Re: 10% refund question
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48.825% of the time you double up; 51.175% of the time, you end up with 10% of your bet. The EV is +$2.76.
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Actually you will win 43.31% of the time, you'll tie 8.8% of the time and lose 47.89% of the time. Now do you see why you are mistaken and how you made your math error? These percentages still allow for blackjack, doubling and splitting. So in your single hand scenario for your max bet the odds are even worse.
It should be aparrent (even to you) why the 10% rebate on your total session losses (yes even a session consisting of one hand) is -EV.
Jimbo
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Ok, assuming your numbers are correct, and that they somehow encompass doubling / splitting / getting a blackjack (I don't see how they could, but whatever), if we bet $100 we would get $200 back 43.31% of the time, $100 back 8.8% of the time, and $10 back 47.89% of the time.
(.4331 * 200) + (.088 * 100) + (.4789 * 10) = 100.199
This is still +EV, and doesn't account for blackjack payouts or doubles, etc.
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