If the expected value is positive, then by all means you should play the lottery. Just bear in mind that the utility of money is nonlinear, so Kelly will overextend you - use something like max log-value and rederive.
Kelly is the betting stake formula - just plug in the expected value and it will tell you how much of your money you should gamble to maximize your winnings over time. But it does that with more or less a 50-50 chance of you losing all your money. Because winning 10 dollars means a lot more to someone who makes minimum wage than a millionaire, you need to skew the formula to take that into account.
The easiest way to do that is to use the log-value of money, and rederive the kelly criterion based on that value instead.
From what I recall the math works out so that unless you have a substantial pile of money, the ideal number of lottery tickets is always between 0 and 1.
If the expected value is positive, then by all means you should play the lottery. Just bear in mind that the utility of money is nonlinear, so Kelly will overextend you - use something like max log-value and rederive.
The only time this happens are either scratch off tickets that are horribly broken or rolling-jackpot lotteries where you can win what other people put in before you.
I’m too stupid to piece together what this means, but I’m interested.
Kelly is a betting stake formula? But deriative of max log-value will provide a better result?
i got you, watch this for understanding of kelly criterion
https://www.youtube.com/watch?v=_FuuYSM7yOo
Kelly is the betting stake formula - just plug in the expected value and it will tell you how much of your money you should gamble to maximize your winnings over time. But it does that with more or less a 50-50 chance of you losing all your money. Because winning 10 dollars means a lot more to someone who makes minimum wage than a millionaire, you need to skew the formula to take that into account.
The easiest way to do that is to use the log-value of money, and rederive the kelly criterion based on that value instead.
From what I recall the math works out so that unless you have a substantial pile of money, the ideal number of lottery tickets is always between 0 and 1.
Even if the math works out that the lottery would be EV+, you still can’t know for sure it isn’t crooked
Lotteries are generally regulated but corruption isn’t unheard of.
But outside regulated state sponsored lotteries - it’s safe to assume it’s crooked in one way or another.