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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.
![Fu Bacc Basic Strategy](/wizfiles/img/2733/fu_bacc_strategy2.jpg)
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.