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Lets say you were writing a program to play checkers. Im simplifying the numbers, but the gist should be obvious.

Your program calculates the odds of Move A to have a 100 chances to win the game and 50 chances to lose. Move B has 1000 chances to win the game and 500 chances to lose.

Both moves result in a 2 to 1 chance to win, but how do you pick which move? Is it statistically better in any way to have more chances to win in the long run?

I think it is, as the more moves that can be made after Move B, the more chances you have to raise the probability of winning with subsequent moves. Am I wrong?

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If your heuristic for estimating the odds are the best you can do, then in fact from what you know at that point move $A$ and move $B$ do have equal chances of being winning moves.

A good AI algorithm would devote more time to going one step further in the tree for moves that heuristic-out to be almost equal, but only if the two moves are near the top of the choice spectrum. For example, if your estimates for five available moves are $\{.50, .50, -75, -80, .85\}$ then it is ineffective to focus on refining the $.50$ moves.

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