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Topic: Prediction of allocation of players in places

Hello. We present that at us is N players with certain indexes of skill P 1... N. We admit that probability to win first place in tournament at the player n = P n / SUMM (P 1... N). Well, that is the probability of a victory is equal to specific skill of the player concerning all group. We admit that in case of a victory (1st place) there is nobody the player n, the probability to take the second place is arranged similarly (only now from an estimation n th player is thrown out). That is remained N - 1 players divide 2nd place the same as all group divided the first. And so to the end, to the last place. It is necessary to receive the table where in each cell there will be a probability of a place for this or that player. Here calculation for three players with ability 50, 30 and 20 accordingly. It is possible to note that the total on each line and a column is equal to unit (that logically and is necessary). Players 1 2 3 Skill 50 30 20 1 place 0,5 0,3 0,2 2 place 0,339285714 0,375 0,285714286 3 place 0,160714286 0,325 0,514285714 Algorithm which I calculated these values, in the front sorts out all variants and considers total probabilities. For 3 players it still where did not go, but for tens we receive very not sickly rows and swaps. It seems to me, in the games theory should be either ready, or the similar decision of the given problem.

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Re: Prediction of allocation of players in places

W> the Algorithm which I calculated these values, in the front sorts out all variants and considers total probabilities. For 3 players it still where did not go, but for tens we receive very not sickly rows and swaps. Calculations can be accelerated with O (n!) to O (2^n) the help of dynamic programming. F (mask) = probability of that in the first k rounds benefit installed k bit in a mask. Then F (mask) = the Total on all installed bits F (mask - (1 <<i)) * Probability that among remained n - (i-1) players k- a round will be benefited i- by the player.