Optimal Play for Multiple Lottery Wins

  • Richard Stong
  • Skip Garibaldi


We determine the optimal strategy for a family of lottery games involving repeated drawings with the same conditions, which includes Brazil's jogo do bicho and games typically offered by state lottery organizations in the United States under names such as Daily 4 or Cash 3.  The proof that the strategy is optimal and the resulting formula for the probability of success both rely on a solution to a recursion that generalizes the usual Pascal recursion for binomial coefficients, which itself relies on a count of lattice paths.  We illustrate how our result can be applied to focus on-the-ground investigations of suspicious patterns of lottery wins.

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