Unless there’s some information I’m missing or something I don’t understand, it is now a RATIONAL decision to buy a MegaMillions ticket.

The chance of winning the jackpot 1/175,711,536 and the cash lump sum payout is $462 million.  That’s a is 0.00000056911% chance to win the jackpot and a 99.99999943089% chance of a $0 payout for a total expected return of $2.63 per ticket purchased. After tax expected return is $1.97 per ticket.

Like I said, unless there’s something I’m missing about how these lotteries work, the IRRATIONAL decision (as described by classical economic theory) is actually to NOT buy a ticket.

Here’s a picture of the math, based on data available at the MegaMillions.com website:

If you want to check out the full spreadsheet of calculations, click here to view it in Google Docs.

For those that are curious, the breakeven cash lump-sum jackpot amount to watch for is actually $202,322,720.43. When it gets above that, that’s when it makes statistical sense to start playing.  That incorporates all the possible prizes.

I’m guessing this happens because every once in a while lucky events happen where a jackpot winner doesn’t get picked and the total keeps rolling.  That doesn’t happen very often, but when it does, a strange situation like this can happen. Over the long-run and in aggregate, the expected payout for all tickets is always negative. But every once in a while it becomes advantageous for players to play.  It’s like playing Blackjack and counting cards — you bet more when the deck is in your favor and bet just enough to not get kicked out when the deck presents poor odds and expected returns.

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Full Disclosure: classical economic theory is broken because humans don’t behave rationally even though every economic model assumes they do. But still.

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UPDATE: it is possible for the jackpot to be split across multiple winners, which, depending on the number of winners and the size of the jackpot at the draw may or may not change the rationality of the decision to buy a ticket.

The idea is to isolate the exact expected return and then relate the difference between the cost to the amount of subjective “utility” derived from holding a ticket.

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