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Even and Odd
Introduction
I first noticed the Even and Odd bets at the baccarat game by Triple PG software, a provider of games for Internet casinos. They are a set of four side bets, as follows:
- Player total is even
- Player total is odd
- Banker total is even
- Banker total is odd
In the Triple PG game, all bets pay 0.86 to one, except the Player Odd total pays 0.9 to 1.
I would later see these side bets at eBET, which pay more generous odds, as follows:
- Player odd: 0.96
- Player even: 0.90
- Banker odd: 0.94
- Banker even: 0.94
Analysis
As usual, when writing about baccarat, I capitalize the names of bets, in particular the Player, to avoid confusion.
The following table shows my analysis of the Player Even bet. The lower right cell shows that at a win pay of 0.86 to 1, the house edge is 5.31%.
Player Even
| Even | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Even | 0.86 | 2,544,590,787,125,760 | 0.509081 | 0.437810 |
| Odd | -1 | 2,453,807,488,377,600 | 0.490919 | -0.490919 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.053109 |
The following table shows my analysis of the Player Odd bet. The lower right cell shows that at a win pay of 0.86 to 1, the house edge is 6.73%.
Player Odd
| Even | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Odd | 0.9 | 2,453,807,488,377,600 | 0.490919 | 0.441827 |
| Even | -1 | 2,544,590,787,125,760 | 0.509081 | -0.509081 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.067254 |
The following table shows my analysis of the Banker Odd bet. The lower right cell shows that at a win pay of 0.86 to 1, the house edge is 6.93%.
Banker Even
| Even | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Even | 0.86 | 2,501,034,641,977,860 | 0.500367 | 0.430316 |
| Odd | -1 | 2,497,363,633,525,500 | 0.499633 | -0.499633 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.069317 |
The following table shows my analysis of the Banker Odd bet. The lower right cell shows that at a win pay of 0.9 to 1, the house edge is 7.07%.
Banker Odd
| Even | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Odd | 0.86 | 2,497,363,633,525,500 | 0.499633 | 0.429684 |
| Even | -1 | 2,501,034,641,977,860 | 0.500367 | -0.500367 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.070683 |
The image is from the eBET live dealer studio.
The following table shows the house edge on all four bets for every pay from 0.85 to 1.03 in groups of 0.01.
Even/Odd House Edge Summary
| Pays | Player Odd | Player Even | Banker Odd | Banker Even |
|---|---|---|---|---|
| 0.85 | 9.18% | 5.82% | 7.57% | 7.43% |
| 0.86 | 8.69% | 5.31% | 7.07% | 6.93% |
| 0.87 | 8.20% | 4.80% | 6.57% | 6.43% |
| 0.88 | 7.71% | 4.29% | 6.07% | 5.93% |
| 0.89 | 7.22% | 3.78% | 5.57% | 5.43% |
| 0.90 | 6.73% | 3.27% | 5.07% | 4.93% |
| 0.91 | 6.23% | 2.77% | 4.57% | 4.43% |
| 0.92 | 5.74% | 2.26% | 4.07% | 3.93% |
| 0.93 | 5.25% | 1.75% | 3.57% | 3.43% |
| 0.94 | 4.76% | 1.24% | 3.07% | 2.93% |
| 0.95 | 4.27% | 0.73% | 2.57% | 2.43% |
| 0.96 | 3.78% | 0.22% | 2.07% | 1.93% |
| 0.97 | 3.29% | -0.29% | 1.57% | 1.43% |
| 0.98 | 2.80% | -0.80% | 1.07% | 0.93% |
| 0.99 | 2.31% | -1.31% | 0.57% | 0.43% |
| 1.00 | 1.82% | -1.82% | 0.07% | -0.07% |
| 1.01 | 1.33% | -2.33% | -0.43% | -0.57% |
| 1.02 | 0.83% | -2.83% | -0.93% | -1.07% |
| 1.03 | 0.34% | -3.34% | -1.43% | -1.57% |