If you know one of the first two cards for the Player hand is an 8 (so the hand is 8x, x8, or 88) then the probability the Player hand wins is 0.542426.

Quote:teliotQuick & dirty & unaudited.

If you know one of the first two cards for the Player hand is an 8 (so the hand is 8x, x8, or 88) then the probability the Player hand wins is 0.542426.

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teliot,

Was that for 6D or 8D?

I tried the 8D calculation and got these numbers:

Player 1st and/or 2nd card 8: 768,984,350,077,440

Banker then wins: 281,013,832,278,016

Player then wins: 413,998,240,079,872

Tie: 73,972,277,719,552

So the player win probability I get is 0.5383701762

Dog Hand

Quote:Ruffian1238In Baccarat, If the first two cards are dealt to the players and bankers hands respectively, and one of the players first two cards is an 8. At that point in the hand, what is the probability that the players will win?

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Others have answered but the question is too ambiguously worded in my opinion.

Is EXACTLY one of the players first two cards an 8? Or are you including hands where both cards are an 8?

It will make a difference.

Player wins: 401612066940928

Banker wins: 268781376348160

Tie: 69869804556544

Total Hands: 740263247845632

p = 0.542526

Are you double counting 88 as 8x or x8?

My loop has this code, where a, b are the first two Player cards:

for (a = 1; a <= 10; a++) {

for (b = 1; b <= 10; b++) {

if (a == 8 || b == 8) {

for (c = 1; c <= 10; c++) {

for (d = 1; d <= 10; d++) {

for (e = 1; e <= 10; e++) {

for (f = 1; f <= 10; f++) {

/games/baccarat/appendix/9/

It's 53.8370%

In this case, the 1st or 3rd card is going to the Player and it's an 8.

You'd have a 17% advantage betting Player.

Functional link referenced in above post.

For fun I then added where it's, say, 8x or x8 but not 88; then just the first card matching - which matches the Wizard's numbers.

Overall Result for 1 decks PW:0.547498300416

Overall Result for 2 decks PW:0.544637722813

Overall Result for 3 decks PW:0.543695673371

Overall Result for 4 decks PW:0.543226762386

Overall Result for 6 decks PW:0.542759247777

Overall Result for 8 decks PW:0.542526010996

Overall Result for 999999 decks PW:0.541828372923

(8 decks, 0) PW:0.439810878569 W:1145831329529856 L:1215213327515648 T:244237261530112 H:2605281918575616

(8 decks, 1) PW:0.420335779817 W:311159129552896 L:361499035424768 T:67605082867968 H:740263247845632

(8 decks, 2) PW:0.420919716684 W:311591396554752 L:360765092896768 T:67906758394112 H:740263247845632

(8 decks, 3) PW:0.419462449621 W:310512635305984 L:362218482546688 T:67532129992960 H:740263247845632

(8 decks, 4) PW:0.408279192681 W:302234081202176 L:366022394228736 T:72006772414720 H:740263247845632

(8 decks, 5) PW:0.439357716912 W:325240370487296 L:341137234632704 T:73885642725632 H:740263247845632

(8 decks, 6) PW:0.456386448913 W:337846114945024 L:322095491033088 T:80321641867520 H:740263247845632

(8 decks, 7) PW:0.489314595706 W:362221611835392 L:298322065131520 T:79719570878720 H:740263247845632

(8 decks, 8) PW:0.542526010996 W:401612066940928 L:268781376348160 T:69869804556544 H:740263247845632

(8 decks, 9) PW:0.549647265983 W:406883670286336 L:262003621957632 T:71375955601664 H:740263247845632

(8 decks, 0 ignoring pairs) PW:0.475233790534 W:1014446612955136 L:907211826659328 T:212967997227008 H:2134626436841472

(8 decks, 1 ignoring pairs) PW:0.425588167298 W:302823917707264 L:343282323464192 T:65435904442368 H:711542145613824

(8 decks, 2 ignoring pairs) PW:0.424943069190 W:302364903215104 L:344079050014720 T:65098192384000 H:711542145613824

(8 decks, 3 ignoring pairs) PW:0.419041489865 W:298165680799744 L:349929012170752 T:63447452643328 H:711542145613824

(8 decks, 4 ignoring pairs) PW:0.392056208353 W:278964515692544 L:363291754524672 T:69285875396608 H:711542145613824

(8 decks, 5 ignoring pairs) PW:0.445853743156 W:317243729035264 L:322335822635008 T:71962593943552 H:711542145613824

(8 decks, 6 ignoring pairs) PW:0.463135552538 W:329540464762880 L:303854615285760 T:78147065565184 H:711542145613824

(8 decks, 7 ignoring pairs) PW:0.495969115569 W:352902928650240 L:281740299829248 T:76898917134336 H:711542145613824

(8 decks, 8 ignoring pairs) PW:0.547017342825 W:389225893801984 L:256548920418304 T:65767331393536 H:711542145613824

(8 decks, 9 ignoring pairs) PW:0.539039892213 W:383549601476608 L:259337485553664 T:68655058583552 H:711542145613824

(8 decks, 0 1st card only) PW:0.415228231230 W:638608023052288 L:761607414185984 T:137753262916608 H:1537968700154880

(8 decks, 1 1st card only) PW:0.415475739352 W:159747170699264 L:189857873692672 T:34887130646784 H:384492175038720

(8 decks, 2 1st card only) PW:0.417196903763 W:160408944947200 L:188725567889408 T:35357662202112 H:384492175038720

(8 decks, 3 1st card only) PW:0.419851964191 W:161429794906112 L:187253976461312 T:35808403671296 H:384492175038720

(8 decks, 4 1st card only) PW:0.423290339627 W:162751823355904 L:184376516966400 T:37363834716416 H:384492175038720

(8 decks, 5 1st card only) PW:0.433346936002 W:166618505969664 L:179969323315200 T:37904345753856 H:384492175038720

(8 decks, 6 1st card only) PW:0.450141495197 W:173075882563584 L:170168183390208 T:41248109084928 H:384492175038720

(8 decks, 7 1st card only) PW:0.483157160459 W:185770147510272 L:157451915216896 T:41270112311552 H:384492175038720

(8 decks, 8 1st card only) PW:0.538370176244 W:206999120039936 L:140506916139008 T:36986138859776 H:384492175038720

(8 decks, 9 1st card only) PW:0.559462281713 W:215108869548032 L:132334879180800 T:37048426309888 H:384492175038720

Quote:charliepatrick..upon reflection I think the confusion is the Wizard's page says that you know one card in the deck. If it's the 1st or if it's the 3rd then you would know one of the Player's cards; similarly if it was the 2nd or 4th, then you would know one of the Dealer's cards; and 5th or 6th would be a draw card if the game got that far. Thus "1 or 3" means which card you know, not that either the 1st or 3rd card is, say, an eight.

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Just for example, if I force the first card to be an 8, this is what I get:

Player: 206999120039936

Banker: 140506916139008

Tie 36986138859776

Total Hands: 384492175038720

Probability of Player win: 0.538370

But that was not the question that was asked.

If you know the first card is 8 then out of 13 possibilities four will total 8 and nine will total 0-7 and 9