Ruffian1238
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May 24th, 2023 at 7:57:05 PM permalink
In 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?
teliot
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Joined: Oct 19, 2009
May 25th, 2023 at 9:51:16 AM permalink
Quick & 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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DogHand
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May 25th, 2023 at 1:14:27 PM permalink
Quote: teliot

Quick & 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.

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
SOOPOO
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May 25th, 2023 at 1:57:00 PM permalink
Quote: Ruffian1238

In 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?

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.
teliot
• Posts: 2871
Joined: Oct 19, 2009
May 25th, 2023 at 2:00:03 PM permalink
8 decks
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++) {`
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jackace
• Posts: 8
Joined: Nov 23, 2021
May 25th, 2023 at 8:05:53 PM permalink
The Wizard of Odds has this on his site:

/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.
Jack Hayes
Dieter
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Joined: Jul 23, 2014
May 25th, 2023 at 11:36:31 PM permalink
https://wizardofodds.com/games/baccarat/appendix/9/

Functional link referenced in above post.
May the cards fall in your favor.
charliepatrick
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May 26th, 2023 at 3:43:30 AM permalink
I get the same numbers as Eliot, these are based on either of the first two cards being and 8. Here are 8s for various shoe sizes, then different cards for 8 decks.

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:0.547498300416Overall Result for 2 decks PW:0.544637722813Overall Result for 3 decks PW:0.543695673371Overall Result for 4 decks PW:0.543226762386Overall Result for 6 decks PW:0.542759247777Overall Result for 8 decks PW:0.542526010996Overall 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`
Last edited by: charliepatrick on May 26, 2023
charliepatrick
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May 26th, 2023 at 4:04:16 AM permalink
..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.
teliot
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Joined: Oct 19, 2009
May 26th, 2023 at 6:28:05 AM permalink
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.

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.
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