On Thu, Jan 22, 2009 at 11:57 AM, Chris Lipe <[email protected]> wrote: >> I hope you'll excuse a possibly naive question, but why do you need to >> simulate many games to compile these lists? Can't they be determined >> statically from the wordlist and the tile frequency/values? > > Wow that's an awesome question. It's the same question as "can the > value of moves in a certain position be calculated mathematically, > instead of using the monte-carlo method to simulate?"
:-) (You read my paper on that I take it? You're absolutely right - that was what gave me the idea that something similar might apply here too.) > It seems like the answer should be "Yes", except that it's probably > very complicated. > > Are any incredibly bored mathematicians up to the task? > > Roughly speaking, it's so hard or impossible to calculate something > like this because tiles frequency doesn't match the likelihood of a > tile being on a rack, because rack leaves aren't random. (There are > only 4 esses, but it's more likely to be on someone's rack than one of > the four U's, because players tend to dump U's more quickly.) Ah, Ok, that's one factor... another one I thought of would be that when there is a choice between a low scoring play and a high scoring play, we usually make the high-scoring play - so hooking to the low-scoring plays may statically evaluate to the same value but simulate to a lower value. But I'm not sure how big a factor these issues are in the long run. I'll give this some thought and see if I can come up with an algorithm to compare. G
