fragmentize the Monolith that Bob controls. In response he will generate the mana to cast the giant Shoal and he has to pick a number.

Then, Alice can cast Awaken the Woods to make her land count a prime number that is bigger than 10^100 so that at end of turn, she can Fling the Primo token at Bob’s face. However, once the trigger goes on the stack to make the token, Bob can Wasteland any of Alice’s non basic lands to make her total land count a composite number, making no token.

But, Alice has a trick! She can sacrifice one of her own Havenwood Battle grounds to make her number of lands 2 less in combination with a wasteland. This would allow her to still have a prime number if she chose the larger of a pair of twin primes as her target land count.

The question is this: Can Alice always make a number of lands bigger than any other number so that if Bob destroys one of her lands, she can sacrifice another, remaining at a prime number, and making the token to Fling for the win?

(So: are there infinite twin primes?)

The game state, courtesy of Quag also.

@pomrania replied:

In plain English:

The question is, then: is it guaranteed that Alice can always pick a prime number that's larger than Bob's number and is still prime after having two subtracted from it, no matter what number Bob picks?

Answering that question requires proving the twin prime conjecture, one of the great unsolved problems of mathematics.

Okay so this is taken from the Three Card Blind discord server from an acquaintance of mine, Quag.

It’s Alice’s turn and she controls Zimone and has a Fling, an Awaken the Woods, and a fragmentize in hand. She controls 2 Forests (green mana), a Plains (white mana), a mountain (red mana), as well as two lands that are here because they can be sacrificed.

Both Alice and Bob have infinite mana colorless mana made via an artifact that can untap itself for more mana.

Bob has 10 life and controls a Wasteland and two Forests. He has a Nourishing Shoal in hand. He also controls a Battle of Wits and has 250 cards in his library.

To win before Bob does next turn, Alice needs to create a large creature token with Zimone by casting Awaken the Woods, and at end step Fling the token. However, Bob with his infinite mana can cast an arbitrarily large Nourishing Shoal, gaining 10^100 life for example. Alice will try to Fragmentize the Monolith that Bob controls. In response he will generate the mana to cast the giant Shoal and he has to pick a number.

Then, Alice can cast Awaken the Woods to make her land count a prime number that is bigger than 10^100 so that at end of turn, she can Fling the Primo token at Bob’s face. However, once the trigger goes on the stack to make the token, Bob can Wasteland any of Alice’s non basic lands to make her total land count a composite number, making no token.

But, Alice has a trick! She can sacrifice one of her own Havenwood Battle grounds to make her number of lands 2 less in combination with a wasteland. This would allow her to still have a prime number if she chose the larger of a pair of twin primes as her target land count.

The question is this: Can Alice always make a number of lands bigger than any other number so that if Bob destroys one of her lands, she can sacrifice another, remaining at a prime number, and making the token to Fling for the win?

(So: are there infinite twin primes?)

The game state, courtesy of Quag also.

I know Exalted 3rd Edition is just using "uncountable" as a game-mechanical term of art because saying "infinite" would clash tonally, but I kind of love the idea that some baddies can punch you so hard that they inflict a non-countably infinite number of levels of damage. I'm not sure what inflicting non-countably infinite damage would look like in practice, but I'd like to see it.

...This implies that there theoretically bigger combos that might potentially be possible in MTG than going infinite.

Well, yes, non-countable infinities are by definition "bigger" than countable infinities (infinitely so, in fact!). However, I'm not aware of any Magic: the Gathering combo which inflicts a non-countably infinite amount of damage, and knowing what I do of the game's rules I'm pretty sure it can't happen. I'd love to be corrected, though!

I'm afraid that would be countably infinite damage.

Technically, this doesn't specify; it could be any infinity. However, the art and flavour text implies recursive infinity, which is necessarily countable.

(And as far as I'm aware, even the silver sets have never printed a creature with power or toughness outside the rational numbers, which would allow us to infer countable infinity. Even if they snuck in a root 2 or something, algebraic numbers are also countable - though maybe WotC has printed a pi/pi creature since I last played Magic.)

While the card itself doesn't specify, MTG's backend rulings come to the rescue.

Specifically, the statement says "Infinity Elemental has the greatest power among creatures on the battlefield (and off the battlefield for that matter), although it will tie with other Infinity Elementals."

By the axiom of countable choice, the supremum of the reals is ℵ0. Thus, Infinity Elemental is countable unless Magic prints a creature with power ℵ0.

Uncountably infinite damage? I've got you fam.

This is countably infinite tokens copies of Doubling Season; after this, all you need is a card that puts a single +1/+1 counter on an attacking creature, which will result in a creature with 2^ℵ0 power and toughness.

(Credit to Reddit user u/lucariomaster2 on r/BadMtgCombos)

The problem here is how to resolve the countably infinite number of Doubling Season activations and proceed to a board state that allows anything else to happen. By RAW, this wouldn't work, as order must be chosen for replacement effects that modify the same event. This would essentially just "crash the game", with the activating player processing Doubling Season forever.

But if you allowed players to "skip" ordering events where every possible ordering would result in the same outcome, then yeah, this checks out. (This is something that any sensible group would do - but violates Turing machine rules.)

I know Exalted 3rd Edition is just using "uncountable" as a game-mechanical term of art because saying "infinite" would clash tonally, but I kind of love the idea that some baddies can punch you so hard that they inflict a non-countably infinite number of levels of damage. I'm not sure what inflicting non-countably infinite damage would look like in practice, but I'd like to see it.

...This implies that there theoretically bigger combos that might potentially be possible in MTG than going infinite.

Well, yes, non-countable infinities are by definition "bigger" than countable infinities (infinitely so, in fact!). However, I'm not aware of any Magic: the Gathering combo which inflicts a non-countably infinite amount of damage, and knowing what I do of the game's rules I'm pretty sure it can't happen. I'd love to be corrected, though!

I'm afraid that would be countably infinite damage.

Technically, this doesn't specify; it could be any infinity. However, the art and flavour text implies recursive infinity, which is necessarily countable.

(And as far as I'm aware, even the silver sets have never printed a creature with power or toughness outside the rational numbers, which would allow us to infer countable infinity. Even if they snuck in a root 2 or something, algebraic numbers are also countable - though maybe WotC has printed a pi/pi creature since I last played Magic.)

While the card itself doesn't specify, MTG's backend rulings come to the rescue.

Specifically, the statement says "Infinity Elemental has the greatest power among creatures on the battlefield (and off the battlefield for that matter), although it will tie with other Infinity Elementals."

By the axiom of countable choice, the supremum of the reals is ℵ0. Thus, Infinity Elemental is countable unless Magic prints a creature with power ℵ0.

Uncountably infinite damage? I've got you fam.

This is countably infinite tokens copies of Doubling Season; after this, all you need is a card that puts a single +1/+1 counter on an attacking creature, which will result in a creature with 2^ℵ0 power and toughness.

(Credit to Reddit user u/lucariomaster2 on r/BadMtgCombos)

I know Exalted 3rd Edition is just using "uncountable" as a game-mechanical term of art because saying "infinite" would clash tonally, but I kind of love the idea that some baddies can punch you so hard that they inflict a non-countably infinite number of levels of damage. I'm not sure what inflicting non-countably infinite damage would look like in practice, but I'd like to see it.

...This implies that there theoretically bigger combos that might potentially be possible in MTG than going infinite.

Well, yes, non-countable infinities are by definition "bigger" than countable infinities (infinitely so, in fact!). However, I'm not aware of any Magic: the Gathering combo which inflicts a non-countably infinite amount of damage, and knowing what I do of the game's rules I'm pretty sure it can't happen. I'd love to be corrected, though!

I'm afraid that would be countably infinite damage.

Technically, this doesn't specify; it could be any infinity. However, the art and flavour text implies recursive infinity, which is necessarily countable.

(And as far as I'm aware, even the silver sets have never printed a creature with power or toughness outside the rational numbers, which would allow us to infer countable infinity. Even if they snuck in a root 2 or something, algebraic numbers are also countable - though maybe WotC has printed a pi/pi creature since I last played Magic.)

While the card itself doesn't specify, MTG's backend rulings come to the rescue.

Specifically, the statement says "Infinity Elemental has the greatest power among creatures on the battlefield (and off the battlefield for that matter), although it will tie with other Infinity Elementals."

By the axiom of countable choice, the supremum of the reals is ℵ0. Thus, Infinity Elemental is countable unless Magic prints a creature with power ℵ0.

I know Exalted 3rd Edition is just using "uncountable" as a game-mechanical term of art because saying "infinite" would clash tonally, but I kind of love the idea that some baddies can punch you so hard that they inflict a non-countably infinite number of levels of damage. I'm not sure what inflicting non-countably infinite damage would look like in practice, but I'd like to see it.

...This implies that there theoretically bigger combos that might potentially be possible in MTG than going infinite.

Well, yes, non-countable infinities are by definition "bigger" than countable infinities (infinitely so, in fact!). However, I'm not aware of any Magic: the Gathering combo which inflicts a non-countably infinite amount of damage, and knowing what I do of the game's rules I'm pretty sure it can't happen. I'd love to be corrected, though!

Most combos in MTG are infinite but require some form of human action (e.g. declaring an ability's activation), so they're only as infinite as the human playing the game is. Even if a combo were to be set up that indefinitely created new state changes without human input, it's impossible to go uncountable because of the stack - even simultaneous objects must be declared to enter the stack in some order, which establishes a bijection between the naturals and your MTG board state no matter how many iterations are completed.

I know Exalted 3rd Edition is just using "uncountable" as a game-mechanical term of art because saying "infinite" would clash tonally, but I kind of love the idea that some baddies can punch you so hard that they inflict a non-countably infinite number of levels of damage. I'm not sure what inflicting non-countably infinite damage would look like in practice, but I'd like to see it.

...This implies that there theoretically bigger combos that might potentially be possible in MTG than going infinite.

Well, yes, non-countable infinities are by definition "bigger" than countable infinities (infinitely so, in fact!). However, I'm not aware of any Magic: the Gathering combo which inflicts a non-countably infinite amount of damage, and knowing what I do of the game's rules I'm pretty sure it can't happen. I'd love to be corrected, though!

I'm afraid that would be countably infinite damage.

I know Exalted 3rd Edition is just using "uncountable" as a game-mechanical term of art because saying "infinite" would clash tonally, but I kind of love the idea that some baddies can punch you so hard that they inflict a non-countably infinite number of levels of damage. I'm not sure what inflicting non-countably infinite damage would look like in practice, but I'd like to see it.

...This implies that there theoretically bigger combos that might potentially be possible in MTG than going infinite.

Well, yes, non-countable infinities are by definition "bigger" than countable infinities (infinitely so, in fact!). However, I'm not aware of any Magic: the Gathering combo which inflicts a non-countably infinite amount of damage, and knowing what I do of the game's rules I'm pretty sure it can't happen. I'd love to be corrected, though!

stumbled across this card on scryfall and oh boy is it a doozy

so. the updated wording of the card (most importantly "gender" and "as you cast") makes this potentially the funniest card in the game rules-wise. no judge has weighed in on it (probably because its an old card out of print and not legal in any format) but it begs the question

what happens if someone comes out as trans in response?

i would love to know from a judge 1) if a players gender is hidden information (and, if so, what zone (if any) its in), 2) if coming out is a special action (similar to taking off your pants to dodge denimwalk) that doesnt use the stack, cannot be responded to (can you fucking imagine getting countered on that?), and can be done whenever the player has priority, and 3) if the reveal affects the "as you cast" clause

This barely scratches the surface of the rules implications:

stumbled across this card on scryfall and oh boy is it a doozy

so. the updated wording of the card (most importantly "gender" and "as you cast") makes this potentially the funniest card in the game rules-wise. no judge has weighed in on it (probably because its an old card out of print and not legal in any format) but it begs the question

what happens if someone comes out as trans in response?

i would love to know from a judge 1) if a players gender is hidden information (and, if so, what zone (if any) its in), 2) if coming out is a special action (similar to taking off your pants to dodge denimwalk) that doesnt use the stack, cannot be responded to (can you fucking imagine getting countered on that?), and can be done whenever the player has priority, and 3) if the reveal affects the "as you cast" clause

Shout-out to TCGs with such rigorous keywording that even the word "card" has a specific definition and each card is obliged to explicitly tell you whether or not the card you're holding in your hand is a card.

Shout-out to TCGs with such rigorous keywording that even the word "card" has a specific definition and each card is obliged to explicitly tell you whether or not the card you're holding in your hand is a card.