On Thu, 1 Jun 2000, Joel Wapnick wrote:

 We just don't know how to infer how the tiles remaining in it are not 
 random, because that depends not just on Jim's previous play of FRAG 
 (the reasons for which we cannot entirely determine anyway), but on 
 previous plays before FRAG.

Actually, we kind of know. Use a Bayesian analysis of the unseen pool at one or multiple steps and ascertain a distribution of the likely distributions between bag and rack. The inclusion of the information from previous moves might make it more tricky to compute, but the s/n should increase for -- and this is just a guess -- at least the first two extra moves.

> Here's an interesting question:  at what point does 
> exhaustive analysis break down?  3 tiles in the bag?  7?  22?  If 
> it's between 6 and 7, or 7 and 8, why does the breakdown occur at 
> that particular point?

Theoretically, never. But like James mentioned regarding his endgame player, sometimes it takes a while to be perfect. At a certain point, depending on the memory and cpu resources available, it would become more workable(well, actually it's always more workable, but you give up "perfection") to switch from complete enumeration to backwards simulation.

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