Do Not Play the Lottery Unless You Are a Millionaire
r6.ca
r6.ca
So, according to your theory, you should buy ONE ticket or ALL the tickets, but nothing in between?
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.
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!
Of course I think the marginal entertainment value is what gets most people playing.
... "assuming that I can avoid picking the same numbers as someone else".
Unfortunately, as the number of tickets purchased increases, the probability that another person chooses the same numbers as you also increases. Thus, when there is a large prize, it becomes very likely that it will be shared.
Or perhaps this is an absurd argument, as proven by the above reductio ad absurdum, and you should keep your money to spend it on things that make sense.
But don't let me stop you. After all, the people who run the lottery need to eat too.
Probability math aside, they were able to raise the funds required to purchase the necessary tickets, but were eventually undone in a rather unexpected way... turns out, it's harder to procure 2 million lottery tickets than they had anticipated. The day of, they simply weren't able to get enough tickets to make it happen.
I honestly don't remember if they won or lost, but I remember expecting them to fail through having to split the winnings, throwing their math off... as if it weren't already off anyway.
that's exactly the opposite of your argument, that if spending $X is good, then you should spend $2*X.
No he answered that in the article. See Kelly Criterion link.
favorable lotteries don't show up very often. if a favorable lottery that you could play existed every day, then the Kelly criterion makes sense (it sort of makes sense in its original context, the stock market).