Remember reading in some book on probability and statistics that one will be better off betting insignificant amounts of money rather than not playing at all.
If I have a lottery, and you have a 1 in a billion chance to gain 10 billion utility, tickets cost 1 utility. How much of your current utility wealth should you put in?
Classical expected value reasoning would pour in everything, even though you are almost guaranteed bankrupt at the end of that transaction.
The Kelly criterion recommends an exact (small) percentage for this style of lotteries, and is therefore probably more sensible than decision making based on expected values.
Also careful; I believe money-to-utility is already logarithmic for most people. We don't have a good intuition for what "billions of utility vs 1 utility" represents.
Surely after you finish playing one game, the next game you play (even if it's a completely different game) is the second round.
It doesn't if you're a house fly.
Average life expectancy at birth in OECD countries is around 4'000 weeks.
Kelly is equivalent to decision making based on expected values (of the logarithm of wealth).
Maybe you wanted to say "[...] gain 10 billion dollars, tickets cost 1 dollar. How much of your current dollar wealth [...]".
risking pocket change to win big is quasi-reasonable, even though it is a loosing bet. Because you don't notice the downside/drawdowns.
risking more than pocket change is not reasonable, because it is a loosing bet.
NB: I don't play the lottery.