Expected value of each player first card vs dealer up card
September 29th, 2014 at 5:17:45 AM
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Is there any calculation for this? I can only find similar stuff, with each player hand (2 cards) vs dealer up card.
Thanks a lot.
Thanks a lot.
September 29th, 2014 at 6:29:00 AM
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Quote: vulnerableIs there any calculation for this? I can only find similar stuff, with each player hand (2 cards) vs dealer up card.
Thanks a lot.
You can get a good approximation with the infinite-deck model as the Wizard did here. He shows the value of each initial player's card. The table below (also generated by the infinite-deck model) shows the value of the player's initial card (P1) vs each dealer's up card:
S 17 up = A up = 2 up = 3 up = 4 up = 5 up = 6 up = 7 up = 8 up = 9 up = 10 Average
P1 = A 0.123700 0.589697 0.612947 0.638938 0.670262 0.709532 0.656885 0.595606 0.511501 0.360796 0.504019
P1 = 2 -0.448476 -0.042092 -0.007657 0.029816 0.076244 0.113986 0.003610 -0.087055 -0.182561 -0.296031 -0.132947
P1 = 3 -0.465495 -0.068847 -0.028009 0.015224 0.063546 0.101197 -0.026273 -0.114835 -0.207590 -0.317567 -0.153950
P1 = 4 -0.482899 -0.083473 -0.045671 -0.005794 0.040984 0.075780 -0.064722 -0.143227 -0.233180 -0.339600 -0.176969
P1 = 5 -0.500552 -0.096775 -0.058368 -0.016486 0.029955 0.062156 -0.095890 -0.171986 -0.259129 -0.361951 -0.196529
P1 = 6 -0.518255 -0.106178 -0.059572 -0.010184 0.041078 0.077605 -0.128375 -0.201135 -0.285154 -0.384417 -0.209834
P1 = 7 -0.522357 -0.065335 -0.021344 0.025280 0.074126 0.124698 -0.024394 -0.194498 -0.277879 -0.367160 -0.180796
P1 = 8 -0.436396 0.037845 0.074093 0.111508 0.149903 0.206077 0.162366 -0.010275 -0.193308 -0.298641 -0.084058
P1 = 9 -0.353164 0.097998 0.129551 0.162107 0.196476 0.236141 0.185002 0.117546 -0.038741 -0.213835 -0.009417
P1 = 10 -0.196865 0.230038 0.253373 0.277488 0.303047 0.333731 0.301068 0.241753 0.159670 -0.009487 0.143489
H 17 up = A up = 2 up = 3 up = 4 up = 5 up = 6 up = 7 up = 8 up = 9 up = 10 Average
P1 = A 0.101718 0.588205 0.611730 0.638095 0.669951 0.707097 0.656885 0.595606 0.511501 0.360796 0.501844
P1 = 2 -0.477328 -0.042480 -0.008017 0.031742 0.077171 0.127210 0.003610 -0.087055 -0.182561 -0.296031 -0.133987
P1 = 3 -0.493467 -0.067074 -0.026423 0.017396 0.064668 0.115771 -0.026273 -0.114835 -0.207590 -0.317567 -0.154469
P1 = 4 -0.509968 -0.081435 -0.043845 -0.003470 0.042420 0.094443 -0.064722 -0.143227 -0.233180 -0.339600 -0.177029
P1 = 5 -0.526703 -0.094434 -0.056269 -0.013914 0.031193 0.078256 -0.095890 -0.171986 -0.259129 -0.361951 -0.196668
P1 = 6 -0.543490 -0.102997 -0.056733 -0.007501 0.042370 0.094398 -0.128375 -0.201135 -0.285154 -0.384417 -0.209714
P1 = 7 -0.549402 -0.065986 -0.021776 0.025379 0.074174 0.125318 -0.024394 -0.194498 -0.277879 -0.367160 -0.182900
P1 = 8 -0.489109 0.034060 0.070686 0.108845 0.148621 0.190134 0.162366 -0.010275 -0.193308 -0.298641 -0.090196
P1 = 9 -0.393678 0.096444 0.128152 0.161309 0.196092 0.231149 0.185002 0.117546 -0.038741 -0.213835 -0.013236
P1 = 10 -0.229539 0.228640 0.252115 0.276744 0.302689 0.329076 0.301068 0.241753 0.159670 -0.009487 0.140328
September 29th, 2014 at 8:40:29 AM
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That's great. Thank you.
May I know how you generate this table?
May I know how you generate this table?
September 29th, 2014 at 10:53:26 AM
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Quote: vulnerableThat's great. Thank you.
May I know how you generate this table?
The Wizard gives a detailed YouTube video here in which he constructs the infinite deck model from scratch. Also, on that page you can click on a link to that Excel workbook in Googledocs.
October 28th, 2014 at 4:35:45 AM
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Just had time to return to this post.
I found a bit weird with the dealer Ace column. For example, the ev of player's initial card 7 against A is -0.522.
However, referring to this Wizard page here, the ev of player hand 7 (maybe 2,5 or 3,4) against A is only -0.31. Does that make so much difference with one card 7?
I found a bit weird with the dealer Ace column. For example, the ev of player's initial card 7 against A is -0.522.
However, referring to this Wizard page here, the ev of player hand 7 (maybe 2,5 or 3,4) against A is only -0.31. Does that make so much difference with one card 7?
October 28th, 2014 at 8:27:55 AM
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Quote: vulnerableJust had time to return to this post.
I found a bit weird with the dealer Ace column. For example, the ev of player's initial card 7 against A is -0.522.
However, referring to this Wizard page here, the ev of player hand 7 (maybe 2,5 or 3,4) against A is only -0.31. Does that make so much difference with one card 7?
As the Wizard states on that page, he shows the values assuming the dealer does not have blackjack. His value for 7 (the hand or the card) vs A is -0.3101. To convert this to the value of 7 vs A (before the dealer checks for blackjack) do this: -0.3101 * ( 9/13 ) - 1 * ( 4/13 ) = -0.5224 .
October 28th, 2014 at 11:43:16 PM
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I see. Thanks a lot ChesterDog.
