Re: Card Sharks
With no risk aversion I think maximum EV is the correct answer, which means bet everything when the odds are favorable (as they are here), nothing (or the minimum) when they are not. I am pretty sure that will maximize your expectation, albeit with a high risk of ruin.
For instance, say you have a 60% favorite and know you will have an 80% favorite next. Betting in this fashion will yield 4K 48% of the time for an expectation of 1920. Lets say we bet 50% on the first and 100% on the second. Then our expectation is:
.48 * 3000 + .32*1000 + 0*0.2 = 1760
I think you can prove that always betting everything when you have a positive expectation maximizes. (Actually I think the proof is pretty simple). The real problem is the no risk aversion. With infinite opportunities, you will eventually go broke exercizing the maximum EV solution, unless you die of old age with more money to your name than is in existence first.
I think a more interesting problem is if you need to reach a certain level, say 4K by the end of the round, and it is either a win/don't win situation (that is there is no bonus for getting 6K vice 4K).
|