Thread

With most information hidden, the game Stratego had stumped AI until now

288 points · 149 comments · PaulHoule

hnedeotes · 1790969271 · focus · HN ↗
I think that what makes these games beatable repeatedly is that they're static. Not saying an algorithm properly trained won't play better than the average player a game like MtG, or my own <a href="https://aethersummon.com" rel="nofollow">https://aethersummon.com (specially now while it has under 90 possible scrolls only) but if you have a regular release cadence (say weekly or bi-weekly) of relevant new "cards", then I think the playing field is much more even for humans.
Those new additions can invalidate the whole training data by a single new "card" that changes completely the dynamics and would be easy for a player to understand and incorporate but not for an algorithm (perhaps with enough compute to re-train it regularly it could) - that along with the decision trees being orders of magnitude deeper, wider and with more conditionalities than go, chess or stratego - even through the same turn with the same cards available and same table state - would probably pose much harder problems for a compute bound algo.
1. qsort · 1790970847 · focus · HN ↗
  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.
  1. hnedeotes · 1790972193 · focus · HN ↗
    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.
    dragontamer · 1790974010 · focus · HN ↗
    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.
    ---------
    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.
    ---------
    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...
    hnedeotes · 1790976015 · focus · HN ↗
    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.
    dragontamer · 1790982235 · focus · HN ↗
    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.
    --------
    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?)
    syradar · 1791014430 · focus · HN ↗
    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.
    hnedeotes · 1791028474 · focus · HN ↗
    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.

Open on Hacker News to reply ↗

Unofficial Hacker News client; not affiliated with Y Combinator.