Yes, and note that Kelly gets much less optimal when you increase bet sizes then when you decrease bet sizes. So from a Kelly perspective, rounding up to a single ticket is probably a bad idea. Your point about sublinearity of utility for money makes it in general an even worse idea. However, I’m not sure that Kelly is the right approach here. In particular, Kelly is the correct attitude when you have a large number of opportunities to bet (indeed, it is the limiting case). However, lotteries which have a positive expected outcome are very rare.So you never approach anywhere near the limiting case. Remember, Kelly optimizes long-term growth.
That raises the question of what the rational thing to do is, when faced with a strictly one-time chance to buy a very small probability of a very large reward.
Yes, and note that Kelly gets much less optimal when you increase bet sizes then when you decrease bet sizes. So from a Kelly perspective, rounding up to a single ticket is probably a bad idea. Your point about sublinearity of utility for money makes it in general an even worse idea. However, I’m not sure that Kelly is the right approach here. In particular, Kelly is the correct attitude when you have a large number of opportunities to bet (indeed, it is the limiting case). However, lotteries which have a positive expected outcome are very rare.So you never approach anywhere near the limiting case. Remember, Kelly optimizes long-term growth.
That raises the question of what the rational thing to do is, when faced with a strictly one-time chance to buy a very small probability of a very large reward.