Expanded version of Baccarat calculations with known cards
December 18th, 2025 at 6:18:14 PM
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Does anyone have a version of these calculations where the first and second card are known?
/games/baccarat/appendix/9/
/games/baccarat/appendix/9/
December 18th, 2025 at 6:23:05 PM
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New account so I can’t post the link, but that’s the url path on wizardofodds
December 18th, 2025 at 6:44:09 PM
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Quote: PtriptNew account so I can’t post the link, but that’s the url path on wizardofodds
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The information you seek is in Beyond counting Exhibit CAA
Happy days are here again
December 18th, 2025 at 6:53:25 PM
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Quote: HunterhillQuote: PtriptNew account so I can’t post the link, but that’s the url path on wizardofodds
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The information you seek is in Beyond counting Exhibit CAA
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I can only find what I believe is the old version of this book for $2k. Any idea where to find this version? Seems to be incredibly rare
December 18th, 2025 at 7:10:16 PM
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Here's what I get with an 8-deck shoe:
| First | Second | Player Win | Banker Win | Tie | Player EV | Banker EV | Tie EV |
|---|---|---|---|---|---|---|---|
0 | 0 | 0.4504571 | 0.46014305 | 0.08939985 | -0.00968595 | -0.0133212 | -0.19540132 |
0 | 1 | 0.44691024 | 0.4650598 | 0.08802996 | -0.01814956 | -0.00510343 | -0.20773037 |
0 | 2 | 0.44316149 | 0.46884408 | 0.08799443 | -0.02568258 | 0.00224038 | -0.20805013 |
0 | 3 | 0.44012527 | 0.47189091 | 0.08798383 | -0.03176564 | 0.00817109 | -0.20814555 |
0 | 4 | 0.43379757 | 0.47860804 | 0.0875944 | -0.04481047 | 0.02088007 | -0.21165043 |
0 | 5 | 0.4206106 | 0.49263617 | 0.08675323 | -0.07202556 | 0.04739376 | -0.21922096 |
0 | 6 | 0.40213627 | 0.50138187 | 0.09648187 | -0.0992456 | 0.07417651 | -0.1316632 |
0 | 7 | 0.37112858 | 0.53016915 | 0.09870227 | -0.15904056 | 0.13253211 | -0.11167956 |
0 | 8 | 0.32835301 | 0.58505952 | 0.08658747 | -0.25670651 | 0.22745354 | -0.22071275 |
0 | 9 | 0.31101648 | 0.60232757 | 0.08665595 | -0.29131108 | 0.2611947 | -0.22009644 |
1 | 0 | 0.45270136 | 0.4582065 | 0.08909214 | -0.00550513 | -0.01740519 | -0.19817075 |
1 | 1 | 0.44769623 | 0.46175019 | 0.09055358 | -0.01405397 | -0.00903354 | -0.18501781 |
1 | 2 | 0.44399495 | 0.46700156 | 0.08900349 | -0.0230066 | -0.00034348 | -0.19896859 |
1 | 3 | 0.44070825 | 0.47032434 | 0.08896742 | -0.02961609 | 0.00609987 | -0.19929325 |
1 | 4 | 0.43237018 | 0.4788712 | 0.08875861 | -0.04650102 | 0.02255746 | -0.20117247 |
1 | 5 | 0.41849131 | 0.49391308 | 0.08759561 | -0.07542177 | 0.05072612 | -0.21163954 |
1 | 6 | 0.39891503 | 0.49984802 | 0.10123695 | -0.10093299 | 0.07594059 | -0.08886746 |
1 | 7 | 0.3703425 | 0.52900678 | 0.10065072 | -0.15866428 | 0.13221394 | -0.09414353 |
1 | 8 | 0.32780683 | 0.58404342 | 0.08814975 | -0.25623659 | 0.22703442 | -0.20665227 |
1 | 9 | 0.31106076 | 0.60066672 | 0.08827252 | -0.28960596 | 0.25957263 | -0.20554734 |
2 | 0 | 0.45494723 | 0.4549798 | 0.09007298 | -0.00003257 | -0.02271642 | -0.18934322 |
2 | 1 | 0.45139389 | 0.45856234 | 0.09004378 | -0.00716845 | -0.01575967 | -0.18960602 |
2 | 2 | 0.44625374 | 0.46226981 | 0.09147645 | -0.01601607 | -0.00709742 | -0.17671191 |
2 | 3 | 0.44262301 | 0.46749706 | 0.08987993 | -0.02487404 | 0.00149919 | -0.19108066 |
2 | 4 | 0.43237593 | 0.47836557 | 0.08925849 | -0.04598964 | 0.02207136 | -0.19667356 |
2 | 5 | 0.41776589 | 0.49035615 | 0.09187796 | -0.07259027 | 0.04807246 | -0.17309834 |
2 | 6 | 0.40074102 | 0.49681285 | 0.10244613 | -0.09607184 | 0.0712312 | -0.07798481 |
2 | 7 | 0.37159966 | 0.52673498 | 0.10166535 | -0.15513532 | 0.12879857 | -0.08501183 |
2 | 8 | 0.3296187 | 0.58116063 | 0.08922067 | -0.25154193 | 0.2224839 | -0.19701393 |
2 | 9 | 0.31230703 | 0.59839679 | 0.08929618 | -0.28608976 | 0.25616993 | -0.19633438 |
3 | 0 | 0.45783476 | 0.45111142 | 0.09105382 | 0.00672335 | -0.02927892 | -0.18051561 |
3 | 1 | 0.45435837 | 0.45469933 | 0.0909423 | -0.00034096 | -0.02239401 | -0.18151934 |
3 | 2 | 0.45067648 | 0.45842119 | 0.09090233 | -0.00774472 | -0.01517634 | -0.181879 |
3 | 3 | 0.44511065 | 0.46279075 | 0.09209859 | -0.0176801 | -0.00545944 | -0.17111268 |
3 | 4 | 0.43287007 | 0.47348269 | 0.09364723 | -0.04061262 | 0.01693849 | -0.15717493 |
3 | 5 | 0.4206132 | 0.48626452 | 0.09312228 | -0.06565132 | 0.04133809 | -0.16189951 |
3 | 6 | 0.40348545 | 0.49371539 | 0.10279916 | -0.09022993 | 0.06554416 | -0.07480757 |
3 | 7 | 0.37436618 | 0.52310008 | 0.10253375 | -0.1487339 | 0.1225789 | -0.07719629 |
3 | 8 | 0.33168664 | 0.57814117 | 0.09017219 | -0.24645453 | 0.21754747 | -0.18845029 |
3 | 9 | 0.31435877 | 0.59539473 | 0.0902465 | -0.28103596 | 0.25126622 | -0.18778148 |
4 | 0 | 0.46137503 | 0.44435057 | 0.0942744 | 0.01702446 | -0.03924199 | -0.15153044 |
4 | 1 | 0.45780227 | 0.44780962 | 0.09438811 | 0.00999264 | -0.03238313 | -0.15050705 |
4 | 2 | 0.45413297 | 0.45192831 | 0.09393872 | 0.00220466 | -0.02480107 | -0.15455149 |
4 | 3 | 0.44973635 | 0.4561616 | 0.09410204 | -0.00642525 | -0.01638283 | -0.1530816 |
4 | 4 | 0.43721282 | 0.45446508 | 0.10832209 | -0.01725226 | -0.00547099 | -0.02510117 |
4 | 5 | 0.42446955 | 0.47896964 | 0.09656081 | -0.0545001 | 0.03055161 | -0.13095269 |
4 | 6 | 0.40663204 | 0.48655076 | 0.1068172 | -0.07991872 | 0.05559118 | -0.03864518 |
4 | 7 | 0.37632115 | 0.51783827 | 0.10584057 | -0.14151712 | 0.11562521 | -0.04743486 |
4 | 8 | 0.33437125 | 0.57266641 | 0.09296234 | -0.23829515 | 0.20966183 | -0.16333891 |
4 | 9 | 0.31703096 | 0.58934793 | 0.09362111 | -0.27231698 | 0.24284958 | -0.15741003 |
5 | 0 | 0.47075751 | 0.43391666 | 0.09532583 | 0.03684085 | -0.05853668 | -0.14206756 |
5 | 1 | 0.46718042 | 0.43753409 | 0.0952855 | 0.02964633 | -0.05152304 | -0.14243052 |
5 | 2 | 0.46337219 | 0.44138246 | 0.09524535 | 0.02198973 | -0.04405885 | -0.14279185 |
5 | 3 | 0.45871965 | 0.44252409 | 0.09875626 | 0.01619555 | -0.03832176 | -0.11119365 |
5 | 4 | 0.45859112 | 0.44287266 | 0.09853622 | 0.01571847 | -0.0378621 | -0.11317401 |
5 | 5 | 0.43463028 | 0.45680544 | 0.10856428 | -0.02217516 | -0.00066511 | -0.02292151 |
5 | 6 | 0.41589737 | 0.47616042 | 0.10794221 | -0.06026305 | 0.03645503 | -0.02852008 |
5 | 7 | 0.38478025 | 0.50821194 | 0.10700781 | -0.12343169 | 0.0980211 | -0.03692971 |
5 | 8 | 0.34237676 | 0.56304009 | 0.09458315 | -0.22066334 | 0.19251133 | -0.14875166 |
5 | 9 | 0.32497221 | 0.58036253 | 0.09466527 | -0.25539032 | 0.2263722 | -0.1480126 |
6 | 0 | 0.48993708 | 0.40876676 | 0.10129615 | 0.08117032 | -0.10160866 | -0.08833464 |
6 | 1 | 0.4873609 | 0.41068771 | 0.10195138 | 0.07667319 | -0.09720757 | -0.08243755 |
6 | 2 | 0.48442275 | 0.41348108 | 0.10209616 | 0.07094167 | -0.09161573 | -0.08113452 |
6 | 3 | 0.48218594 | 0.41601727 | 0.1017968 | 0.06616867 | -0.08696953 | -0.08382884 |
6 | 4 | 0.4763471 | 0.41962205 | 0.10403085 | 0.05672504 | -0.07770615 | -0.06372236 |
6 | 5 | 0.46541814 | 0.43063031 | 0.10395155 | 0.03478782 | -0.05631934 | -0.06443605 |
6 | 6 | 0.41467962 | 0.42226368 | 0.1630567 | -0.00758406 | -0.01352913 | 0.46751029 |
6 | 7 | 0.38864128 | 0.5008929 | 0.11046582 | -0.11225161 | 0.08720697 | -0.00580763 |
6 | 8 | 0.35468216 | 0.5437264 | 0.10159145 | -0.18904424 | 0.16185792 | -0.08567699 |
6 | 9 | 0.33724503 | 0.5605044 | 0.10225058 | -0.22325937 | 0.19523415 | -0.0797448 |
7 | 0 | 0.52027168 | 0.37842814 | 0.10130019 | 0.14184354 | -0.16076495 | -0.08829831 |
7 | 1 | 0.51746975 | 0.38036244 | 0.10216781 | 0.13710732 | -0.15612544 | -0.08048968 |
7 | 2 | 0.51468709 | 0.38318724 | 0.10212567 | 0.13149985 | -0.15065922 | -0.08086895 |
7 | 3 | 0.51128243 | 0.3863891 | 0.10232847 | 0.12489333 | -0.14421278 | -0.07904381 |
7 | 4 | 0.50662337 | 0.38942446 | 0.10395218 | 0.11719891 | -0.13667013 | -0.06443042 |
7 | 5 | 0.495812 | 0.40037557 | 0.10381243 | 0.09543644 | -0.11545522 | -0.06568811 |
7 | 6 | 0.49327325 | 0.39608431 | 0.11064244 | 0.09718894 | -0.11699315 | -0.004218 |
7 | 7 | 0.41491243 | 0.42236633 | 0.16272124 | -0.0074539 | -0.01366442 | 0.46449116 |
7 | 8 | 0.38039669 | 0.51746819 | 0.10213512 | -0.1370715 | 0.11119809 | -0.08078396 |
7 | 9 | 0.36336672 | 0.53461183 | 0.10202146 | -0.17124511 | 0.14451452 | -0.0818069 |
8 | 0 | 0.57508554 | 0.33571064 | 0.08920382 | 0.23937489 | -0.25616042 | -0.19716562 |
8 | 1 | 0.57239594 | 0.33786371 | 0.08974035 | 0.23453223 | -0.25142541 | -0.19233683 |
8 | 2 | 0.56899256 | 0.34127331 | 0.08973414 | 0.22771925 | -0.24478291 | -0.19239277 |
8 | 3 | 0.56623693 | 0.34375764 | 0.09000543 | 0.22247929 | -0.23966717 | -0.18995111 |
8 | 4 | 0.56138957 | 0.34749674 | 0.09111369 | 0.21389282 | -0.23126766 | -0.1799768 |
8 | 5 | 0.55049656 | 0.3580178 | 0.09148564 | 0.19247877 | -0.21037966 | -0.17662924 |
8 | 6 | 0.53604767 | 0.36214337 | 0.10180896 | 0.17390429 | -0.19201146 | -0.08371936 |
8 | 7 | 0.50999678 | 0.38783285 | 0.10217037 | 0.12216393 | -0.14155557 | -0.08046671 |
8 | 8 | 0.42311875 | 0.43077589 | 0.14610536 | -0.00765713 | -0.01388166 | 0.31494822 |
8 | 9 | 0.40619378 | 0.50069363 | 0.09311259 | -0.09449984 | 0.06946516 | -0.16198672 |
9 | 0 | 0.59225211 | 0.31844793 | 0.08929996 | 0.27380417 | -0.28972657 | -0.19630034 |
9 | 1 | 0.58894917 | 0.32118792 | 0.08986291 | 0.26776124 | -0.28382064 | -0.19123382 |
9 | 2 | 0.58616923 | 0.32400146 | 0.08982931 | 0.26216776 | -0.27836784 | -0.19153624 |
9 | 3 | 0.58337928 | 0.32652012 | 0.0901006 | 0.25685916 | -0.27318517 | -0.18909461 |
9 | 4 | 0.57797723 | 0.33032472 | 0.09169805 | 0.24765251 | -0.26416874 | -0.17471754 |
9 | 5 | 0.56764084 | 0.34085301 | 0.09150615 | 0.22678783 | -0.24383048 | -0.17644461 |
9 | 6 | 0.5527942 | 0.34474914 | 0.10245666 | 0.20804506 | -0.22528251 | -0.07789008 |
9 | 7 | 0.52695997 | 0.3710051 | 0.10203493 | 0.15595487 | -0.17450513 | -0.08168565 |
9 | 8 | 0.49296949 | 0.41391726 | 0.09311325 | 0.07905223 | -0.09974809 | -0.16198072 |
9 | 9 | 0.42289408 | 0.43070568 | 0.14640024 | -0.0078116 | -0.01372368 | 0.31760212 |
