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Maximizing the Expected Value of a Lottery Ticket



The Powerball jackpot now stands at $550 million, and the Mega Millions jackpot is up to $750 million. You can increase your odds of winning ever-so-slightly by buying a ticket. But how much is that $2 investment really worth, and how can we increase the odds of claiming those jackpots for ourselves without having to share with some other winner?

We propose and analyze a practical scheme to increase the likelihood of single winners, or equivalently to minimize the probability of sharing. Paradoxically, this manages to increase the expected value of a lottery ticket without costing the central authorities any additional contributions to the payoff pool. Given that larger potential winnings attract more players, we anticipate that implementation of our scheme would generate increased interest in these games, and enlarge the ostensible benefits for or from the governments running them.

Further, we demonstrate that the number of Powerball tickets bought increases quadratically with pool size, which implies that tickets become increasingly less valuable after the pool passes a critical threshold. This analysis makes it possible to determine the range of pool sizes where tickets have positive expected value. In particular, it establishes that Powerball tickets bought (under the current sales model) with pool sizes between $775.2 million and $1.6656 billion have positive expected value.

What this extremely complex mathematical analysis misses is that the "value" of a lottery ticket lies more in the pleasant fantasy it creates for the buyer than in the actual outcome. And if you win, how horrible is it to have to share a windfall that you'll never be able to spend in your lifetime anyway? In any case, the recommendations are mostly for the system that sells the tickets, in generating numbers that will be less likely to produce duplicates, although there are some tips for buying tickets. Read the calculations at Chance magazine. -via Metafilter


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