Hello Kef,
I'm glad to see that you're perusing our message board. You raise some interesting points in your posts, particularly the one about measuring difficulty using the probability of making a good move. Unfortunately, I know far too little about chess to make any comparison between chess and checkers along these lines. As a (continually failing) perfectionist, I think of the difficulty of a game in terms of how difficult it is to play perfectly, and I am convinced that neither chess nor checkers can be perfected by a human. So, using this very crude measure, chess and checkers would be called equally difficult. But, as you pointed out, there are many other, perhaps more useful, measures of difficulty.
Now, to your point about Chinook's weak solution. Yes, Chinook weakly solved checkers, meaning that the program determined that checkers is a draw from its standard starting position, and moreover the program will always achieve at least a draw. However, this does not mean Chinook will play perfectly. Chinook may turn a winning position into a drawn position (though, as you pointed out, perfect play will not turn a win into a draw). Chinook does not need to know the outcome for each position in its search; in many cases, an inequality is good enough for the determination of its weak solution. For instance, if you browse Chinook's game tree (
http://chinook.cs.ualberta.ca/users/chinook/), you will notice that Chinook has not determined whether or not 11-15 22-17 is a draw or a black win. It does not matter for the purposes of a weak solution: Chinook knows enough - that 11-15 22-17 is not a white win and that white has a drawing response to 11-15.
