Comment by hnedeotes | Hacker News Reader

Comment by hnedeotes | Hacker News Reader

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MTG is also severely constrained (small hand, mana -> possible moves) although I don't think it's anywhere near the same. In my opinion the rules are effectively what change the whole dynamics. You can't plan as efficiently without knowing what your opponent holds and having to take into account all possibilities (with infinite energy/compute time perhaps)... I don't doubt you can train a model to play well, I just think it should be much more level to the human player. In MtG you also have the randomness which is not easy to model nor account for - the perfect play by an LLM can be the worse once the opponet draws next.

In my own game you don't have shuffle/draw randomness but the pool of options is statistically tending to infinite (if I would have 500 or 1000 scrolls designed and MtG depending on the format has that depth) when compared to something like chess, or this game. On the other hand in my own game you have to account for much more depth on the possible options your opponent has.

There's only so many card interactions that strong players actually think about.

Ex: you don't really care if the opponent plays Giant Growth or Chastise. The effect is that the opponent is playing a combat trick, and combat has moved from attackers favor into defenders favor.

To defeat an instant speed combat trick requires a combat trick of your own, or a generic counter spell of some kind. Some have interactions (ex: Doom Blade beats Giant Growth but not Chastise), but the overall gist is that opponents can do things after combat is declared. You only need to keep track of how many combat tricks you think the opponent has.

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Other situations are card advantage (ex: 2 for 1. If the opponent spends 1 cards to defeat only 2 cards of yours). The traditional card for this is Mindrot, but well placed counterspell can turn a combat trick into. 2-for-1 reversal.

You don't necessarily keep track of how your opponent makes 2-for-1 opportunities. You just have vague gists of them.

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Good spells have huge applicability. Doom blade or Murder is high because killing opponent creatures at instant speed handles the vast majority of creature buffed combat tricks, and also serves as a way to stop enemy combos and other such tricks.

In contrast, chastise is very niche. If the opponent were playing like Swords to Plowshares (powerful white instant speed removal), it's pretty much always better than chastise.

If the opponent plays chastise instead, you take that as a win because you know they could have had a deck of better cards. But for whatever reason decided to play with weaker cards...

I agree in a way, but at the same time, and I think it's a bit more applicable to MtG due to the limit of cards you can have as possible plays at any given time (outside of combos), and I believe too that you can train a bot to be good, better than average - I doubt arena doesn't have bots - but I still think that without unbound compute/time it's a game where human players have much better odds to outsmart an AI if they're good players. MtG has for the past 10 or more years been re-hashing the same play patterns, while introducing some new mechanics on most cycles, but pretty much you have staples throughout most editions that are just variations on that - card advantage, denial, combat tricks, removal, curve and then the rarity enabled bombs/combos

But even then (not saying I'm right) I think the depth of choices, effects and so on, on a format like modern, or legacy, would be very difficult for an AI to top against pros. If you add draft into the mix it gets worse for the AI in my view too.

Because a good play in most situations can easily be a bad play under others. That doesn't happen in chess for instance, given enough decision depth to the algos to see the future game. In my own game I think those situations can occur much easier due to you always having your full deck available. Also, in MtG it's easy to get into table states that are either ahead/behind and then you kinda just have to protect your position (like with denial decks). Then you have the effects that you might remove a creature threat (graveyard) but then that enabling a combo you weren't expecting that needs a creature on the grave, or enabling delve cards or whatever have you. It's much less clear cut for a probabilistic model to make the optimal play at every single interaction. So the more you train the model on all the variations and possible follow ups, the more you dilute its certainty isn't it? In chess, or this game, or RTS such as starcraft, that doesn't really happen in my view.

I'm also a Poker player and the way Poker AIs solved this problem was by making the best estimate of the Nash Equalibrium and playing around it.

No human can possibly keep up with all the possibilities or combinations that are accounted for.

Games of incomplete information have been IMO soft-solved as of.... Maybe 5 years ago? As in, stronger than any human can possibly reach (ie: massive GB-sized matricies accounting for all information iterated over millions of iterations of "he thinks that I think that he thinks that I think that....")

It's not a true Nash Equalibrium, which remains outside of the realm of even computers to compute. But a computer can always reach a closer / better estimate of any Nash Equalibrium, which covers all games of incomplete information.

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For Poker, it turns out that a few types of bet sizes (3x pot, 1.5x pot, pot, half pot, quarter pot) covered enough betting patterns to reach superhuman.

And frankly, MtG is simpler than the bluffing game in Poker. Like MtG has bluffs but it's no where close to Pokers level.

There's no crazy deep game for Red Deck Wins vs Control. The game basically plays itself out (Red tries to win before Control comes online. Control tries to stall before Red Deck Wins). There are some games with complex board states but they're largely a game of bluffing + card counting (opponent holds 4 cards, two of which were since the start of game and 2 were top decked in the last two turns. He at best has only planned for 2 responses or got lucky with the other two newest cards. Do I have a play that beats two cards yet?)

The card counting is harder since we can hide which cards were top decked or held since the start by just rearranging/shuffling our hand. We could have 0-4 counters or setups waiting for the gating decision.

The possible game state is also much larger than poker. Deck construction alone is 60 cards out of about 30,000 unique cards. Sure, not all cards are viable in all decks, but we can have 1-4 copies of a card in our deck.

So we might not even know if we’re playing against mono-red or multicolored since the decklist is unknown. You can think you’re playing mono-red and then they suddenly play a Plains. Poker at least always has the same 52 cards to reason about.

I do think AI could be great at coming up with decklists though.

Yeah I am of the same opinion. And of those unique cards (although formats will limit the total number) they all can play differently in different contexts/states of the game - even a "bear" (2/2 vanilla), can be just a bear, or part of a strategy (if other cards pump those specific cards being played, or enhance them), while poker they're always evaluated in aggregate from 52 cards that are split between players, so you can always remove the ones you're holding, the ones on the table. So 48 cards to calculate possibilities after initial deal + whatever is on the table. The fact that they're shared also means you can exclude immediately what is revealed and what you hold on your hand from those calculations.

Hm, I don't really agree. I think that bluffing feels more important in poker because of the usual monetary value attached, and is more of a strategic hindrance when playing against bots, while it's very important between humans because (usually) of the money involved - even in this article there's a mentioning that the bots don't care about bluffing and that for humans that is part of the normal gameplay and mastery.

There's also the decision points, in poker it's way less. You're dealt cards, the table reveals cards, you bet/ante, move to the next, bet/ante. It's a very finite sequence of moves until disclosure. Plus it's 52 cards divided by the table players while on MtG it's 60 per players that you can't know (even lands can interact beyond being a resource and in competitive lists usually they do, specially in older formats) - although with enough/infinite time/memory you can probably generate a table for all possibilities, you still have to contend with the interactions other than the card types. A 9 Diamond is a 9 diamond. A Skull Clamp is a Skull Clamp but the way it interacts, its value/threat is highly dependent on context that can/might be hidden.

While I think that MtG is indeed "poker" like underneath the keywords, it's many more levels and I think bluffing can be way more "complex" but simply isn't because even at the pro-tour level prize pools are insignificant when compared to serious poker tables. Some MtG players are known to also dabble/play poker regularly.

I also think that the structure of poker game-play is more prone to be exploited by a competent bot - if you have a "budget" and you assign a bot to a table where the antes are "in-line" with the "budget" it has, it can mathematically (within a very high degree of probability) always turn a profit - ultimately humans fail in part because they enter "bluff" kingdom against a bot as the bots can just rely on mathematical probabilities. Made up numbers but the idea being, you have $200 to play. Choose a table where this allows you to play X games at least, say antes of cents, it should be able to make money most of the time at some point.

Yes, but as the other reply mentioned, the thing is you don't know if it's red deck wins, or a RDW with a tweak for the metagame and building the "he thinks that I think that he thinks" tables would probably require for practical terms what could amount to infinite storage and any of these chains, if followed through, can land the bot in a losing position hard to come back from. Now, to be honest, most MtG players aren't that good either, they play it more like a hobby/fun game, rather than approach it as poker/probabilities.

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