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Natural Hand Side Bets
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Introduction
There are various baccarat Bets connected to a Banker or Player achieving a natural hand. This section highlights those I've come across.
Natural 8
The Natural 8 wager pays out if the selected side, either Banker or Player, reaches a natural hand value of 8. Payouts can be either 8 to 1 or 9 to 1, with consistent odds for both sides.
While I've yet to see these types of side bets, I understand they gained popularity in the 1960s, during which Ed Thorp published insights in the Journal of the American Statistical Association about winning strategies for this bet and the Natural 9 through card counting techniques. This may clarify their current rarity.
This table illustrates the odds associated with winning at 9 to 1. The cell in the bottom right corner reflects a house edge of 5.47%.
Natural 8 — Win Pays 9 to 1
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 9 | 472,508,456,071,680 | 0.094532 | 0.850788 |
| Loss | -1 | 4,525,889,819,431,680 | 0.905468 | -0.905468 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.054680 |
This table lays out the odds for the Natural 8 bet, with a winning payout of 8 to 1. The bottom right cell indicates a house edge of 14.92%.
Natural 8 — Win Pays 8 to 1
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 8 | 472,508,456,071,680 | 0.094532 | 0.756256 |
| Loss | -1 | 4,525,889,819,431,680 | 0.905468 | -0.905468 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.149212 |
It's apparent that both this wager and the Natural 9 would be particularly sensitive to card counting strategies. Below, in the External Links section, you can find more details on this subject.
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Natural 9
The Natural 9 bet pays when the selected side, either Banker or Player, achieves a natural total of 9. Payouts can either be 8 to 1 or 9 to 1, with the same odds for both.
The table presented shows the winning odds at a rate of 9 to 1, with a house edge of 5.10% noted in the lower right cell.
Natural 9 — Win Pays 9 to 1
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 9 | 474,361,430,409,216 | 0.094903 | 0.854124 |
| Loss | -1 | 4,524,036,845,094,140 | 0.905097 | -0.905097 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.050973 |
The subsequent table reveals the odds for a Natural 8 bet at an 8 to 1 winning rate. The lower right corner shows a house edge of 14.59%.
Natural 9 — Win Pays 8 to 1
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 8 | 474,361,430,409,216 | 0.094903 | 0.759222 |
| Loss | -1 | 4,524,036,845,094,140 | 0.905097 | -0.905097 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.145876 |
Natural 8 or 9
The Natural 8 and 9 side bets are wagers on whether the chosen Banker or Player hand will total a natural 8 or 9 with two cards. You can find these bets in online casinos that utilize Ezugi software, specifically in their Knockout Baccarat variant.
The following table indicates the odds for both side bets priced at a winning rate of 9 to 1, with a house edge of 5.28% shown in the lower right cell.
Natural 8 or 9
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 4 | 946,869,886,480,896 | 0.189435 | 0.757739 |
| Loss | -1 | 4,051,528,389,022,460 | 0.810565 | -0.810565 |
| Total | 4,998,398,275,503,360 | 1.000000 | -0.052827 |
Live casinos powered by SA Gaming offer these two side bets, however, they only payout 3.5, which raises the house edge to 14.75%.
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External Links
- A Beneficial Side Bet for Nevada Baccarat. Authored by Edward O. Thorp and William E. Walden, originally published in the Journal of the American Statistical Association, Volume 61, Number 314, Part 1 (June 1966), pages 313-328.