American Mahjong · 5 hands

13579 Hands in American Mahjong: How They Work, Scoring and Odds

In American mahjong, the 13579 category is the odd-number twin of 2468: only 1, 3, 5, 7 and 9, never an even number. Some lines add a pair of flowers. Our House Card has five 13579 hands, worth 25 to 30 points.

What counts as a 13579 hand

• Only 1, 3, 5, 7 and 9 suit tiles, plus flowers when the line prints them — no winds or dragons on any of our 13579 lines
• A line doesn't have to use all five odd numbers: ours use three, four or all five
• Colors decide which groups share a suit (see reading the card); all five lines are X, so you may call discards
• Jokers can fill any group of three or more, never a single or a pair

Every 13579 hand on our card

• 1s, 3s, 5s and 7s in one suit — two pungs and two kongs, all the same color.
• Pairs and pungs, then 7s and 9s — pairs of 1s and 5s with a pung of 3s in one suit, a pung of 7s and a kong of 9s in another.
• Flowers and three kongs — 5s, 7s and 9s, each in a different suit.
• Kongs across three suits with a pair of 3s — the 1s alone, the 3s and 5s together, the 7s in the third suit.
• 1-3-5-7 and two kongs of 9s — the run of singles gives the highest value.

How jokers work in 13579 hands

Most groups in 13579 hands are pungs and kongs, so jokers fit almost everywhere.

The pairs and the 1-3-5-7 singles must be real tiles:

How 13579 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.

13579 odds

How close your deal is

Odd numbers make up more than half of the suit tiles, but each line needs them in exact amounts. Before the Charleston, a 13-tile deal is within 6 tiles of the nearest 13579 hand 0.89% of the time; after the Charleston, that rises to 4.5%.

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 13579 wins

When the computers play normally, 13579 hands were 3.1% of all wins, collecting 138 points on average. 33% of those wins were self-drawn and 7.0% 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 13579?

We had the player whose deal was closest to 13579 play nothing but 13579 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 13579 played only 13579 hands; the other three played normally. Money is the card value as paid in the game.

The answer: forcing 13579 never beat playing normally.

• From a deal within 7 tiles, forcing 13579 worked 25% of the time for an average of +1; the same kind of deal played normally averaged +16. Deals within 6 tiles are too few (see the Hands column) to say more than that they were no better.
• From within 8 tiles, it worked only 17% of the time (−13 against +18), with someone else winning first 74% of the time.
• Odd tiles are just as useful for Like Numbers and runs, which win far more often. Locking into 13579 gives that up.

Tips for 13579 hands

• Pass evens, winds and dragons in the Charleston — no line here uses a wind or a dragon.
• 9s are the backbone. Three lines need a kong of 9s, and the top line needs two, so a deal with several 9s is a good start.
• Read the colors. The one-suit line and the three-suit lines want very different tiles; decide which by the end of the first Charleston.
• Pairs need real tiles, and a pair can only be called for Mahjong — keep the pairs of 1s and 5s in mind when choosing the second line.

When to switch: if your odd tiles are mostly 3s and 9s with some 6s, look at 369; if they come in pairs, Singles & Pairs has a line of odd pairs too. To get a feel for it, play a few hands of free American mahjong online — the helper shows your closest hands as you go.

Other mahjong styles

The first 13579 line is a single suit made only of pungs and kongs. Chinese and Japanese styles score those two ideas separately: a one-suit hand is Full Flush — qing yi se in Taiwanese mahjong, chinitsu in Japanese riichi — and an all-pungs hand is peng peng hu or toitoi.

FAQ

What is a 13579 hand in mahjong?

A 13579 hand is a line on the American mahjong card made only from the odd numbers 1, 3, 5, 7 and 9, sometimes with flowers. Our card has five of them.

Do you need all five odd numbers?

No. Each line uses only the odd numbers it prints — three, four or all five of them.

Can you use jokers in a 13579 hand?

Yes, in any group of three or more identical tiles. Singles such as the 1-3-5-7 run and every pair must be real tiles.

How many points is a 13579 hand worth?

On our House Card, 13579 hands are worth 25 to 30 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

2468 5 hands Hands built only from 2s, 4s, 6s and 8s — every hand on our card, joker rules, scoring and odds. 369 5 hands Hands built only from 3s, 6s and 9s — 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.