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.
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.