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Natural Hand Side Bets
Introduction
There are various baccarat side bets based on a Banker or Player obtaining a natural hand. This page lists those I have heard of.
Natural 8
The Natural 8 bet pays if the chosen side, Banker or Player, has a natural total of 8. Wins can pay either 8 or 9 to 1. The odds are the same on both the Banker and Player side.
I have never actually seen these side bets but believe they were popular in the 1960's, when Ed Thorp wrote a paper for the Journal of the American Statistical Association on how to beat this bet, and the Natural 9, by card counting. Perhaps that explains why it seems to be no longer around.
The following table shows the odds for a win of 9 to 1. The lower right cell shows 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 |
The following table shows the odds for the Natural 8 bet at a win of 8 to 1. The lower right cell shows 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 |
Obviously, this bet, and the Natural 9, would be highly vulnerable to card counters. There are some links below in the External Links section for more information on that.
Natural 9
The Natural 9 bet pays if the chosen side, Banker or Player, has a natural total of 9. Wins can pay either 8 or 9 to 1. The odds are the same on both the Banker and Player side.
The following table shows the odds for a win of 9 to 1. The lower right cell shows a house edge of 5.10%.
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 following table shows the odds for the Natural 8 bet at a win of 8 to 1. The lower right cell 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 or 9 is a pair of side bets on the Banker and Player hands that the chosen side will have a natural two-card total of 8 or 9. The bets can be found at Internet casinos using Ezugi software in their Knockout Baccarat game.
The following table shows the odds for both at a win of 9 to 1. The lower right cell shows a house edge of 5.28%.
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 gaming casinos by SA Gaming offer this pair of bets, but wins pay only 3.5. This increases the house edge to 14.75%.
External Links
- A Favorable Side Bet in Nevada Baccarat by Edward O. Thorp and William E. Walden, first published in the Journal of the American Statistical Association, Vol. 61, No. 314, Part 1 (Jun., 1966), pp. 313-328.
- Review of “A Favorable Side Bet in Nevada Baccarat,” by Thorp and Walden by Eliot Jacobson from A.P. Heat.
- Card Counting the Natural 9 and Natural 8 Baccarat Side Bets by Eliot Jacobson from A.P. Heat.