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0 pointsecshafer2y ago0 comments

There is a point where the expected return is positive. Its around $1B or some large number like that. Sure the expected return is like 1% positive, but its positive.

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angry_moose2y ago

Only if you don't factor in taxes and multiple winners.

This article added in sales numbers to estimate the actual expected value and it peaks around a $500 million jackpot with an expected value of $.85 from a $2.00 ticket. (very close to the bottom)

https://bigthink.com/starts-with-a-bang/math-of-powerball/

panarky2y ago

You can use the Kelly Criterion [0] to compute the optimum bet amount given the odds, the payoff, the cost of a ticket, and the size of your bankroll.

Usually the optimum bet is zero because the expected value is negative.

But when the jackpot gets big enough, occasionally the Kelly Criterion will advise buying a ticket or two if your bankroll is really big, like $10 million.

[0] https://en.wikipedia.org/wiki/Kelly_criterion

vikingerik2y ago

If the jackpot splits in the case of multiple winners, it's not positive - enough tickets will be bought until the expected number of winners is more than one and the expected value is no longer positive.

assbuttbuttass2y ago

How does that work? By linearity of expectation, if the expected value of buying 1 ticket is negative then the expected value of buying multiple tickets should be even more negative

leoedin2y ago

Typically lotteries roll over the jackpot if nobody wins. So if there's a streak of no winners, the total jackpot amount can be more than the cost of buying every possible ticket.

Of course, if you did this you might get unlucky and find that there's another winner in that draw, in which case you'd have to split the winnings and probably wouldn't make your money back.

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