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Fan Tan
Introduction
Fan Tan is a game found at the larger casinos in Macau. The game uses a pile of white buttons, a cup, and a wand. The game is played on a table about the size of a large craps table. The middle is the dealer's territory, which is covered by a clear plastic dome. On either side of the table are betting areas where up to about six players on each side may play comfortably. The betting portions of the table are plastic. After the outcome is determined all winning bets will be illuminated, the same way as in Sic Bo.
Play starts with the dealer placing a cup over some of the buttons, in my experiece an average of about 60. Then players will place bets among many to choose from. Next, the dealer will remove the cup and use the wand to count off the buttons underneath in groups of four. Bets will pay according to the number of buttons in the last row, which will be from one to four. All wins pay fair odds, less a 5% commission, applied to the win amount. The 5% commission is not applied to pushes. The table belows shows the win on a "to one" basis, after adjusting for the 5% commission.
Following are the types of bets available. I got the names from the Venetian Macau rule booklet.
- Fan: A bet on a single number. Wins pay 3 to 1 before commission, or 2.85 after. House edge is 3.75%.
- Nim: A bet on two numbers, one of which is indicated as a push. The winning number pays 2 to 1 before commission, or 1.9 after. House edge is 2.50%.
- Kwok: A bet on two numbers, both of which win. The winning number pays 1 to 1 before commission, or 19 to 20 after. House edge is 2.50%.
- Nga Tan: A bet on three numbers, one of which is indicated as a push. The winning numbers pay 1 to 2 before commission, or 19 to 40 after. House edge is 1.25%.
- Sheh-Sam-Hong: A bet on three numbers, all of which win. The winning numbers pay 1 to 3 before commission, or 19 to 60 after. House edge is 1.25%.
The following table breaks down the possible outcomes of each bet.
Fan-Tan
| Bet | Win Pays | Prob. Win | Prob. Push | Prob. Loss | Return |
|---|---|---|---|---|---|
| Fan | 2.85 | 0.25 | 0 | 0.75 | -0.0375 |
| Nim | 1.9 | 0.25 | 0.25 | 0.5 | -0.0250 |
| Kwok | 0.95 | 0.5 | 0 | 0.5 | -0.0250 |
| Nga Tan | 0.475 | 0.5 | 0.25 | 0.25 | -0.0125 |
| Sheh-Sam-Hong | 0.316667 | 0.75 | 0 | 0.25 | -0.0125 |
Super Fan Tan
Gameplay Interactive, a provider of live dealer games for Internet casinos, uses cards instead of beads to randomize fan tan. Here is how they do it:
- Cards are scored as follows:
- Ace = 1 point
- 2-10 = Pip value
- J = 11 points
- Queen = 12 points
- King = 13 points
- Deal out 6 or 12 cards (I've seen them do it both ways) and add the points.
- As with conventional fan tan, divide by four and take the remainder, to get a random number from 0 to 3.
They also add three side bets, based on the total points? Here they are, based on the six-card version.
Small Bet — Six Cards
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 1 to 41 | 1 | 3,322,961,668,192 | 0.478660 | 0.478660 |
| 42 to 78 | -1 | 3,619,258,158,896 | 0.521340 | -0.521340 |
| Total | 6,942,219,827,088 | 1.000000 | -0.042680 |
The Big bet is just the flip version, winning on a total of 43 to 78. Note how a total of 42 loses both ways. However, they have a bet for that too. The following table shows the bet on 42, which pays 19 to 1, has a house edge of 14.64%.
Total of 42 — Six Cards
| Bet | House Edge | |||
|---|---|---|---|---|
| 42 | 19 | 296,296,490,704 | 0.042680 | 0.810927 |
| All other | -1 | 6,645,923,336,384 | 0.957320 | -0.957320 |
| Total | 6,942,219,827,088 | 1.000000 | -0.146393 |
Next, here are the same tables for a total of 12 cards. Note the average total if 84. The first table shows the Small bet, which wins on a total of 12 to 82, has a house edge of 9.22%.
Small Bet — 12 Cards
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 12 to 82 | 1 | 21686454012209442525456 | 0.453891 | 0.453891 |
| 83 to 156 | -1 | 26092505493378898333464 | 0.546109 | -0.546109 |
| Total | 47778959505588340858920 | 1.000000 | -0.092217 |
A total of 83 to 85 is the middle where both Big and Small bets lose. The next table shows a bet on falling in that range, which pay 7 to 1, has a house edge of 26.23% (ouch!).
Total of 83 to 85 — 12 Cards
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 83 to 85 | 7 | 4406051481169455808008 | 0.092217 | 0.645522 |
| All other | -1 | 43372908024418885050912 | 0.907783 | -0.907783 |
| Total | 47778959505588340858920 | 1.000000 | -0.262261 |
Acknowledgements
My thanks to 7craps and Pari/GP for their help getting more than 15 decimal places in the 12-card tables above.