Rebate Question

Hey everyone,

Suppose someone was offered the following opportunity. It's similar to other casino rebates I've heard about, with a slight twist.

He can choose to play blackjack, craps or roulette. He can bet up to $25,000 a hand for blackjack and $5,000 for anything with roulette or craps. If he loses $500,000, he gets a 20 percent rebate. But, he only gets this rebate of $100,000 if he loses all $500,000. However, he doesn't get the rebate if he loses less than $500,000.

Assuming he plays optimal strategy at anything he does and he has sufficient bankroll requirements, is this a profitable opportunity?

I'm guessing playing roulette would have the highest EV since you either want to win quickly or lose quickly, but outside of intuition, I'm not sure how to solve this problem.

Any help would be greatly appreciated!

JohnG

Quote: JohnG

Hey everyone,

Suppose someone was offered the following opportunity. It's similar to other casino rebates I've heard about, with a slight twist.

JohnG

Sure. Remove a few zeros to make it sound more real-world. Let's say that if he loses $500, he gets a $100 rebate.

To further simplify, let's just say that he bets it all--$500--on the Pass Line. His outcomes are that he loses $400 (net with rebate), or wins $500. He is, in effect, getting paid 5:4 odds, and since the odds against him are much better than 4:5 (they're about 197:200), he has a positive expectation.

If he makes smaller bets, the benefit to him is if and when he is behind exactly $400, he is freerolling for the next $100. If he loses any more up to that $100, he gets that money back anyway. So the overall benefit to him is that losing an amount up to $400 is cushioned by the fact that if he reaches the $400 loss mark, he can keep betting, but won't lose any more than that (assuming, of course, that he has the sense to stop at minus $500).