Manmoth
Manmoth
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Joined: Jan 4, 2014
January 4th, 2014 at 6:48:45 AM permalink
Hi, i am currently doing a research project on blackjack for college. In the wizards appendix 9 for a 1 deck game where the dealer stands on a soft 17, he has an expected return for a player standing on a hand of 10, 10 against a dealer ace of 0.583.

I have tried to calculate this expected value in excel, or at least calculate a range that contains the expected value.

Player stands

Player Dealer
20 A
Card count prob result outcome
2 4 8.16% 13 -
3 4 8.16% 14 -
4 4 8.16% 15 -
5 4 8.16% 16 -
6 4 8.16% 17 player win
7 4 8.16% 18 player win
8 4 8.16% 19 player win
9 4 8.16% 20 push
10 14 28.57% 21 player lose
A 3 6.12% 12 -

max loss 67% player win 24.49%
minloss 28.57% max expected value 0.346938776 player lose 28.57%
maxwin 63.27% min expected value -0.428571429 remainder 38.78%
min win 24% push 8.16%

As you can hopefully see my range does not contain the wizards expected return value. Can anyone help me as to why?
Sorry if my calculations are hard to read - i copied from excel. Thanks.
ThatDonGuy
ThatDonGuy
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January 4th, 2014 at 11:44:16 AM permalink
The Wizard's numbers don't include situations when the dealer has a blackjack - they're meaningless when calculating strategy (you don't need to know whether to hit or stand on 17 if the game is already over). You are including those situations when you include the possibility that the dealer's down card is a 10.
AxiomOfChoice
AxiomOfChoice
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January 4th, 2014 at 11:53:44 AM permalink
I am assuming that the Wizard's numbers assume that the dealer has checked for blackjack and doesn't have it (as you point out, it would be impossible to have an EV of +65% otherwise)

I think that the point of the Wizard's table is to show you what the EV of the various playing decisions are. Once you are making a playing decision, you already know that the dealer doesn't have blackjack.
Manmoth
Manmoth
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January 4th, 2014 at 12:58:21 PM permalink
Thanks alot
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