## 2012-03-31

### Say What?

In a story on the giant Mega Millions lottery this weekend:
Accountant Ray Lousteau, who bought 55 Mega Millions tickets Friday in New Orleans, knows buying that many tickets doesn't mathematically increase his odds, and that his $55 could have gone elsewhere. He spent it anyway. "Mathematically, it doesn't make a difference, and intellectually we know that. But for some reason buying more tickets makes you feel more lucky," Lousteau said. "Even people who know better are apt to feel that way." Um... having more tickets in a lottery doesn't increase your chance of winning? How the hell does that work? And how did this get by both an accountant and the journalist writing the story? #### 6 comments: 1. Well, buying 55 tickets doesn't increase your expected value by more than a hair, so I'd let it slide. What the accountant said is more accurate than what the journalist said*, which is what one would expect. (*Buying more tickets does increase your odds of winning, but your investment had to increase too, so your expected value is pretty close to the same. I haven't worked out all the math, so I hope I have this right.) 2. I think Sue's on to something. The accountant could have correctly said something to the effect of his EV not being increased with more tickets, but he was indulging his non-rational side to feel more lucky. And the journalist may have incorrectly summarized that as him knowing it "doesn't mathematically increase his odds". 3. ^ My problem with this (interpreting the accountant's statement as being about expected value) is that it can only be true if the expected value is exactly zero. And that doesn't make sense in a couple ways: (a) by measure theory, it's almost impossible for that to be the case, (b) the statement "buying more tickets makes you feel more lucky" is clearly about chance-of-winning, not expected value, and (c) if you knew the expectation was zero, then what are you doing buying 55 tickets? Now, here's a guy claiming that the expected value of last week's lottery was still negative by a good margin ($1 buys 63 cents value); particularly interesting is the "ticket sales as function of jackpot size" which implies that after a certain point, high jackpots drive down EV because of the likelihood of shared jackpots:

http://www.circlemud.org/~jelson/megamillions/

So I have to be very skeptical that this accountant did the math differently and came out exactly EV=0. My best reading is that: (a) he knows that no particular number has a better chance of winning than any other number; and (b) he incorrectly mangled that into thinking that multiple numbers together maintain the property of of "no different chance of winning".

Based on what I see teaching probability, I would bet \$1 that's the case. :-)

4. Good point. FWIW I was thinking of the expected value on the worth of each ticket (which would remain constant at, say, 63 cents, regardless of how many he bought) vs the expected value of his "profit" on each ticket.
But since he is, presumably, wanting to win money, the latter is the only one that is reasonable for him to focus on.

5. If you get to choose your numbers, and you always choose the same numbers, then buying more tickets really doesn't make you more likely to win. It sounds really dumb, but it's plausibly the sort of superstitiousness that gambling tends to inculcate in the vulnerable.

6. ^ Wow, now there's a thought that hadn't occurred to me! Hard to imagine someone doing that, but it's the one thing that would make that accountant's statement a true one.