I would really love to see a serious research effort take a crack at contract bridge. Bridge, like Stratego, is an imperfect information game with a big hidden information space. Bridge also adds another wrinkle of explainability which is, I think, very interesting.

Bridge is played as a pair vs pair game, with North/South and East/West being the two pairs and seated around the table in these compass directions. A bridge hand consists of two phases: there is first an auction phase, where players go around the table bidding on contracts (agreeing to take a certain number of tricks with a certain trump suit) until a final contract is decided. Then there is the cardplay phase, where the player who won the auction is the declarer, their partner is the dummy, and the other pair are defenders. The dummy's hand is placed face up on the the table and the declarer controls which cards are played from dummy, so the cardplay phase is effectively played by only three players now, with each of the three knowing one common hand (dummy) and one private hand (their own) and not knowing the other two hands.

In both the auction and (for the defense) the cardplay phases, it is important for players to exchange some information about their hand to their partner. However, any information you exchange about your own hands also helps your opponents. You might naturally conclude that you want to come up with some secret scheme to exchange information which your opponents don't know (and it is even possible to exchange encrypted information which your opponents can't know--if the defense is known to hold a certain card, but declarer doesn't know in which hand it is, the defense could say that a signal means one thing if the card is in one defender's hand, but means a different thing if it's in the other defender's hand).

But it turns out that this ends up being very uninteresting to play, so instead, when playing bridge, there is an important rule: all of your partnership agreements must be public. If a certain bid that I make promises that I have at least 5 spades in my hand, it is the opponents' right to know that this is our agreement. You must be able to explain the information which your action provides, and you must be able to use the information that the opponents give you themselves.

This poses several problems for self-play reinforcement learning. First, a naive self-play approach will produce agreements that cannot be explained to a human. What really needs to happen is that your partner, when determining what hands you might have as part of search, must not do so simply by sampling its own system (ie by asking what it itself would have done with hand X or hand Y). The information and possibilities really need to be mediated by some kind of intermediate, rules-based description, which can be provided to the opponents as well.

You also need to be able to encode and ingest the opponents' agreements, and to use this information to inform your own decisions. And you need, in particular, to be able to handle a wide variety of agreements from your opponents; it's not enough to force them to play the same system as you.

You must also account for deceit. If, for example, I have a bid which promises that I have at least 2 cards in every suit, it's perfectly legal for me to lie and make this bid when I only have 1 card in some suit--as long as my partner is in the dark about this just as much as the opponents. So if you make this bid, and your machine opponents assume there is a 0% probability of you having lied about your hand, it is possible that they will make gross errors by not accounting for this possibility (for example, they may be in a position where all of their actions are equivalent if you told the truth, but where one action is clearly better if you didn't--a human player will naturally take this action, but a robot may just select an action randomly).

It's an interesting game and a very interesting AI challenge.