| If I'm understanding you correctly, you're saying that the rules of Stratego let you apply an abstraction rule which drastically simplifies the game. I agree you can do this. I think this point is remarkably similar to the technique of blueprint abstraction. Of course, we ought to be focused on the situations which lead to these nice situations - which leads us back to the imperfect information situations which lead to those positions we can reason about. Interestingly, you can invert your point and get a similar rule more generally. The trick is to backward induction on the abstracted category transitions. So your point is actually so valid that is valid even in situations where your examples don't apply. I hope you can see I'm strong manning here. I agree with you that this should be done and is critical to making things tractable. There is an issue though, at least in the generalized case, which is that perfect information is much easier than imperfect information. See, in perfect information games when you do the backward induction step you actually just flat out solve the game. Meanwhile, in imperfect information games, this backward induction step merely makes solving the game more tractable. Chess endgames are the backward induction version of your forward induction from the rules abstraction, but the abstraction rule is so hard to determine we wouldn't usually think of it that way. Notice that chess is hard enough that we don't have endgame tables that go all the way back to the start of the game? Yet the average game length in Stratego is hundreds of moves longer and there are more then double the number of pieces. I still think your point is right and someone who pushes hard enough in this direction would manage to tackle the complexity. So I basically agree with you. But if you take standard approaches like counterfactual regret minimization and throw it at the game without adjusting them for the fact that the problem is "hard" then they just wont terminate. |
Without perfect information, the number of states is still mostly a red herring, because the differences between the states are immaterial. The moves aren't super important. If you decide to move frontline unit A against the frontline unit on the opposite side of the field, there may be several moves between that but you've only made one noteworthy decision. Could be bad intuition. I think a more abstract model here would do better and be far simpler with some minor tactical move prioritization or whatever.