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But if you have a large enough bankroll to do so, you should buy as many tickets as you can get your hands on - assuming #1.) the expected value is positive and

But if you have a large enough bankroll to do so, you should buy as many tickets as you can get your hands on - assuming #1.) the expected value is positive and #2.) your total investment falls below your Kelly criterion. I believe a city in Texas did this once when the lotto odds were in their favor but my google-fu escapes me. So, according to your theory, you should buy ONE ticket or ALL the tickets, but nothing in between?

colins_pride 17y ago
There have been syndicates put together to do this: to buy hundreds of thousands of tickets in lotteries were the expected value is positive. There are a few problems with this approach, though. One is that there is a real risk of split pots, where multiple winners drive the ex post probabilistic payoffs negative. The larger issue is operational hurdles: it is tough to buy a million tickets, even if one has the coin. The retailers simply aren't setup to handle that sort of flow, and the state lottery officials have setup measures to prevent this sort of things (mostly as a result of being picked off in the past). To them, it is a business, they expect to make money, and they just change the rules relating to ticket sale mechanics to limit/punish outlets that collaborate with the syndicates.
JacobAldridge 17y ago
And don't forget to factor split winnings into the calculations. Here in Qld (Australia) the media coverage of lottery prizes starts well before the Kelly criterion tips in your favour, which means prizes are almost always split - there was one case where $20-odd million was split so many ways that the first division prize was less than $750K. In that situation, even buying ALL the tickets wouldn't help ... you'd need to buy MULTIPLE copies of ALL the tickets, so you would have several shares in the split. I'd like to see the math for that!
- joshu 17y ago
  This just lowers your odds, and can be factored into the likelyhood (although I assume that this actually tops the expected return below zero.)
mikedouglas 17y ago
Maybe I'm misreading your post, but the Kelly Criterion says nothing about a single bet. What it tries to maximize is your overall return over a series of bets. The charts in the OP are with regards to buying only a single ticket/draw. Re-running the numbers for more than one ticket would result in an even larger necessary bankroll.

colins_pride 17y ago

There have been syndicates put together to do this: to buy hundreds of thousands of tickets in lotteries were the expected value is positive. There are a few problems with this approach, though. One is that there is a real risk of split pots, where multiple winners drive the ex post probabilistic payoffs negative. The larger issue is operational hurdles: it is tough to buy a million tickets, even if one has the coin. The retailers simply aren't setup to handle that sort of flow, and the state lottery officials have setup measures to prevent this sort of things (mostly as a result of being picked off in the past). To them, it is a business, they expect to make money, and they just change the rules relating to ticket sale mechanics to limit/punish outlets that collaborate with the syndicates.

JacobAldridge 17y ago

And don't forget to factor split winnings into the calculations. Here in Qld (Australia) the media coverage of lottery prizes starts well before the Kelly criterion tips in your favour, which means prizes are almost always split - there was one case where $20-odd million was split so many ways that the first division prize was less than $750K. In that situation, even buying ALL the tickets wouldn't help ... you'd need to buy MULTIPLE copies of ALL the tickets, so you would have several shares in the split. I'd like to see the math for that!

joshu 17y ago
This just lowers your odds, and can be factored into the likelyhood (although I assume that this actually tops the expected return below zero.)

mikedouglas 17y ago

Maybe I'm misreading your post, but the Kelly Criterion says nothing about a single bet. What it tries to maximize is your overall return over a series of bets. The charts in the OP are with regards to buying only a single ticket/draw. Re-running the numbers for more than one ticket would result in an even larger necessary bankroll.