American Mahjong · 5 hands

369 Hands in American Mahjong: How They Work, Scoring and Odds

In American mahjong, the 369 category uses only three numbers — 3, 6 and 9 — usually with flowers, winds or a dragon to fill the hand. Our House Card has five 369 hands, worth 25 to 35 points.

What counts as a 369 hand

• Only 3s, 6s and 9s among the suit tiles, plus flowers, winds or dragons when the line prints them
• Every line uses all three numbers at least once
• Colors decide which groups share a suit (see reading the card); a dragon in the same color goes with that suit (Green with bams, Red with craks, Soap with dots)
• X hands may expose groups by calling discards; the C line stays concealed
• Jokers can fill any group of three or more, never a single or a pair

Every 369 hand on our card

• 3-6-9 in one suit plus a dragon kong — the dragon belongs to a different suit.
• Flowers and 3-6-9 in three suits — a kong, a pung and a kong.
• Pairs of 3-6-9 and two kongs — the pairs in one suit, kongs of 3s and 6s in another.
• NEWS and 3-6-9 in three suits — the four winds are singles.
• 3-6-9 and a matching dragon, concealed — one suit plus that suit's dragon, worth the most.

How jokers work in 369 hands

Pungs and kongs take jokers in every line, including the concealed one — concealed only means you can't call discards to expose groups.

The pairs in the third line and the NEWS singles in the fourth must be real:

How 369 hands are scored

Each hand pays its card value, and a hand built with no jokers at all is worth double. On a discard, the player who discarded pays twice the value and the other two pay once; on a self-drawn win, all three pay twice. The tables are worked out by the game's own scoring code.

369 odds

How close your deal is

Three numbers out of nine is a narrow target, but most lines spread across suits and add flowers or winds. Before the Charleston, a 13-tile deal is within 6 tiles of the nearest 369 hand 0.98% of the time; after the Charleston, that rises to 5.5%.

Source: 20,000 random 13-tile deals (jokers and flowers included), before the Charleston.

Source: 1,500 games of computer-vs-computer play on this site (normal level, Charleston included). Each computer has its own slight taste for categories.

How often 369 wins

When the computers play normally, 369 hands were 4.0% of all wins, collecting 145 points on average. 45% of those wins were self-drawn and 1.8% used no jokers.

Source: 1,500 games of computer-vs-computer play on this site (normal level, Charleston included). Each computer has its own slight taste for categories.

Is it worth forcing 369?

We had the player whose deal was closest to 369 play nothing but 369 hands — Charleston, discards, calls and wins — while the other three played normally, and compared the result with the same kind of deal played normally.

Source: 1,500 games of computer play on this site. In each, the player whose deal was closest to 369 played only 369 hands; the other three played normally. Money is the card value as paid in the game.

The answer: forcing 369 cost money in every group.

• From a deal within 7 tiles, forcing 369 worked 26% of the time for an average of +4; the same kind of deal played normally averaged +34.
• From within 8 tiles, it worked 20% of the time (−7 against +19), and someone else won first 69% of the time.
• Deals within 6 tiles made it more often, but there were only a few dozen of them, so that row is a rough guide at best. With only three numbers to work with, two thirds of the suit tiles are dead weight to a 369 chaser.

Tips for 369 hands

• Pass 1s, 2s, 4s, 5s, 7s and 8s in the Charleston once 369 is your plan — none of them fit.
• Count across suits. Four of the five lines use two or three suits, so 3s in bams and 6s in craks still help.
• Hold flowers and winds. One line needs a pung of flowers, another NEWS, another a pair of flowers.
• 3s and 9s overlap with 13579. If they keep coming but the 6s don't, the odd-number lines may be closer.

When to switch: with lots of 3s, 9s and other odd numbers, move to 13579; with pairs of 3s, 6s and 9s in two suits, the 369 pairs line in Singles & Pairs may be closer. Play a few hands of free American mahjong online — the helper shows your closest hands as you go.

FAQ

What is a 369 hand in mahjong?

A 369 hand is a line on the American mahjong card that uses only the numbers 3, 6 and 9, often with flowers, winds or a dragon. Our card has five of them.

Can you use jokers in a 369 hand?

Yes, in any group of three or more identical tiles — even in the concealed line. Singles such as NEWS and every pair must be real tiles.

What does the concealed 369 line mean?

You can't call discards to expose groups for it; you build it from your own draws and can only take a discard for the tile that wins.

How many points is a 369 hand worth?

On our House Card, 369 hands are worth 25 to 35 points, doubled if you use no jokers.

Is this the official NMJL card?

No. The National Mah Jongg League publishes a new copyrighted card every year. This site uses its own original card with the same kinds of categories, so the exact lines differ.

Related categories

13579 5 hands Hands built only from 1s, 3s, 5s, 7s and 9s — every hand on our card, joker rules, scoring and odds. 2468 5 hands Hands built only from 2s, 4s, 6s and 8s — every hand on our card, joker rules, scoring and odds. Singles & Pairs 5 hands Seven pairs, no jokers, always concealed — every hand on our card, why jokers don't work, scoring and odds.