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Winning Total
Introduction
The Knockout Blackjack game by Ezugi, a provider of live dealers for Internet casinos, features bets on the total of the winning hand. I don't know that these bets have a particular name, so I will call them the "Winning Total" bets.
Rules
To avoid confusion, I capitalize the names of the bets in baccarat while using lower case to refer to the people playing the game.
- The drawing rules are the same as in conventional baccarat, which I assume the reader is familiar with.
- In addition to the usual bets, and a pair of bets on a Player or Banker natural, there are five different bets on the total points in the winning hand. The player does not need to specify which hand will be the winning hand, just how many points it will have.
- The bet on a winning total of 9 pays 2 to 1.
- The bet on a winning total of 8 pays 3 to 1.
- The bet on a winning total of 7 pays 4 to 1.
- The bet on a winning total of 5 or 6 pays 3 to 1.
- The bet on a winning total of 1 to 4 pays 7 to 1.
Analysis
The following table shows the probability of all possible winning totals as well as a tie.
Winning Combinations
| Winning Total |
Combinations | Probability |
|---|---|---|
| 9 | 1,199,924,299,542,530 | 0.240062 |
| 8 | 1,085,737,655,808,000 | 0.217217 |
| 7 | 792,323,304,390,656 | 0.158515 |
| 6 | 581,891,199,647,744 | 0.116416 |
| 5 | 339,554,206,113,792 | 0.067933 |
| 4 | 249,525,561,229,312 | 0.049921 |
| 3 | 135,874,201,878,528 | 0.027184 |
| 2 | 89,010,106,982,400 | 0.017808 |
| 1 | 48,930,313,437,184 | 0.009789 |
| Tie | 475,627,426,473,216 | 0.095156 |
| Total | 4,998,398,275,503,360 | 1.000000 |
The following table shows the probability and expected return of all five Winning Total bets as well as for a Tie.
Expected Returns
| Winning Total |
Pays | Combinations | Probability | Expected Return |
|---|---|---|---|---|
| 9 | 2 | 1,199,924,299,542,530 | 0.240062 | -0.279815 |
| 8 | 3 | 1,085,737,655,808,000 | 0.217217 | -0.131132 |
| 7 | 4 | 792,323,304,390,656 | 0.158515 | -0.207423 |
| 5 or 6 | 3 | 921,445,405,761,536 | 0.184348 | -0.262607 |
| 1 to 4 | 7 | 523,340,183,527,424 | 0.104702 | -0.162387 |
| Tie | 8 | 475,627,426,473,216 | 0.095156 | -0.143596 |
| Total | 4,998,398,275,503,360 | 1.000000 |
Strategy
With a house edge ranging from 13.11% to 27.98%, I would leave the Winning total bets alone, at least at the pays above. If someone points a gun to your head and forces you to bet one of them, the best bet is on a winning total of 8. I might add these bets are probably countable (shut up Wiz!), although they have a long house edge hole to climb out of. I'll leave the details of how to do that as an exercise for the reader.
External Links
Discussion about the Winning Total bets in my forum at Wizard of Vegas.