American Mahjong · 5 hands

2468 Hands in American Mahjong: How They Work, Scoring and Odds

In American mahjong, the 2468 category is made only from the even numbers 2, 4, 6 and 8 — no odd numbers at all. Some lines add flowers or a dragon. Our House Card has five 2468 hands, worth 25 to 30 points.

What counts as a 2468 hand

• Only 2, 4, 6 and 8 suit tiles, plus flowers or dragons when the line prints them
• The colors on the card decide which groups share a suit and which must differ (see reading the card)
• X hands may expose groups by calling discards; C hands must stay concealed
• Jokers can fill any group of three or more identical tiles, never a single or a pair

Every 2468 hand on our card

• Pungs and kongs in one suit — the first line keeps every group the same color, so the whole hand is one suit.
• Flowers plus three kongs — two suits: the 4s and 8s match, the 6s must be different.
• Pairs, pungs and four dragons — the dragon kong matches the third suit (Green with bams, Red with craks, Soap with dots).
• Three flowers, two pairs, a pung and a kong — the pairs need real tiles, so this line is harder than it looks.
• 2468 twice — the run of singles in two suits gives the category its name, and it is worth the most.

How jokers work in 2468 hands

Jokers are what make most 2468 hands possible: any pung, kong or flower group of three or more can take them.

The singles in 2468 and every pair must be real tiles. In the last line only the two pungs can take a joker:

How 2468 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 under each example above are worked out by the game's own scoring code.

2468 odds

How close your deal is

Most deals are a long way from any single category. Before the Charleston, a 13-tile deal is within 6 tiles of the nearest 2468 hand 2.0% of the time; after the Charleston, with three rounds of passing to shape the hand, that rises to 8.8%.

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 2468 wins

When the computers play normally — each one picks whatever its hand leans toward — 2468 hands were 6.5% of all wins, collecting 141 points on average. 34% of those wins were self-drawn and 5.6% 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 2468?

We also had the player whose deal was closest to 2468 play nothing but 2468 hands — Charleston, discards, calls and wins — while the other three played normally, and compared the result with the same deals played normally.

Source: 1,500 games of computer play on this site. In each, the player whose deal was closest to 2468 played only 2468 hands; the other three played normally. Money is the card value as paid in the game.

The answer was clear: forcing 2468 cost money in every group.

• Even from a deal within 6 tiles of a 2468 hand, forcing it worked 30% of the time, for an average result of +11; the same kind of deal played normally averaged +28.
• From within 8 tiles, forcing it worked only 17% of the time (−12 against +8 playing normally), and someone else won first 73% of the time.
• The reason is flexibility. A player who plays normally keeps every category open and drifts to whatever the Charleston and the draws support — usually Like Numbers or a run. Locking into 2468 throws that away.

Tips for 2468 hands

• Pass odd numbers and winds early in the Charleston, but keep jokers — you can't pass them anyway.
• Count your even tiles across all three suits, not just one: two of the five lines use two or three suits.
• Pairs are the bottleneck. Pairs can't take jokers and can only be called for Mahjong, so a line with two pairs is harder than one with only pungs and kongs.
• Watch the discards. Once two 6s of a suit are gone, any line that needs a pair or kong of 6s in that suit is in trouble.

When to switch: if the Charleston brings you mostly odd numbers or consecutive tiles, move to 13579 or a consecutive run instead of fighting for evens. The best way to learn the feel is to play a few hands of free American mahjong online — the helper shows your closest hands as you go.

Other mahjong styles

American mahjong is the only style built around a card. Taiwanese 16-tile mahjong scores tai, Japanese riichi uses yaku, and Hong Kong mahjong counts fan.

FAQ

What is a 2468 hand in mahjong?

A 2468 hand is a line on the American mahjong card made only from the even numbers 2, 4, 6 and 8, sometimes with flowers or a dragon. Our card has five of them.

Can you use jokers in a 2468 hand?

Yes, in any group of three or more identical tiles. Singles and pairs — including the 2-4-6-8 run of singles — must be real tiles.

How many points is a 2468 hand worth?

On our House Card, 2468 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.

Which category is easiest to win with?

In our computer games, 2468 was 6.5% of all wins. Like Numbers and consecutive runs were won more often because they can use any number.

Related categories

Like Numbers 5 hands One number, any number, across all three suits — every hand on our card, joker rules, scoring and odds. 13579 5 hands Hands built only from 1s, 3s, 5s, 7s and 9s — every hand on our card, joker rules, scoring and odds. 2026 5 hands Hands that spell the year with 2s, 6s and Soap as the zero — every hand on our card, joker rules, scoring and odds.