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Our main contributions to Monte Carlo Tree Search include using inferior cell analysis and connection strategy computation to prune the search tree. In particular, we run our random game simulations not on the actual game position, but on a reduced equivalent board.

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Let Q n be the random number of comparisons made by quicksort in sorting n distinct keys, when we assume that all n! possible orderings are equally likely. Known results concerning moments for Q n do not show how rare it is for Q n to make large deviations from its mean. Here we give a good approximation to the probability of such a large deviation, and find that this probability is quite small. As well as the basic quicksort we consider the variant in which the partitioning key is chosen as the median of (2t + 1) keys.

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