How to beat the massachusetts numbers game

Summary

The gambler intent on beating the Massachusetts Numbers Game must cope with a 40% take of the state, gambler’s ruin, and regression to the mean. Preliminary estimates based on the first 851 plays of the lottery and assumptions of stability or linear trend and homoscedasticity (common standard deviation for all numbers) predicted that certain numbers would be profitable. Subsequent experience proved disappointing.

A more elaborate model which assumes (1) that there is no basic shift in bettor preferences but that there is a gradual trend in payoffs and variability of payoffs for the first 720 games and stability thereafter, and (2) that the standard deviation of the payoff is proportional to the mean payoff for various numbers, leads to a new choice of desirable numbers.

This new list is so short that variability and luck are very important in the short run. For the long run income tax rules make it more difficult for the system to be financially profitable.

A final complication is that if the system were good and this became well known, the resulting popularity of the numbers constituting the system would destroy their value.

More details appear in [1].