Maximum Entropy and the Lottery
最大熵与彩票
The distribution on m-tuples of the first M integers is estimated from marginals of the distribution. This problem is of interest in determining unpopular numbers in lotto games. In Canada's Lotto 6/49 the proportion of tickets purchased in previous games containing each number is available. Under certain conditions the limiting distribution subject to the observed marginals is the constrained maximum entropy distribution. This distribution is estimated, and Monte Carlo…