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Scoring curves

Every Hong Kong table converts fan into money with a lookup table, and they do not agree. What the common curves are, why the same hand can pay sixteen times more at one table than another, and how much a self-draw is actually worth on each.

26 Aug 2026 scoringrulesetshouse rules

Before anyone pays, a table converts the hand's fan into points. That conversion is a lookup table — the curve — and rulesets differ in how steeply it climbs. The slope sets how far apart a small hand and a large one land.

4 16 64 256 1024 4096 16384 cap 10 cap 13 Doubles every 2 fan, smoothed Doubles every 2 fan Flat through 4–6 fan Linear Doubles every fan +64 ×3.00 +80 ×2.25 +96 ×2.00 +160 ×2.25 +192 ×2.00 +320 ×2.25 +384 ×2.00 +256 ×1.50 HK standard 3–10 +64 ×3.00 +32 ×1.50 +128 ×3.00 +64 ×1.50 +256 ×3.00 +128 ×1.50 +512 ×3.00 +256 ×1.50 HK (doubling) 3–10 +8 ×3.00 +16 ×3.00 +32 ×3.00 +64 ×3.00 +80 ×2.25 +96 ×2.00 +160 ×2.25 +192 ×2.00 +320 ×2.25 +384 ×2.00 +256 ×1.50 Old-school HK 0–10 +64 ×3.00 +32 ×1.50 +128 ×3.00 +64 ×1.50 +256 ×3.00 +128 ×1.50 +512 ×3.00 +256 ×1.50 LIU (family) 3–10 +20 ×3.00 +25 ×2.25 +30 ×2.00 +35 ×1.88 +40 ×1.80 +45 ×1.75 +50 ×1.71 +55 ×1.69 +60 ×1.67 +50 ×1.50 TVB Championship 2026 1–10 +16 ×3.00 +32 ×3.00 +40 ×2.25 +48 ×2.00 +80 ×2.25 +96 ×2.00 +64 ×1.50 Seattle Rules 2–8 +64 ×3.00 +80 ×2.25 +96 ×2.00 +160 ×2.25 +192 ×2.00 +320 ×2.25 +384 ×2.00 +256 ×1.50 South Wind 3–10 +64 ×3.00 +32 ×1.50 +32 ×1.50 +128 ×3.00 +64 ×1.50 +64 ×1.50 +256 ×3.00 +128 ×1.50 Mahjong Time 3–10 +64 ×1.70 +32 ×1.26 +32 ×1.26 +128 ×2.03 +64 ×1.34 +64 ×1.34 +256 ×2.36 +128 ×1.41 MJB 3–10 0 150 300 450 600 cap 10 cap 13 ↗ off scale ↗ off scale Flat through 4–6 fan Linear ↗ off scale +64 ×3.00 +80 ×2.25 +96 ×2.00 +160 ×2.25 +192 ×2.00 +320 ×2.25 +384 ×2.00 +256 ×1.50 HK standard 3–10 +64 ×3.00 +32 ×1.50 +128 ×3.00 +64 ×1.50 +256 ×3.00 +128 ×1.50 +512 ×3.00 +256 ×1.50 HK (doubling) 3–10 +8 ×3.00 +16 ×3.00 +32 ×3.00 +64 ×3.00 +80 ×2.25 +96 ×2.00 +160 ×2.25 +192 ×2.00 +320 ×2.25 +384 ×2.00 +256 ×1.50 Old-school HK 0–10 +64 ×3.00 +32 ×1.50 +128 ×3.00 +64 ×1.50 +256 ×3.00 +128 ×1.50 +512 ×3.00 +256 ×1.50 LIU (family) 3–10 +20 ×3.00 +25 ×2.25 +30 ×2.00 +35 ×1.88 +40 ×1.80 +45 ×1.75 +50 ×1.71 +55 ×1.69 +60 ×1.67 +50 ×1.50 TVB Championship 2026 1–10 +16 ×3.00 +32 ×3.00 +40 ×2.25 +48 ×2.00 +80 ×2.25 +96 ×2.00 +64 ×1.50 Seattle Rules 2–8 +64 ×3.00 +80 ×2.25 +96 ×2.00 +160 ×2.25 +192 ×2.00 +320 ×2.25 +384 ×2.00 +256 ×1.50 South Wind 3–10 +64 ×3.00 +32 ×1.50 +32 ×1.50 +128 ×3.00 +64 ×1.50 +64 ×1.50 +256 ×3.00 +128 ×1.50 Mahjong Time 3–10 +64 ×1.70 +32 ×1.26 +32 ×1.26 +128 ×2.03 +64 ×1.34 +64 ×1.34 +256 ×2.36 +128 ×1.41 MJB 3–10 0135791113 fan winner collects (log)winner collects
each arrow is one hand won by self-draw instead of off a discard — points gained, and the multiple
Overlay a table
Each curve is drawn only where it is defined: below a table's minimum a hand does not win, so there is no value to plot. Linear is drawn at TVB's 2.5 points per fan. Values are what the winner collects, not the internal base-point number — so TVB reads 10 a fan, 20 for two, 30 for three, the way its players count it. Curves have no payment scheme of their own and are shown at the 4× discard collect every ruleset here uses. On the log scale equal ratios look equal, which makes the shapes comparable; the linear scale shows how large the jumps actually are, and stops at 600 so that doubling-every-fan running to 32,768 does not flatten everything else against the axis.
Self-draw multiplier, with the stakes divided out. Arrow length on the plot above carries a table's stake size as well as its jump, so two tables are only comparable there if they use the same chips. Here they are comparable regardless.
×1.5 ×2.0 ×2.5 ×3.0 settlement alone 0135791113 HK standard HK (doubling) Old-school HK LIU (family) TVB Championship 2026 Seattle Rules South Wind Mahjong Time MJB fan before the self-draw bonus

Select a table above to compare.

The curves

Doubles every 2 fan, smoothed

fan 3–10, winner collects
32 · 64 · 96 · 128 · 192 · 256 · 384 · 512

The ladder the HK old-style reference publishes as the standard conversion — it doubles every 2 fan and fills the gap between, so every fan step changes the payout.

Doubles every 2 fan

fan 3–10, winner collects
32 · 64 · 64 · 128 · 128 · 256 · 256 · 512

Doubles every 2 fan by repeating each value rather than interpolating it. Odd fan adds nothing, so the payout moves in steps at even fan.

Flat through 4–6 fan

fan 3–10, winner collects
32 · 64 · 64 · 64 · 128 · 128 · 128 · 256

Long plateaus — 4, 5 and 6 fan all pay the same. The payout changes only at tier boundaries, so intermediate fan is often worth nothing.

Linear

fan 3–10, winner collects
30 · 40 · 50 · 60 · 70 · 80 · 90 · 100

A fixed number of points per fan, so two fan pays exactly twice one. The flattest shape here: over 1–10 fan the top is 10× the bottom.

Doubles every fan

fan 3–10, winner collects
32 · 64 · 128 · 256 · 512 · 1024 · 2048 · 4096

2^fan, with no flattening at all. Over 3–13 fan the top is 1024× the bottom, which is why tables using it normally cap well below 13.

The spread from smallest to largest hand

One way to compare tables is the ratio between the smallest hand that pays and the largest the table allows. It is the curve evaluated at the two ends of the window, so it depends on the shape and on where the floor and ceiling sit — the three are not separable.

RulesetWindowCurveBottomTopRatio
Mahjong Time3–10 fanFlat through 4–6 fan 8648×
MJB3–10 fanFlat through 4–6 fan 8648×
TVB Championship 20261–10 fanLinear 2.52510×
HK standard3–10 fanDoubles every 2 fan, smoothed 812816×
HK (doubling)3–10 fanDoubles every 2 fan 812816×
LIU (family)3–10 fanDoubles every 2 fan 812816×
Seattle Rules2–8 fanDoubles every 2 fan, smoothed 23216×
South Wind3–10 fanDoubles every 2 fan, smoothed 812816×
Old-school HK0–10 fanDoubles every 2 fan, smoothed 1128128×

Both inputs move it, and here by the same amount. Holding the smoothed ladder fixed and dropping the floor from 3 fan to 0 takes the spread from 16× to 128×; holding the window at 3–10 and swapping that ladder for doubling every fan does the same.

ConfigurationBottomTopRatio
Smoothed ladder, 3–10 fan812816×
Smoothed ladder, 0–10 fan1128128×
Doubling every fan, 3–10 fan81024128×

Two entries in the main table make the point on their own. Seattle Rules has an 8-fan ceiling and a top hand of 32 against HK standard's 128, but it runs the same ladder at half stakes, so its ratio is identical at 16×. Old-school HK runs that same ladder and has the widest spread here at 128×, because it sets no minimum: a 雞糊 chicken hand wins and pays, putting the bottom of the window at 1 point rather than 8.

Self-draw

Self-draw is paid twice over, and the two parts are easy to conflate. The settlement multiple goes from 4× base to 6×, a flat 1.5× that 8 of the 9 rulesets here share and that does not move with fan or curve. On top of that, 自摸 scores a fan of its own — all six systems in the reference give it 1 — so a 3-fan hand self-drawn is a 4-fan hand, and it moves up the curve as well.

Multiply the two and a self-draw at 3 fan pays 3.0× a discard win on the same hand, not 1.5×. How much more depends on where that extra fan lands, which is a property of the curve:

Hand worth HK standardHK (doubling)Mahjong TimeTVB Championship 2026
3 fan 3.00× 3.00× 3.00× 2.00×
4 fan 2.25× 1.50× 1.50× 1.88×
5 fan 2.00× 3.00× 1.50× 1.80×
6 fan 2.25× 1.50× 3.00× 1.75×
7 fan 2.00× 3.00× 1.50× 1.71×
8 fan 2.25× 1.50× 1.50× 1.69×
9 fan 2.00× 3.00× 3.00× 1.67×
10 fan 1.50× 1.50× 1.50× 1.50×

HK (doubling) holds each value for two fan, so the self-draw fan either steps off a plateau or onto one: it is worth 3.00× from even fan and 1.50× from odd, alternating all the way up. Mahjong Time's longer plateaus make it lumpier still. Smoothing the ladder removes the lottery — HK standard stays between 2.00× and 2.25× across its whole window — and a linear scale decays gently from 2.00× to 1.67×.

At the cap the extra fan has nowhere to go, so every table collapses to the bare 1.50×. On a doubling ladder that halves the self-draw's worth between a 9-fan hand and a 10-fan one — 3.00× against 1.50× — and on the smoothed ladder it drops from 2.00× to 1.50×.

Separately, the payment scheme decides which seats fund the premium — the winner's total is unaffected, but the risk each seat carries is not.

SchemeDiscard: discarderDiscard: each other seatSelf-draw: each seat
Spread 2× base 1× base 2× base
Discarder pays all 4× base nothing 2× base

Under spread, a self-draw leaves the discarder's exposure unchanged at 2× base and doubles what the other two seats pay. Under discarder-pays-all the effect runs the other way: the seat that would have paid 4× base pays 2×, and the two that would have paid nothing pay 2× each.

One ruleset breaks the flat 1.5× on the total as well. MJB adds 20 chips per paying seat, and that part does not scale with fan, so it dominates at the bottom of the window: MJB's settlement premium alone is 1.17× at 3 fan and 1.41× at 10.