Re: Card Sharks
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The correct ammount to wager is your edge odds times your bankroll. With a 10 its like 37/63 in your favor? So your edge is 26% ((.63-.5)+(.5-.37)). So bet 26% of your bankroll or 260 dollars.
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This is approximately what the Kelly criterion recommends, but that assumes you are risk averse, and the balance you have on the game show represents every asset you have in the world.
Under the original poster's assumption that you are not risk averse, you should bet everything and let it ride whenever you don't have an 8. randomstumbl and fnord_too are correct.
To make this clearer, suppose you get 5 chances to double-up as a 3:1 favorite. What fraction fi of your balance should you bet on the ith opportunity? Your average balance at the end is (1+f1/2)(1+f2/2)(1+f3/2)(1+f4/2)(1+f5/2). To maximize this, you want to maximize each term individually, which means fi=1. Conclusion: Bet everything and let it ride.
It is common for people to make the same mistake, applying something like the Kelly criterion to their stack in a tournament. They reason that they will get good opportunities in the future, and if they bust out, they will miss them. The result is that they often have too few chips to take full advantage of good opportunities later.
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