ROCKY HILL, Conn. — Three asset managers from Connecticut’s affluent New York suburbs claimed a $254 million Powerball jackpot on Monday off a $1 ticket.

Lottery tickets are generally a terrible deal in terms of expected value – the lottery pays out far less in winnings than it receives in ticket sales. It has to pay expenses and show a profit. Then the winner has to pay a big income tax bill.

But occasionally, after no one wins the big prize several drawings in a row, the jackpot gets so big that the expected value is positive.

[Edit 1/7/2016: This is ~~rare~~ unrealistic. For instance the current record jackpot is quoted as $800m. The lump-sum payout would be only $496m. The odds of winning a single bet is 1/292,201,338. So a $2 bet is only worth $1.69. This disregards the possibility of a split pot, which is significant. If you pay the top Federal tax rate of 39.6%, that $1.69 is only worth $1.02. NYC rate maxes out at 12.7%, bringing the top combined income tax rate to 52.3%, leaving $0.81 per $2 bet.]

You might think that when there’s positive expected value, it’s a good time to buy a ticket. Actually, it turns out that’s still a losing strategy. Why? Because unless you’re a millionaire, the correct amount to bet is very small. And if you’re not a millionaire, a single ticket is an overbet. You almost always go broke before you hit the jackpot. Paradoxically, even though each individual bet has positive expected value, your expected long-run profit if you bet every week is less than zero.

What’s the right amount to bet on a risky, but profitable proposition?

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