I find it fascinating how Chess is, in a way, stateless. Other than whether some rules like castling are still valid, you don’t need to have played the previous moves to be able to play the next moves effectively. This got me thinking: is that common in games? If I take someone’s place at a Risk board, can I play well? But in both cases, there is perhaps still some state… At least if you’re playing a human. You might…
> take someone’s place at a risk board
Not the case because Risk has unshared knowledge (the contents of your cards) and taking someone’s place makes it so the game doesn’t have perfect recall. You need shared knowledge and perfect recall, or complete knowledge (in which case recall doesn’t really matter) for a game to have a sub game perfect equilibirium - in simplified terms, for there to be an optimal strategy that applies equally well regardless of the game’s prior events.
That might be hard to reason about with Risk, but consider how information “leaks” by when players choose to use their cards or not and when they received the cards. Having a card for a long time but not using it suggests something else than having just received the card, which is why perfect recall is important. For a game to be “stateless” (ie have a one shot sub game perfect equilibrium), when cards were received would also have to not be important, but it is in Risk.