Re: 10% refund question
I ignore Jimbo, but another person's text has his text in it...and it is a reply to one of my posts...so I guess I should acknowledge it... While this falls as a reply to another poster, it is really a reply to Jimbo.
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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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I'll accept your numbers. But they do not get worse for the no double/split possibility. In fact, the win/loss rate actually IMPROVES if you never double. (Since you can take a second card when you double against a high card and get an A, your chances of winning improve by not doubling; but your EV suffers because you are not getting extra money out there when you are better than 50/50 to win.)
So, we will accept your numbers and say you can never double or split AND you only get paid even money on a blackjack...and it STILL comes out slightly +EV! (This has already been shown, so I will not bother showing it again.)
Add in the (correct) 3:2 payout on blackjacks and the bonus becomes even better. Approximately 4.7% of the time, you will be dealt a blackjack. In approximately 4.7% of *those* cases, the dealer will also have BJ and you push (this is included in the 8.8% of the time you mention as being pushes).
So adjusting your numbers to allow the 3:2 payoff on BJ, you get something very close to:
4.47% of the time you win 3:2
38.84% of the time you win even money
8.8% of the time you push
47.89% of the time you lose
Adding in the payouts...on a $100 bet with no doubles/splits:
4.47% of the time you end up with $250
38.84% of the time you end up with $200
8.8% of the time you end up with $100 (and can start over)
47.89% of the time you end up with $10
Doing the math, the EV comes to $2.44. So the offer is clearly +EV. And if allow yourself to split and/or double, your EV will climb a bit higher than this. (Also notice that the degree to which it is +EV is close to my earlier rough calculation of $2.76.)
Somehow I expect you will continue to claim you are correct...after all, there is no reason to let the math get in your way!
Acme
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