On Thu, May 20, 2010 at 7:57 AM, Isaac Deutsch <i...@gmx.ch> wrote: > [...] > > All clear up to here. :) I guess the "P(raise | two_aces)" bit could be > extracted from professional games, for example?
That would be a very good way to do it, yes. But this is part of how you create the quick mapping from game situations to probability distributions over actions, and I didn't get into how to do that. > Is it possible to update these probabilities incrementally? So, in the > example, you start with a uniform probability. Then, you see that > the opponent raises, and you update the probability for the hand "two aces" > to 0.04. Let's say he does another action that makes two aces more > (or less) likely, can we use P(two_aces) = 0.04 as a starting point? Does it > matter if the 2 actions correlate or not? You can simply take the P(two_aces) = 0.04 as your prior when you find the second action. This is part of the beauty of Bayes' theorem. > I see, this scaling method seems easier indeed. But, in tichu, everyone has > 14 cards at the beginning. So, it is impossible to do this for all possible > hands. How should this problem be tackled? It seems beneficial to simulate > the most likely hands first. Correct: This is not feasible in Tichu the way I described it. However, you don't have to compute those probabilities in advance. Instead, deal the cards first and then revisit the history of the game to figure out the correct weight for this hand. Alternatively, you could have a pool of hands whose probabilities you keep track of, and perhaps you generate new ones as they become impossible (because someone plays a card they wouldn't have, for example). The tricky part is making sure that you don't introduce biases doing this. I wouldn't try this at first. > > Notice that P(raise) = Sum_over_all_possible_hands ( P(raise | hand) ). > > Again, we cannot calculate all possible hands most of the time. Should we > say that all hands except the most likely ones should be neglected because > their weight would be minimal anyway? This is potentially a more serious obstacle, I am not sure. Perhaps you can skip the normalization step, so the weights you'll get are not really probabilities anymore, but this shouldn't be a problem because all of them have the same P(action) factors missing. You may have problems with underflow in long games, but I would deal with those when you find them. Álvaro. _______________________________________________ Computer-go mailing list Computer-go@dvandva.org http://dvandva.org/cgi-bin/mailman/listinfo/computer-go
