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Fu Bacc
Introduction
Fu Bacc could be loosely described as a combination of baccarat and Three Card Poker. It has the card and hand scoring of baccarat and the raise or fold decision of Three Card Poker.
It began a field trial on June 24, 2021, at the Hard Rock in Take Tahoe and I hear it has previously been seen in Washington state.
Rules
- A single 52-card deck is used.
- Cards are scored as in baccarat, as follows:
- Aces = 1 point
- 2 to 9 = Pip value
- 10 to K = 0 points
- As in baccarat, the total points of a hand is taken by adding the points in all cards in a hand. If that total is greater than 9, then the terminal digit is used as the score. Thus, the point value of a hand ranges from 0 to 9. Example: If the player has a 6,7, and 8, then the total points are 21. The tens digit is dropped, for a point value of one for the hand.
- Play starts with the player making an Ante bet. At this time, the player may also make the optional Tie or Lucky Monkey side bets, which are explained later.
- After wagering is closed, the dealer shall give the player two cards and himself one. All cards are dealt face up.
- Certain situation are eligible for a bonus. If the player accepts a bonus, it is treated like an instant win and the player does not need to play out the hand. The player keeps his original wager if he accepts a Bonus. These situations are:
- Player 9 points — Bonus of 2x the Ante.
- Player 8 points — Bonus of 1.5x the Ante.
- Player has two face cards and dealer shows a 9 — Bonus of 1x the Ante.
- Otherwise, if no Bonus is eligible or is refused, the player may either make a Play wager equal to 2x the Ante or fold.
- If the player chose to Play, then he may either take a third card or stand.
- After the player has acted, the dealer shall take a second card automatically.
- The dealer shall take a third card if his two-card hand has a point total of five or less.
- The player's hand shall be compared against the dealer's hand.
- If the player hand has more points, then the Ante and Raise shall both pay 1 to 1.
- If the dealer hand has more points, then the Ante and Raise shall both lose.
- If the player and dealer hand tie, then the Ante shall lose and Raise shall push.
- The Tie side bet win if the player and dealer tie after all cards are dealt. Wins pay 7 to 1.
- The Lucky Monkey side bet pays if the player's initial two cards are both 0-point cards (10 or face cards). Wins pay according to the dealer up card as follows:
- Player 0,0 and Dealer 9 — Pays 30 to 1
- Player 0,0 and Dealer 8 — Pays 20 to 1
- Player 0,0 and Dealer 7 — Pays 15 to 1
- Player 0,0 and Dealer 6 — Pays 10 to 1
- Player 0,0 and Dealer 0 to 5 — Pays 5 to 1
Strategy
The following strategy can be found on the Fu Bacc rack card and was confirmed by Gordonnm888, as known at my Wizard of Vegas.
Ante Analysis
The following table shows my analysis of the Ante bet. The lower right cell shows a house edge of 3.05%.
Ante Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Player raises and wins | 3 | 1,403,360,904 | 0.382958 | 1.148873 |
| Player has two-card 9 and takes bonus | 2 | 24,761,856 | 0.006757 | 0.013514 |
| Player has two-card 8 and takes bonus | 1.5 | 50,629,152 | 0.013816 | 0.020724 |
| Player has two face cards and dealer has 9 | 1 | 26,530,560 | 0.007240 | 0.007240 |
| Tie | -1 | 317,913,976 | 0.086754 | -0.086754 |
| Fold | -1 | 684,046,272 | 0.186667 | -0.186667 |
| Player raises and loses | -3 | 1,157,290,880 | 0.315809 | -0.947426 |
| Total | 3,664,533,600 | 1.000000 | -0.030496 |
The probability the player will make the Play bet is 78.552%. This makes the average wager 2.571041 by the end of the hand. That makes the ratio of the expected loss to total amount bet, what I call the Element of Risk, 3.05%/2.571 = 1.19%.
Tie Analysis
The player is allowed to bet the Tie only. The following is a basic strategy for betting the Tie only.
- Player's two-card total equals dealer's card -- Stand
- Player's two-card total is 6 or more and does not equal dealer's card -- Stand
- Player's two-card total is 5 or less and does not equal dealer's card -- Hit
Following this strategy will result in a house edge of 10.41%.
There are several composition-dependent exceptions to this strategy, which would lower the house edge to 10.30%. Since this figure is still significantly higher than the house edge of the Ante bet, I won't bother to list the Tie bet basic strategy exceptions.
Lucky Monkey Analysis
The following table shows my analysis of the Lucky Monkey side bet. The lower right cell shows a house edge of 5.88%.
Lucky Monkey Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Player 0-0 and dealer 9 | 30 | 480 | 0.007240 | 0.217195 |
| Player 0-0 and dealer 8 | 20 | 480 | 0.007240 | 0.144796 |
| Player 0-0 and dealer 7 | 15 | 480 | 0.007240 | 0.108597 |
| Player 0-0 and dealer 6 | 10 | 480 | 0.007240 | 0.072398 |
| Player 0-0 and dealer 0 to 5 | 5 | 4,080 | 0.061538 | 0.307692 |
| All other | -1 | 60,300 | 0.909502 | -0.909502 |
| Total | 66,300 | 1.000000 | -0.058824 |
Acknowledgements
Usually I do all my own math, but this game is a rare exception. A discussion began about it in my Wizard of Vegas forum while I was on a two-week vacation. By the time I got home, there was a rock solid and confirmed analysis completed.
That said I would like to thank, in no particular order, CharliePatrick, Gordonm888, and ssho88 (as known at Wizard of Vegas) for their outstanding work analyzing this game. The only credit I can take is for the Lucky Monkey side bet, which was easy to analyze.