SleightOfHand said:
But because of the risk involved, wouldn't the CE would be lower than the WR?
It might be, or it could be higher. Lots of people play the lottery even though the EV is lower than their CE. Insurance policies are the same way. It all depends on what your personal utility function looks like and where it intersects with the EV function. Some people are willing to make a few bad bets if it could bring them some form of happiness or security. Other people are more willing to take a smaller payoff that involves less effort.
blackjack avenger said:
The ev is about $50.
If I were offered $60 for the free play I would sell it.
If I were offered $40 for the free play I would keep it.
So it seems the CE and the EV are the same.:joker::whip:
In your case they are. Your personal utility is directly proportionate to the EV of the game because the risk has been neutralized and the opportunity to use the "free play" coupon is available to you. Your utility function might change under different circumstances (e.g. you must match the coupon with live money, you are unable to play the coupon yourself, you want to avoid attention at that casino, you must give up your identity to receive the coupon, etc.), but in this case the EV and CE are the same for you. The game is risk-free from the outset so there are no risk-less alternatives to compare it to.
For a scavenger bet you are required to risk some of your money so things will be different. Now you have to have a better idea of your personal risk aversion utility.
SleightOfHand said:
But let me ask to the mathematically superior out there (as it appears they may not necessarily know the answer to my question): how inaccurate is the equation in the OP for the other kinds of advantage plays?
It’s fine as long as your personal risk utility is equal to the Kelly utility. If you are concerned about factors other than optimal growth than it might not be correct in all cases. It's a very personal thing.
-Sonny-