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Fan-tan is a casino game in which a bet wins when the remainder of a pile of small objects, after dividing it by four, matches the number you chose. A single-number bet pays 3:1 before commission; at a 5% commission the house edge is 3.75%.
The croupier gathers a pile, covers it with a cup, then removes objects in groups of four. The remainder decides the result; no bet changes it.
That 3.75% assumes an even remainder: each possible result is equally likely. Commission makes a substantial difference: at 2.5% commission, the single-number house edge is 1.875%; at 25%, it is 18.75%. If the remainder is uneven, the break-even probability for a single number at 5% commission is 25.97%.
What fan-tan is
English Wikipedia, in the article “Fan-tan”, describes a commission range of 5–25% across different times and places. It also reports that the game is still played in some Macau casinos, with a commission of 5%.
How a round runs step by step
A round produces a winning position when the croupier has reduced the pile to one, two, three or four objects.
- The croupier gathers a pile of small objects.
- The pile is covered with a cup.
- The croupier removes objects in groups of four.
- The number left identifies the winning position. If the original total divides evenly by four, the game represents that result with four objects remaining.
This counting mechanism is described in English Wikipedia’s article “Fan-tan”. Wizard of Odds says the pile averages about 60 objects, but that is the author’s observation, not a required pile size or a betting rule.
What decides the outcome: the remainder, and why earlier rounds do not change it
The current pile determines the remainder. Earlier rounds do not change how many objects are in that pile, and a number’s absence from recent results does not make it due.
The gambler’s fallacy simulator illustrates why expecting a sequence to compensate for earlier results is not a basis for predicting the next outcome. An even remainder is a calculation assumption, not something established merely by looking at a short run of results.
Bets and payouts
The five bets differ in which numbers win, which produce a push, and how much profit a win pays. The table follows Wizard of Odds’ payouts and house-edge calculations, assuming a 5% commission on winnings and an even remainder.
A payout of X to 1 means profit per unit staked, not counting the stake returned with a win. For Nga Tan and Sheh-Sam-Hong the payout is below 1:1, so it is written as a fraction: 1 to 2 is 0.5:1, 1 to 3 is 1/3:1.
| Bet | What to guess | Payout before commission | After 5% | P(win) | P(push) | House edge |
|---|---|---|---|---|---|---|
| Fan | 1 number | 3:1 | 2.85:1 | 25% | 0% | 3.75% |
| Nim | 2 numbers, one push | 2:1 | 1.9:1 | 25% | 25% | 2.50% |
| Kwok | 2 numbers, both win | 1:1 | 0.95:1 | 50% | 0% | 2.50% |
| Nga Tan | 3 numbers, one push | 0.5:1 | 0.475:1 | 50% | 25% | 1.25% |
| Sheh-Sam-Hong | 3 numbers, all win | 1/3:1 | 0.3167:1 | 75% | 0% | 1.25% |
Educational card: five fan-tan bets with payouts after the 5% commission and house edges of 3.75%, 2.50% and 1.25%Educational card based on Wizard of Odds rules. The 5% commission is the Macau figure; this is not a casino interface.
- Fan: choose one number; it wins, and all others lose.
- Nim: choose a winning number and a push number; all others lose.
- Kwok: choose two numbers; either wins, and all others lose.
- Nga Tan: choose three numbers; two win, one produces a push, and the remaining number loses.
- Sheh-Sam-Hong: choose three numbers; any of them wins, and the remaining number loses.
A push returns the stake with no win or loss, so no commission is taken from it. The 0.3167:1 payout is rounded; for a check use 1/3 × 0.95.
House edge
With an even remainder, the house edge for these bets equals the commission multiplied by the probability of winning and the payout before commission:
House edge = commission × P(win) × payout before commission.
For all five bets, P(win) × payout before commission equals P(loss), so the calculation can also be written as:
House edge = commission × P(loss).
Use the payout before commission; using the after-commission payout would count the deduction twice.
The $40 Fan example
A winning $40 Fan bet produces $114 in net profit at a 5% commission on winnings:
3 × $40 × 0.95 = $114.
The winning stake is also returned; a loss costs $40. This example assumes the payout and commission above, with no additional rounding adjustment. It describes individual outcomes, not the average result of a session.
At a 5% commission and an even remainder, 3.75% is the expected loss per unit staked—not a deduction applied to every round. The house edge calculator explains that measure, but ToolsGambling has no dedicated fan-tan calculator.
How commission changes Fan’s house edge
Higher commission increases the expected loss when the probabilities and payout before commission stay the same. The 0% and 2.5% rows are for comparison only; the Macau figure in the description is 5%.
| Commission | Fan house edge |
|---|---|
| 0% | 0% |
| 2.5% | 1.875% |
| 5% | 3.75% |
| 10% | 7.5% |
| 25% | 18.75% |
The conclusion is conditional: at a 5% commission and an even remainder, Fan has a 3.75% house edge. A different commission changes that figure without changing how the remainder is determined.
What changes the calculation: an uneven remainder
If the remainder is uneven, the calculation must use the actual probability of the chosen number rather than automatically assuming equal probabilities. At a 5% commission, a single-number bet’s break-even probability is 25.97%, or about 26%.
| Probability of the chosen number | Player’s expected result relative to the stake |
|---|---|
| 25% | −3.75% |
| 26% | +0.1% — close to zero |
| 27% | +3.95% |
These figures assume a Fan payout of 3:1 before commission and a 5% commission on winnings. The 25.97% break-even threshold is rounded. The four remainder probabilities sum to 100%: if one number gets 26%, the other three get 74% together.
If a real table’s remainders are uneven, the expected result can change sign. We have no data on real-table remainder distributions: checking this would require reliable outcome frequencies and the table’s actual payout and commission terms. The conditional figures do not establish that a profitable opportunity exists.
Online tables and the card variant Super Fan Tan
The standard fan-tan table above does not automatically apply to online tables or to Super Fan Tan. Wizard of Odds describes Gameplay Interactive’s Super Fan Tan as a card variant, rather than the Macau pile-counting game: the small bet on 6 cards has a 4.27% house edge, the bet on a total of 42 has a 14.64% house edge, and the bet on 83–85 with 12 cards has a 26.23% house edge. These are separate bets in a different variant.
Limits and mistakes
These calculations describe the game conditions above, not verified rules for a particular casino table. We have not verified a specific Macau casino’s rules, online table rules including Evolution’s, or the Venetian Macau rule booklet; the 5% commission comes from a description of the game rather than a check of a current table.
Changing bets changes payouts and the chances of a win or push, but not the remainder. Increasing the stake after a loss does not change the mechanism that decides the outcome.
One session is not the average result: its outcome can differ substantially from mathematical expectation. The session simulator explores that distinction; it does not calculate fan-tan specifically.
A single-number bet swings widely between wins and losses. Decide how much you can afford to lose before playing, and do not increase that limit to chase losses; the guide to how to manage a bankroll explains this approach.
Frequently Asked Questions
The result is decided by the remainder after the croupier removes objects from the pile in groups of four. The final one, two, three or four objects identify the winning position.
A player can choose the bet and stake, but neither changes the remainder. The bet determines which numbers produce a win, a push or a loss.
With an even remainder, Fan has a 25% probability of winning and pays 3:1 before commission. A 5% commission on winnings gives a 3.75% house edge under the formula: commission × P(win) × payout before commission.
A betting strategy does not change the remainder or remove the house edge while the probabilities and commission remain the same. A genuinely uneven remainder would change the calculation, but there is no real-table distribution evidence here to support such a strategy.
Evgeniy Volkov
Verified ExpertFullstack developer with a background in mathematics. I build the calculators and game-style tools on ToolsGambling with Pixi.js and modern web tech, and every result uses transparent probability formulas you can verify yourself.