Dice have no memories, but I do: a defence of the reverse gambler's belief
We investigate the problem of predicting the outcomes of a sequence of discrete random variables that are almost uniform, in the sense that they are generated from a random process that is designed to produce independent uniform outcomes but may not do so exactly. Using assumptions based around this notion we derive a useful stochastic ordering. We reject the gambler’s belief as unsound and find that the reverse gambler’s belief is the optimal prediction method. This method arises under a wide...[Show more]
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