Powerball: finally +ev?

[EnderW27]

My calculations and assumptions seem to imply that it is.

Assumption #1: you buy every number combination. Cost ~$146 million

Total winnings outside the main jackpot: $28.8 million. This comes from (total number combination/odds of winning * payout).

Total winnings, pre-tax, on main jackpot with lump-sum payout: $177.3 million.

Total payout: $206 million

Assumption #2: total tickets in play (outside your own), 50 million.
Odds of splitting main jackpot with someone else: 1 in 3.

Total winnings on a split: 88.7 + 28.8 = 117.5 million

(117.5*.333) + (206*.666) = 176.5 million or an average profit of 30 million dollars, pre-tax

Of course, this brings about assumption #3: you find a good tax shelter...

[cardcounter0]

No.

$146.1 million cost > $176.5 million avg winnings - $61.7 million taxes.

[sekrah]

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No.

$146.1 million cost > $176.5 million avg winnings - $61.7 million taxes.

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Could you deduct your losing tickets as "gambling losses" here?

[AvivaSimplex]

Yes, if you have other gambling winnings and you itemize your return, you can deduct losing tickets.

But add in expected utility and this is still not a good idea. $150,000,000 will not make you 150,000,000 times happier than $1.

[EnderW27]

I'm willing to gamble $1 that I will, indeed, be 150,000,000 times happier than I am right now.

[pzhon]

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Assumption #2: total tickets in play (outside your own), 50 million.

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Try doing your analysis again with this figure revised upward substantially. The stated jackpot increased by about $65 million. How many tickets do you think it took for the jackpot to increase that much?

To simplify the analysis, assume that if anyone hits the jackpot, the money is spread evenly among everyone who bought a ticket. That avoids a doable but complicated combinatorial sum.

[CORed]

Several factors to consider: Taxes, cash equivalent (the prize advertized is the total of a 20 year annuity, I believe), probability of a split. When the prize gets big, a lot of people play, so split jackpots are fairly common. Most likey it's not +EV.

As a practical matter, EV is pretty meaningless for something with as low a probability as a lottery jackpot. It's not like your going to buy 10,000,000,000 tickets so you have a high probablility of making a profit.

As a matter of principle, I stay away from gambling games with aN overall 50% house advantage, even on those rare occasions when they are +EV.

[napawino]

Not to mention the time it would take to complete all combinations of numbers on all of the tickets. If you started filling them out today, you might be ready for the next $365 jackpot in 2010.

[RickyG]

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To simplify the analysis, assume that if anyone hits the jackpot, the money is spread evenly among everyone who bought a ticket.

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Yes but it also ignores other prizes that can pay up to $250,000 and are not included in the "jackpot" number

[BobJoeJim]

No, it was not positive EV. First, non-jackpot numbers contribute a total of 18 cents of EV per ticket. The $365 million was the expected total payout of a 30 year annuity, if you took it all in immediate cash, the prize was somewhere around $180 million. After taxes this will become maybe $100 million, tops. Even if you're guaranteed not to split, that still only contributes about 68 cents to the EV of a ticket, making the total EV -14 cents on each $1 ticket purchased. Even worse, since when the jackpot was $300 million, there were about 200 million tickets sold. Assuming a 50% increase, with the jackpot at a record level, there will on average be two other winners to split the jackpot with you if you do win. Sorry, but even with a record jackpot, the EV on Powerball was only somewhere around a 50% return.