Fan Tan Calculator: Understanding the Bead Counting Game

Fan Tan is an ancient Chinese game where beads are divided by four and the remainder determines the winner. Our calculator reveals the mathematics behind this simple yet elegant game and why all bets share the same 5% house edge.

What Is Fan Tan?

Fan Tan is a traditional Chinese gambling game where a handful of beads, buttons, or coins are covered by a cup. The dealer removes beads four at a time until 1-4 remain. Players bet on which number (1, 2, 3, or 4) will be left. It's pure chance with elegant simplicity.

Quick Answer: Fan Tan = count beads, remainder wins. Divide by 4, remainder is 1-4. All bets have 5% house edge. Even odds, but commission/reduced payout creates edge. Similar to roulette in simplicity. Can't improve odds. Equal probability for each outcome.

How to Use Our Calculator

Use the Fan Tan Calculator →

Calculate odds and edge for all Fan Tan bet types.

Step-by-Step Instructions

1. Select Bet Type: Single number, pair, etc.

2. View Probability: Mathematical odds

3. See Payout: What it pays

4. Calculate House Edge: True cost

5. Compare Options: All identical edge

Input Fields Explained

Field	Description	Example
Bet Type	Wager chosen	Single (3)
Outcome	Remainder	3
Probability	Win chance	25%
Payout	If win	2.85:1
House Edge	True cost	5.0%
Fair Payout	Break-even	3:1

Game Mechanics

The Counting Process

How it works:

1. Beads placed under cup
2. Dealer removes 4 at a time
3. Continue until 1-4 remain
4. Remainder = winning number

Example:
45 beads total
45 ÷ 4 = 11 remainder 1
Number 1 wins

Possible Outcomes

Only four results:

1: One bead remains
2: Two beads remain
3: Three beads remain
4: Four beads remain (divisible)

Each has 25% probability
Perfectly fair outcomes

Bet Types

Single Number Bets

Bet on 1, 2, 3, or 4:

Probability: 25% (1 in 4)
Fair payout: 3:1
Actual payout: 2.85:1 (varies)

House edge: 5%
From reduced payout

Pair Bets (Nim)

Two numbers win:

Bet covers two adjacent numbers
Example: 1-2 Nim wins on 1 or 2

Probability: 50%
Fair payout: 1:1
Actual payout: 0.95:1

House edge: 5%
Same as single bets

Three-Way Bets (Kwok)

Three numbers win:

Cover three of four numbers
One number loses

Probability: 75%
Fair payout: 0.33:1
Actual payout: ~0.32:1

House edge: 5%
All bets equal

Ssh (Single Bet Variant)

Specific Fan Tan betting:

Bet on number to win outright
Or partial on neighbor
Complex payout structure

Same 5% edge overall
Just different structure

House Edge Analysis

Universal 5% Edge

All bets have same edge:

Single number: 5%
Nim (pairs): 5%
Kwok (three-way): 5%
Ssh variations: 5%

Why same edge?
Mathematical equivalence
Casino sets payouts
Creates uniform margin

Edge Mechanics

How 5% is created:

Fair single bet: 3:1
Actual payout: 2.85:1

Loss: 3 - 2.85 = 0.15
Edge: 0.15/3 = 5%

Alternative:
Commission on wins
Same result

Comparison to Other Games

Fan Tan vs others:

Fan Tan: 5.0%
Roulette (US): 5.26%
Roulette (EU): 2.70%
Baccarat: 1.1%
Craps pass: 1.4%

Moderate house edge
Not great, not terrible

Probability Analysis

Equal Distribution

Each number equally likely:

Number 1: 25%
Number 2: 25%
Number 3: 25%
Number 4: 25%

Perfect randomness
No bias possible
Pure chance game

No Pattern Possible

Why strategies fail:

Each count is independent
Previous results don't matter
No "due" numbers

Like roulette:
Each spin is fresh
No memory in beads

Real-World Examples

Example 1: Single Number Bet

Standard play:

Bet: $20 on Number 3
Beads remaining: 3

Result: WIN

Payout: $20 × 2.85 = $57
Plus original: $77 total return

If lost: -$20
EV: 0.25($57) + 0.75(-$20) = -$1
Edge: 5%

Example 2: Nim Bet

Two-number coverage:

Bet: $20 on 1-2 Nim
Beads remaining: 2

Result: WIN

Payout: $20 × 0.95 = $19
Plus original: $39 total return

50% win rate
Same 5% edge as single

Example 3: Kwok Bet

Three-number coverage:

Bet: $20 on 1-2-3 Kwok
(Loses only on 4)
Beads remaining: 4

Result: LOSE

Lost: $20
75% win rate didn't save you
Same expected loss over time

Example 4: Session Expectations

Playing 100 rounds:

$10 bets on single number:
Expected wins: 25
Expected losses: 75

Wins: 25 × $28.50 = $712.50
Losses: 75 × $10 = $750

Net: -$37.50
Edge: 3.75%... wait

Let me recalculate properly:
Win $28.50, lose $10
EV = 0.25(28.50) + 0.75(-10)
EV = 7.125 - 7.50 = -$0.375
Per $10 bet = 3.75%

Note: Edge varies by payout
Check local rules

Strategy Considerations

No Optimal Strategy

Can't improve odds:

All bets have same edge
No skill element
Pure random outcome

Strategy = bet selection only
Which coverage you prefer
Not mathematical advantage

Bankroll Management

For session play:

Low-moderate variance
25× minimum for singles
Lower for Nim/Kwok

Example:
$500 bankroll
$20 bets = 25 units
Reasonable session length

Social Aspects

Fan Tan is often social:

Group betting allowed
Spectator atmosphere
Traditional in Asian casinos

Part of the experience
Not just mathematical

Common Mistakes

1. Expecting Patterns

Mistake: Tracking previous numbers Problem: Each round independent Fix: Accept randomness

2. Thinking One Bet Is Better

Mistake: Single vs Nim preference Problem: All have same edge Fix: Choose coverage you like

3. Chasing Losses

Mistake: Doubling after loss Problem: Edge remains 5% Fix: Flat betting preferred

4. Misunderstanding Nim/Kwok

Mistake: Thinking coverage reduces risk Problem: Same expected loss rate Fix: Understand EV equivalence

Frequently Asked Questions

Is Fan Tan beatable?

No. 5% house edge on all bets. No skill or strategy can overcome the mathematical disadvantage.

Which bet is best?

All bets have identical 5% house edge. Choose based on preference for payout size vs win frequency.

Can I count to predict outcomes?

No. The number of beads is random. Counting previous rounds provides no advantage.

Is Fan Tan better than roulette?

Similar edge (5% vs 5.26% US, 2.7% EU). Fan Tan is simpler with fewer bet types. Personal preference.

Why do casinos offer Fan Tan?

Popular in Asian markets. Simple to run. Consistent 5% margin. Cultural tradition.

Are online versions fair?

If licensed, yes. RNG determines outcome. Same probabilities as physical game.

Pro Tips

• All bets equal: 5% edge

• Choose by preference: Coverage vs payout

• Accept randomness: No patterns

• Budget appropriately: Entertainment expense

• Simple game: No strategy needed

Related Calculators

• Roulette Odds Calculator - Similar simplicity
• Sic Bo Calculator - Another Asian game
• Baccarat Calculator - Lower edge option
• House Edge Calculator - Compare games
• Probability Calculator - General odds

Conclusion

Fan Tan's elegant simplicity—counting beads until 1-4 remain—creates a pure chance game where all bets share identical 5% house edge. Our calculator reveals why no bet type offers advantage and how the mathematics create this uniform margin.

Calculate Fan Tan Odds Now →

Whether you bet on single numbers at 2.85:1 or Nim pairs at 0.95:1, the house takes the same 5% edge. Our calculator shows the mathematics behind this ancient game's enduring appeal.