This comes up frequently in gambling and statistics circles. “Citation please” is the correct response—casinos do NOT expect to make a profit by offering losing (for them) bets and letting “gambler’s ruin” pay them off. It just doesn’t work that way.
The fact that a +moneyEV bet can be -utilityEV for a gambler does NOT imply that a -moneyEV bet can be +utilityEV for the casino. It’s -utility for both participants.
The only reason casinos offer such bets ever is for promotional reasons, and they hope to make the money back on different wagers the gambler will make while there.
The Kelly calculations work just fine for all these bets—for cyclic bets, it ends up you should bet 0 when -EV. When +EV, bet some fraction of your bankroll that maximizes mean-log-outcome for each wager.
This comes up frequently in gambling and statistics circles. “Citation please” is the correct response—casinos do NOT expect to make a profit by offering losing (for them) bets and letting “gambler’s ruin” pay them off. It just doesn’t work that way.
The fact that a +moneyEV bet can be -utilityEV for a gambler does NOT imply that a -moneyEV bet can be +utilityEV for the casino. It’s -utility for both participants.
The only reason casinos offer such bets ever is for promotional reasons, and they hope to make the money back on different wagers the gambler will make while there.
The Kelly calculations work just fine for all these bets—for cyclic bets, it ends up you should bet 0 when -EV. When +EV, bet some fraction of your bankroll that maximizes mean-log-outcome for each wager.