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buybuydandavis comments on How much to spend on a high-variance option? - Less Wrong Discussion

9 Post author: RolfAndreassen 03 January 2013 06:38PM

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Comment author: buybuydandavis 04 January 2013 08:04:27AM 2 points [-]

so, supposing you win, the probability of someone else also winning is 1 - (1 - 1/14e6)^{250000}=2%

How'd you come up with only 250000 other tickets being purchased? When expected payoffs (by some estimates) exceed ticket cost, number of tickets purchased tends to skyrocket.

Comment author: RolfAndreassen 04 January 2013 05:52:16PM 1 point [-]

Admittedly this is the weakest part of the argument. I looked at the revenue for 2011, 42 million, and divided by the number of drawings, 3 per week for 52 weeks. Obviously this would miss a recent spike in sales. However, I tried the probability with some theoretical numbers, and to get a probability of someone else winning that significantly affects the expectation value, the number of tickets sold has to go way, way up from that baseline quarter million. A full order of magnitude increase in sales, to 2.5 million, only gets you a 17% probability of sharing the jackpot, conditioned on you winning.

Comment author: JRMayne 05 January 2013 12:25:52AM 1 point [-]

I went wandering around ohiolottery.com (For instance, http://www.ohiolottery.com/Games/DrawGames/Classic-Lotto#4) and found this out:

  1. The cash payoff is half the stated prize.
  2. The odds to win the jackpot, as noted by the OP, are about 14 million-1.
  3. The amount of money being spent on individual draws is very low. The jackpot increase was $100K for the last drawing; I don't know exactly what their formula is, but I'd be shocked if they sold more than 400K tickets for the last drawing.
  4. Ohio is running a lot of lottery games; this is good for players who pick their spots.

There are also payoffs below the jackpot level, so I'm confident there's a positive EV per ticket.

The question as to how many tickets to buy, assuming you can effectively do so, is "All of them." Buy each individual ticket, take your 14 million tickets, and probably profit. (Remember, the jackpot kick will include some fraction of your 14 million, also. Plus, you'll have all the side prizes.) In practice, unfortunately, this requires a method to buy them effectively, some armored cars, and a staff of people to do it right. Failure to purchase all tickets results in some drama, for sure.

The execution expenses and risk are troubling; if those could be effectively mitigated, it's a great investment.

Assuming you're a few million short of that, though, it's harder. I buy CA lottery tickets when EV>1.20 per $1 invested. I have no strong justification for that number.

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