How to use Baccarat Calculator
June 3rd, 2025 at 8:42:29 AM
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Hi Wizards,
I would like to check if possible to use Baccarat Calculator to get the combinations and probability?
Let's say I want to know combinations and probability of Player wins with 6 points over Banker (5 points and below), and total card on Player side is 2 cards while total cards on Banker is either 2 or 3 cards.
Or maybe, what if player wins with 6 points but with 3 cards instead. If it is possible, please show me how to do the calculation.
Otherwise, if needed other file or source, please show me where can I take a look into it.
Thanks in advance.
I would like to check if possible to use Baccarat Calculator to get the combinations and probability?
Let's say I want to know combinations and probability of Player wins with 6 points over Banker (5 points and below), and total card on Player side is 2 cards while total cards on Banker is either 2 or 3 cards.
Or maybe, what if player wins with 6 points but with 3 cards instead. If it is possible, please show me how to do the calculation.
Otherwise, if needed other file or source, please show me where can I take a look into it.
Thanks in advance.
Last edited by: TheSeeker on Jun 3, 2025
June 3rd, 2025 at 5:29:08 PM
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If you can tell me how much these bets pay and where they can be played, I can run them though my software and give you the answer.
June 4th, 2025 at 8:27:58 AM
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For now, assume an "infinite deck" - that is, every card dealt has a 1/13 chance of being a 1, a 1/13 chance of being a 2, and so on through 9, and a 4/13 chance of being a 0
For the 2-card player win with 6:
First, note that the player must be dealt a 6-value hand - there are 10 ways to do this:
{0,6}, {1,5}, {2,4}, {3,3}, {4,2}, {5,1}, {6,0}, {7,9}, {8,8}, {9,7}
There is a 4/169 chance of being dealt 0,6, a 4/169 chance of being dealt 6,0, and a 1/169 chance of being dealt each of the other three, so the probability of a 2-card player 6 is (4/169 x 2 + 1/169 x 8) = 16 / 19.
Since the player does not take a third card, the banker does take a third card on hands of 0-5, but not on 6-9; however, if the banker is dealt a hand of 6-9, it cannot lose to a 6, so the banker will always take a third card.
Note that, for each of the six possible values of the banker's hand, there are 6 card values that will result in a hand of 0-5, which loses, and 4 which result in a 6-9, which ties or wins.
Look at each one separately:
Each pair of columns is a banker hand - the first two cards, then the third card - and the number of times out of 13^3 that it will appear:
If you add up all of the numbers in the even columns, you get 945, so the probability of the banker losing to a player 6 is 945 / 13^3.
The overall probability of player winning with a 2-card 6 is 16 / 13^2 x 945 / 13^3 = 15,120 / 13^5, or about 1 in 24.5564.
This becomes somewhat harder to calculate if limited to an 8-deck shoe, as the probability of each card now depends on what cards were dealt before it; however, the result should be fairly close to the infinite-deck number.
Calculating for a 3-card player hand is done the same way, except:
(a) You have to count how many ways you can get a 3-card player hand of 6;
(b) You have to take the player's third card into account when determining what the banker's hand is, as you have to allow for the possibility that the banker will stand on a 5 or less.
For the 2-card player win with 6:
First, note that the player must be dealt a 6-value hand - there are 10 ways to do this:
{0,6}, {1,5}, {2,4}, {3,3}, {4,2}, {5,1}, {6,0}, {7,9}, {8,8}, {9,7}
There is a 4/169 chance of being dealt 0,6, a 4/169 chance of being dealt 6,0, and a 1/169 chance of being dealt each of the other three, so the probability of a 2-card player 6 is (4/169 x 2 + 1/169 x 8) = 16 / 19.
Since the player does not take a third card, the banker does take a third card on hands of 0-5, but not on 6-9; however, if the banker is dealt a hand of 6-9, it cannot lose to a 6, so the banker will always take a third card.
Note that, for each of the six possible values of the banker's hand, there are 6 card values that will result in a hand of 0-5, which loses, and 4 which result in a 6-9, which ties or wins.
Look at each one separately:
Each pair of columns is a banker hand - the first two cards, then the third card - and the number of times out of 13^3 that it will appear:
| 0 0 0 | 64 | 1 9 0 | 4 | 2 8 0 | 4 | 3 7 0 | 4 | 4 6 0 | 4 | 5 5 0 | 4 | 6 4 0 | 4 | 7 3 0 | 4 | 8 2 0 | 4 | 9 1 0 | 4 |
| 0 0 1 | 16 | 1 9 1 | 1 | 2 8 1 | 1 | 3 7 1 | 1 | 4 6 1 | 1 | 5 5 1 | 1 | 6 4 1 | 1 | 7 3 1 | 1 | 8 2 1 | 1 | 9 1 1 | 1 |
| 0 0 2 | 16 | 1 9 2 | 1 | 2 8 2 | 1 | 3 7 2 | 1 | 4 6 2 | 1 | 5 5 2 | 1 | 6 4 2 | 1 | 7 3 2 | 1 | 8 2 2 | 1 | 9 1 2 | 1 |
| 0 0 3 | 16 | 1 9 3 | 1 | 2 8 3 | 1 | 3 7 3 | 1 | 4 6 3 | 1 | 5 5 3 | 1 | 6 4 3 | 1 | 7 3 3 | 1 | 8 2 3 | 1 | 9 1 3 | 1 |
| 0 0 4 | 16 | 1 9 4 | 1 | 2 8 4 | 1 | 3 7 4 | 1 | 4 6 4 | 1 | 5 5 4 | 1 | 6 4 4 | 1 | 7 3 4 | 1 | 8 2 4 | 1 | 9 1 4 | 1 |
| 0 0 5 | 16 | 1 9 5 | 1 | 2 8 5 | 1 | 3 7 5 | 1 | 4 6 5 | 1 | 5 5 5 | 1 | 6 4 5 | 1 | 7 3 5 | 1 | 8 2 5 | 1 | 9 1 5 | 1 |
| 0 1 9 | 4 | 1 0 9 | 4 | 2 9 9 | 1 | 3 8 9 | 1 | 4 7 9 | 1 | 5 6 9 | 1 | 6 5 9 | 1 | 7 4 9 | 1 | 8 3 9 | 1 | 9 2 9 | 1 |
| 0 1 0 | 16 | 1 0 0 | 16 | 2 9 0 | 4 | 3 8 0 | 4 | 4 7 0 | 4 | 5 6 0 | 4 | 6 5 0 | 4 | 7 4 0 | 4 | 8 3 0 | 4 | 9 2 0 | 4 |
| 0 1 1 | 4 | 1 0 1 | 4 | 2 9 1 | 1 | 3 8 1 | 1 | 4 7 1 | 1 | 5 6 1 | 1 | 6 5 1 | 1 | 7 4 1 | 1 | 8 3 1 | 1 | 9 2 1 | 1 |
| 0 1 2 | 4 | 1 0 2 | 4 | 2 9 2 | 1 | 3 8 2 | 1 | 4 7 2 | 1 | 5 6 2 | 1 | 6 5 2 | 1 | 7 4 2 | 1 | 8 3 2 | 1 | 9 2 2 | 1 |
| 0 1 3 | 4 | 1 0 3 | 4 | 2 9 3 | 1 | 3 8 3 | 1 | 4 7 3 | 1 | 5 6 3 | 1 | 6 5 3 | 1 | 7 4 3 | 1 | 8 3 3 | 1 | 9 2 3 | 1 |
| 0 1 4 | 4 | 1 0 4 | 4 | 2 9 4 | 1 | 3 8 4 | 1 | 4 7 4 | 1 | 5 6 4 | 1 | 6 5 4 | 1 | 7 4 4 | 1 | 8 3 4 | 1 | 9 2 4 | 1 |
| 0 2 8 | 4 | 1 1 8 | 1 | 2 0 8 | 4 | 3 9 8 | 1 | 4 8 8 | 1 | 5 7 8 | 1 | 6 6 8 | 1 | 7 5 8 | 1 | 8 4 8 | 1 | 9 3 8 | 1 |
| 0 2 9 | 4 | 1 1 9 | 1 | 2 0 9 | 4 | 3 9 9 | 1 | 4 8 9 | 1 | 5 7 9 | 1 | 6 6 9 | 1 | 7 5 9 | 1 | 8 4 9 | 1 | 9 3 9 | 1 |
| 0 2 0 | 16 | 1 1 0 | 4 | 2 0 0 | 16 | 3 9 0 | 4 | 4 8 0 | 4 | 5 7 0 | 4 | 6 6 0 | 4 | 7 5 0 | 4 | 8 4 0 | 4 | 9 3 0 | 4 |
| 0 2 1 | 4 | 1 1 1 | 1 | 2 0 1 | 4 | 3 9 1 | 1 | 4 8 1 | 1 | 5 7 1 | 1 | 6 6 1 | 1 | 7 5 1 | 1 | 8 4 1 | 1 | 9 3 1 | 1 |
| 0 2 2 | 4 | 1 1 2 | 1 | 2 0 2 | 4 | 3 9 2 | 1 | 4 8 2 | 1 | 5 7 2 | 1 | 6 6 2 | 1 | 7 5 2 | 1 | 8 4 2 | 1 | 9 3 2 | 1 |
| 0 2 3 | 4 | 1 1 3 | 1 | 2 0 3 | 4 | 3 9 3 | 1 | 4 8 3 | 1 | 5 7 3 | 1 | 6 6 3 | 1 | 7 5 3 | 1 | 8 4 3 | 1 | 9 3 3 | 1 |
| 0 3 7 | 4 | 1 2 7 | 1 | 2 1 7 | 1 | 3 0 7 | 4 | 4 9 7 | 1 | 5 8 7 | 1 | 6 7 7 | 1 | 7 6 7 | 1 | 8 5 7 | 1 | 9 4 7 | 1 |
| 0 3 8 | 4 | 1 2 8 | 1 | 2 1 8 | 1 | 3 0 8 | 4 | 4 9 8 | 1 | 5 8 8 | 1 | 6 7 8 | 1 | 7 6 8 | 1 | 8 5 8 | 1 | 9 4 8 | 1 |
| 0 3 9 | 4 | 1 2 9 | 1 | 2 1 9 | 1 | 3 0 9 | 4 | 4 9 9 | 1 | 5 8 9 | 1 | 6 7 9 | 1 | 7 6 9 | 1 | 8 5 9 | 1 | 9 4 9 | 1 |
| 0 3 0 | 16 | 1 2 0 | 4 | 2 1 0 | 4 | 3 0 0 | 16 | 4 9 0 | 4 | 5 8 0 | 4 | 6 7 0 | 4 | 7 6 0 | 4 | 8 5 0 | 4 | 9 4 0 | 4 |
| 0 3 1 | 4 | 1 2 1 | 1 | 2 1 1 | 1 | 3 0 1 | 4 | 4 9 1 | 1 | 5 8 1 | 1 | 6 7 1 | 1 | 7 6 1 | 1 | 8 5 1 | 1 | 9 4 1 | 1 |
| 0 3 2 | 4 | 1 2 2 | 1 | 2 1 2 | 1 | 3 0 2 | 4 | 4 9 2 | 1 | 5 8 2 | 1 | 6 7 2 | 1 | 7 6 2 | 1 | 8 5 2 | 1 | 9 4 2 | 1 |
| 0 4 6 | 4 | 1 3 6 | 1 | 2 2 6 | 1 | 3 1 6 | 1 | 4 0 6 | 4 | 5 9 6 | 1 | 6 8 6 | 1 | 7 7 6 | 1 | 8 6 6 | 1 | 9 5 6 | 1 |
| 0 4 7 | 4 | 1 3 7 | 1 | 2 2 7 | 1 | 3 1 7 | 1 | 4 0 7 | 4 | 5 9 7 | 1 | 6 8 7 | 1 | 7 7 7 | 1 | 8 6 7 | 1 | 9 5 7 | 1 |
| 0 4 8 | 4 | 1 3 8 | 1 | 2 2 8 | 1 | 3 1 8 | 1 | 4 0 8 | 4 | 5 9 8 | 1 | 6 8 8 | 1 | 7 7 8 | 1 | 8 6 8 | 1 | 9 5 8 | 1 |
| 0 4 9 | 4 | 1 3 9 | 1 | 2 2 9 | 1 | 3 1 9 | 1 | 4 0 9 | 4 | 5 9 9 | 1 | 6 8 9 | 1 | 7 7 9 | 1 | 8 6 9 | 1 | 9 5 9 | 1 |
| 0 4 0 | 16 | 1 3 0 | 4 | 2 2 0 | 4 | 3 1 0 | 4 | 4 0 0 | 16 | 5 9 0 | 4 | 6 8 0 | 4 | 7 7 0 | 4 | 8 6 0 | 4 | 9 5 0 | 4 |
| 0 4 1 | 4 | 1 3 1 | 1 | 2 2 1 | 1 | 3 1 1 | 1 | 4 0 1 | 4 | 5 9 1 | 1 | 6 8 1 | 1 | 7 7 1 | 1 | 8 6 1 | 1 | 9 5 1 | 1 |
| 0 5 5 | 4 | 1 4 5 | 1 | 2 3 5 | 1 | 3 2 5 | 1 | 4 1 5 | 1 | 5 0 5 | 4 | 6 9 5 | 1 | 7 8 5 | 1 | 8 7 5 | 1 | 9 6 5 | 1 |
| 0 5 6 | 4 | 1 4 6 | 1 | 2 3 6 | 1 | 3 2 6 | 1 | 4 1 6 | 1 | 5 0 6 | 4 | 6 9 6 | 1 | 7 8 6 | 1 | 8 7 6 | 1 | 9 6 6 | 1 |
| 0 5 7 | 4 | 1 4 7 | 1 | 2 3 7 | 1 | 3 2 7 | 1 | 4 1 7 | 1 | 5 0 7 | 4 | 6 9 7 | 1 | 7 8 7 | 1 | 8 7 7 | 1 | 9 6 7 | 1 |
| 0 5 8 | 4 | 1 4 8 | 1 | 2 3 8 | 1 | 3 2 8 | 1 | 4 1 8 | 1 | 5 0 8 | 4 | 6 9 8 | 1 | 7 8 8 | 1 | 8 7 8 | 1 | 9 6 8 | 1 |
| 0 5 9 | 4 | 1 4 9 | 1 | 2 3 9 | 1 | 3 2 9 | 1 | 4 1 9 | 1 | 5 0 9 | 4 | 6 9 9 | 1 | 7 8 9 | 1 | 8 7 9 | 1 | 9 6 9 | 1 |
| 0 5 0 | 16 | 1 4 0 | 4 | 2 3 0 | 4 | 3 2 0 | 4 | 4 1 0 | 4 | 5 0 0 | 16 | 6 9 0 | 4 | 7 8 0 | 4 | 8 7 0 | 4 | 9 6 0 | 4 |
If you add up all of the numbers in the even columns, you get 945, so the probability of the banker losing to a player 6 is 945 / 13^3.
The overall probability of player winning with a 2-card 6 is 16 / 13^2 x 945 / 13^3 = 15,120 / 13^5, or about 1 in 24.5564.
This becomes somewhat harder to calculate if limited to an 8-deck shoe, as the probability of each card now depends on what cards were dealt before it; however, the result should be fairly close to the infinite-deck number.
Calculating for a 3-card player hand is done the same way, except:
(a) You have to count how many ways you can get a 3-card player hand of 6;
(b) You have to take the player's third card into account when determining what the banker's hand is, as you have to allow for the possibility that the banker will stand on a 5 or less.
June 5th, 2025 at 11:37:26 AM
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Quote: TheSeekerHi Wizards,
I would like to check if possible to use Baccarat Calculator to get the combinations and probability?
Let's say I want to know combinations and probability of Player wins with 6 points over Banker (5 points and below), and total card on Player side is 2 cards while total cards on Banker is either 2 or 3 cards.
Or maybe, what if player wins with 6 points but with 3 cards instead. If it is possible, please show me how to do the calculation.
Otherwise, if needed other file or source, please show me where can I take a look into it.
Thanks in advance.
link to original post
TheSeeker,
Looks like you are considering two separate sidebets:
1. Player wins with a 2-card total of 6
2. Player wins with a 3-card total of 6
What does each sidebet pay?
The Wiz has a page on the "Ox 6" sidebet (https://wizardofodds.com/games/baccarat/side-bets/ox-6/) where a player 3-card winning 6 pays 40-to-1.
Dog Hand
