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Comment by trotro | Hacker News Reader

Notwithstanding the extremely low probability of winning, lotteries aren't even fair, i.e. the ticket price is far lower than the expected earnings. I wonder if it would make sense to democratize cheap high risk, high rewards instruments, for example deep out of the money options, to replace lotteries. At least their prices should be fairer (under the efficient market hypothesis).

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Expected value on some jackpot lotteries does occasionally go over 1. For example, I did the math on Canada's 6/49 about 20 years ago. Whenever the jackpot was over ~$30M, the expected payout was over 1. If you bought a ticket for every jackpot the expected payout was 0.5, the expected payout of any lottery without a jackpot was < 0.2 in hindsight. For $30M prizes the number of players and the odds of sharing a prize went up, but not enough to compensate.

It would have had to go well above $45M to make the "buy every number" strategy have expected value of > 1 since buying every number increases the expected people sharing the prize by 1.

Next time you’re in 7-Eleven instead of a scratcher you pick up a put option on the 7-Eleven holding company.

In the UK we have premium bonds that largely serve this purpose. You are most likely to win small prizes but £1 million is possible. Average return is around 4% I think.

This could be solved by mandating some sufficiently high return say 80%. Still losing proposition, but would make it lot fairer.

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