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> Those new additions can invalidate the whole training data by a single new "card" that changes completely the dynamics

This doesn't follow. You're basically proposing that new combo decks be added all the time, and it's far simpler for an agent to scan the new cards for potential interactions with the thousands of other cards in circulation than for a human to remember all of them.

Your analogy is akin to saying that all you have to do is keep landing new code all the time, and since the agents weren't trained on the code they won't be able to identify and respond to security vulnerabilities in it as fast as humans, which hasn't turned out to be correct

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No, well, in MtG you could interpret it as meaning such but what I mean is that if in the training set sequence A-B-B-A when state is C-A-X-Y is the play 80% of the time, then you have a new card (that doesn't need to be combo) that by sheer mechanics thwarts that then that strategy won't stick by the addition of that single card to the opposing deck (that you can't know if your opponent is playing or not) and having one or 2 or 3 or 10 different cards renders every calculation very problematic as a play can be the best or the worst depending on such simple things diluting further the best play as the pool grows. Then you need to take into account in MtG shuffling and drawing. I think it's fair to say it's much more difficult to model... And while an agent can learn new combos, you just need to read the card once, the agent needs to be retrained.
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Doesn't this entirely depend on the latent embeddings of strategies and game space in the AI model, which may not be so concrete and explicit as you've described? That's kind of the magic of LLMs with coding, they can generalize because the abstract patterns are encoded in latent space, not the specifics.
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I might be wrong but what I was thinking was that in chess (or even imperfect information games with a much smaller "range" such as Stratego,) a model can calculate all possibilities for all moves and following moves, by itself and opponent up to a depth that the human cannot. So it can see everything that can happen if it does move X-Y, then Y-Z, then A-C and figure out one that is unbeatable no matter what (or at worse leads to a draw).

But on MtG in particular that never really applies in full due to drawing new cards. You can play perfectly and still lose due to sheer randomness of draws.

The latent space I'm not sure how it translates to a game playing bot, but I would imagine that it would open it up to fail in the same ways a human fails.

On the game I'm designing it could do that (calculate all possibilities up to X depth, for all possible scrolls and table states) but it would be extremely expensive to do so (not a very good argument if compute power keeps increasing), but more than that, in contrast to something like chess, there can be many more paths and decision points where a bad decision turns into a loss, so if it assumes that the best play is X at some point, a sequence that it discarded due to not being the most probable can exist and the bot can never be sure, so if it makes a decision that plays into a "trap" he can't undo to a favourable position. While in Chess it's much clearer what is possible from a given state, it's unambiguous and the rules are fairly limited.

In stratego you have a 10x10 board game, a very clear objective and at most 40 pieces (with repeated pieces and simple mechanics amongst them), while in MtG and similar games a single piece (card) can have probably hundreds of different interactions depending on everything else going (and everything else hidden), at many points of decision. In stratego it also seems that for humans at least, most moves are "inconsequential", as it probably plays more at the psychological/bluff level. Maybe a human player that was given the same budget for training could spend a month training against bots might fare better as the strategies might be then better understood (by the article it's mentioned that the agent recovered from bad positions, so it seems that it was mostly human error, as the human was playing better up to that point).

While on MtG or Asummon, although there can be inconsequential moves (they don't matter given the context/stage of the game), every move carries with it a possibility of being consequential in unpredictable ways. Anyway, there should be ways of training models with just a rule abiding client for these games, without codifying all rules, that they can just keep playing to figure out the interactions, so if that theory is true then it should be possible to create an unbeatable bot - I'm just not sure it is without infinite time/compute and less so if the "meta" keeps changing rendering possible training inconsequential regularly.

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You can definitely try to regularize against ruleset changes by generating a bunch of cards and making the agent play in randomized subsets of those cards.

I didn't look for prior work on this, but my estimate is that it's probably within 2-3 orders of magnitude of additional training compared to a static game. (Still a lot!)

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But wouldn't (couldn't) the model then hallucinate play patterns and get itself into problems when playing against a real opponent?
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Well, if your training includes regularization against ruleset changes, the model should simply handle it. (that would be the expensive option, and require vastly more training)

When the Dota 2 bot was made, they retrained the bot only partially when new patches came in, so it was definitely cheaper to adapt.

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There are very few missing pieces for a game like MTG. The main reasons we don't have a Stockfish for MTG is that it's a PITA to implement the rules and that nobody cares (or at least not enough to make it happen.)

There is nothing that, in principle, makes MTG different from poker or bridge, and we have superhuman engines for both.

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>There is nothing that, in principle, makes MTG different from poker or bridge, and we have superhuman engines for both.

We don't have superhuman play for bridge.

Poker and bridge are quite different from each other in terms of solving them. Among other things, the hidden information space in poker (at least, in hold'em) is far smaller than in bridge (or Stratego, for that matter, as discussed in the linked paper). This makes hold'em solvable using CFR, an algorithm which essentially optimizes play by considering all the possible holdings than the opponent might have and their best strategy with each one. Even going from two to four hidden cards per player (Omaha) requires a slightly different approach although you can still use CFR as the basis for the search algorithm.

Bridge has 13 hidden cards per player which makes CFR basically impossible to apply, at least in any obvious way--just way too many states. Similarly you see it's not used at all in this Stratego paper.

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> There is nothing that, in principle, makes MTG different from poker or bridge

There is - metagame. There is no universal optimal strategy in a trading card game, because what is optimal depends on what decks and strategies other people are playing.

I'm sure you could train a neural network to play a specific deck within a specific metagame of a specific card game, but you would probably have to keep re-training it when there are new decks/combos/releases/rotations/banlists/metagame shifts.

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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.

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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...

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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.

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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?)

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> There is nothing that, in principle, makes MTG different from poker or bridge

Only in the most general form they are games with cards and hidden information with a state space that some form of tree search can theoretically play out.

The difference is the size of the search space. In MTG the search space is unimaginably huge. It would make Go's search space look like a spec of hydrogen in the middle of the universe.

It would require completely different techniques to produce a computer good at MtG than one that is good at bridge.

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Hearthstone is absolutely swarming with bots that beat humans regularly.
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Which humans? Many people are simply not that good at Hearthstone. Are the bots regularly achieving high legend ranks?
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