Predicting Numbers

Niche modeling is about using probability distributions to predict. From the obscure journal article department comes a strategy for winning at Lotto using niche modeling.

Schemes have often been proposed to predict the best numbers for lotteries. One of the most common uses the fact that some numbers are bet more than others, thus betting the unpopular numbers increases returns. A paper entitled Estimating the Frequency Distribution of the Numbers Bet on the California Lottery by Mark Finkelstein, November 15, 1993, presented evidence supporting this hypothesis.

As the distribution of numbers bet in the California Lotto is not public information, the distribution was estimated by a complex analysis from the public data on winning numbers. The results agreed with the Canadian Lotto where the distribution of numbers is made public. Based on the winning numbers for 176 games, they estimated the non-uniformity of the probability of a number being in the winning 6 numbers as below.

lotto.png

Estimate of the probability of numbers from 1 to 51 being in the set of 6 numbers bet.

The distribution is uneven, with the smallest numbers being the most popular, and the largest the least popular. They then go on to calculate the value of winning strategy, based on abstaining from betting unless the payout exceeds a certain figure, then picking the least popular numbers.

Suppose we modify our strategy, then, by playing the 6 least popular numbers but only entering the lottery when the payoff is at least $18 million (which occurs once every 7 weeks). In this case, based on the data we have, our expected returns for a $1.00 bet are as follows: for the 6 least popular numbers, $1.14; for 6 “average” numbers, $0.89; and for the 6 most popular numbers, $0.59.

The least and most popular numbers are as follows:

Least popular: 50, 46, 49, 43, 48, 51.

Most popular: 9, 7, 3, 8, 11, 6

However, despite their success they conclude that ones chances of winning are low.

Thus, a favorable strategy appears to be at hand; the only drawback to it (other than its widespread adoption) is the expected waiting time for a win: 2.3 million years.

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