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Fan Tan

Introduction

Fan Tan is a traditional game commonly seen at the major casinos in Macau. It utilizes a collection of white buttons, a cup, and a wand. The game is played on a table similar in size to a large craps table, with the central area being designated for the dealer, encapsulated within a transparent plastic dome. On both sides of this table are designated betting sections, comfortably accommodating up to six players each. The betting areas are constructed from plastic material. Once the outcome is revealed, winning bets are highlighted, reminiscent of the way winners are displayed in Sic Bo.

The game begins when the dealer places a cup over a selection of buttons, typically around 60. Following this, players can place bets from a variety of options. Afterward, the dealer lifts the cup and utilizes the wand to count the buttons beneath in groups of four. Payouts are determined by the number of buttons revealed in the final row, which can range from one to four. All winning bets are paid at standard odds, with a deduction of a 5% commission applied to the winning amount, though this commission does not affect bets that result in a push. The table below illustrates the payouts on a 'to one' basis after taking the 5% commission into account.

Below are the different types of bets you can place. I've gathered these names from the official rule booklet of Venetian Macau.

  • Fan : A wager on a specific number. Payouts are 3 to 1 before the commission is deducted, or 2.85 after. The house edge stands at 3.75%.
  • Nim : A wager on a pair of numbers, where one number is designated as a push. The winning number yields a payout of 2 to 1 prior to the commission, or 1.9 after. The house edge is 2.50%.
  • Kwok : A bet on two numbers, where both must win. The payout for the winning number is 1 to 1 before commission, or 19 to 20 following it. The house edge is again set at 2.50%.
  • Nga Tan : A bet covering three numbers, where one is considered a push. Payouts for the winning numbers amount to 1 to 2 before the commission, or 19 to 40 after. The house edge is a low 1.25%.
  • Sheh-Sam-Hong : A wager on three numbers, with all of them needing to win. The payouts are 1 to 3 before commission is taken out, or 19 to 60 after. The house edge remains at 1.25%.

The table that follows provides a detailed breakdown of potential outcomes for each type of 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

Interactive gameplay featuring super Fan Tan with six cards.

Gameplay Interactive A company that provides live dealer games for online casinos utilizes cards instead of beads to determine outcomes in Fan Tan. Here’s their approach:

  1. Cards are scored as follows:
    • Ace = 1 point
    • 2-10 = Pip value
    • J = 11 points
    • Queen = 12 points
    • King = 13 points
  2. They deal out either 6 or 12 cards (I've witnessed both methods) and tally up the total points.
  3. Similar to traditional Fan Tan, divide the total by four and note the remainder to generate a random number that ranges from 0 to 3.

They also incorporate three additional side bets based on the accumulated points. Here’s a detailed overview for the version using six cards.

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 mirrors the straightforward version, winning when the total is between 43 and 78. Note that a total of 42 results in a loss for both bets. Nonetheless, there’s an option for that scenario as well. The subsequent table illustrates the bet on 42, which offers a payout of 19 to 1 and 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

fan tan gameplay interactive

Next, let’s review similar tables for a scenario involving 12 cards. The average total here is 84. The first table outlines the Small bet, which wins for totals between 12 and 82, and carries 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

When the total falls between 83 and 85, both Big and Small bets lose. The next table indicates a wager for totals within this range, which pays out at 7 to 1 and has a house edge of 26.23% (quite steep!).

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 We appreciate their assistance in achieving over 15 decimal places for the 12-card tables above.