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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