Taiwanese Mahjong · 8 tai

Eight Flowers (Ba Xian Guo Hai) in Taiwanese Mahjong: Tai and Odds

In Taiwanese mahjong, Eight Flowers (八仙過海, ba xian guo hai) is worth 8 tai: all eight flowers of the set — Spring, Summer, Autumn, Winter, Plum, Orchid, Bamboo and Chrysanthemum — end up with one player. You win the moment the eighth arrives, whatever your tiles look like; you don't even need to be ready.

The rules for Eight Flowers

• All eight flowers are yours: completed during the opening flower replacement, or by drawing the eighth during play
• Your tiles don't matter: your 16 tiles can be anything; no ready hand, no winning shape needed
• You win the moment you have all eight, and the hand ends
• It counts as a self-draw: all three other players pay

How Eight Flowers is scored

Eight Flowers ignores your tiles, so hand tai such as self-draw, concealed hand or concealed self-draw don't count; flower tai do. Eight flowers always include both of your own flowers and complete both sets. The tai below are computed live by the same scoring code the game uses (dealer and dealer-streak tai are added on top).

How it relates to other hands

• Seven Rob One: also all eight flowers, but the eighth is drawn by someone else and you rob it; same tai, and only that player pays.
• Flower Set: one set of four flowers is 2 tai. Eight flowers are two sets, which is why a normal win has at most one Flower Set.
• Own seat flower: each seat has two flowers of its own, and Eight Flowers always has both.

Eight Flowers odds

Eight Flowers is too rare to measure directly from computer play. In 12,000 hands of four normal-level computers on this site it came up 1 times in 11,677 wins — far too few to estimate a probability. So we used a separate "flower model":

1. Shuffle, deal and replace flowers exactly as the game does, then let the four players draw in turn, but nobody claims and nobody wins, all the way to an exhaustive draw. Over 2,000,000 shuffled walls, one player collected all eight flowers 0.0048% of the time, about once in 20,800 hands. That's an upper bound: real hands often end with a win long before the wall runs out.
2. Then we weighted each eight-flower moment by how often real hands (from the computer play) are still going at that point: the later the eighth flower arrives, the more likely the hand is already over. That estimate gives about 0.0011% at a real table, once in about 91,600 hands.

This is a model estimate, not a measurement: claims at a human table change who draws which tile, and slower tables come closer to the upper bound. But the size is right: Eight Flowers happens once in tens of thousands of hands — far more often than a Heavenly Hand, yet still pure luck.

Eight Flowers in other mahjong styles

• Hong Kong mahjong also has Eight Flowers and Seven Rob One as limit hands, scored straight at the limit (10 fan by default on our Hong Kong site) (Hong Kong mahjong fan list)
• Chinese Official (Guobiao): each flower is 1 fan, and there is no Eight Flowers hand (Guobiao fan list)

To see whether all eight ever land with you, open a table of online Taiwanese mahjong — flower replacement and tai are handled for you.

FAQ

How many tai is Eight Flowers?

In Taiwanese mahjong Eight Flowers is worth 8 tai. This site adds two own seat flowers and two flower sets, 14 tai in total, plus dealer tai.

Do you need a ready hand for Eight Flowers?

No. You win the moment you have all eight flowers, whatever your tiles.

Who pays for Eight Flowers?

It counts as a self-draw, so all three other players pay. In Seven Rob One only the player who drew the eighth flower pays.

What's the difference from Seven Rob One?

If you draw the eighth flower yourself, it's Eight Flowers; if you already hold seven and someone else draws the eighth, you rob it — that's Seven Rob One.

Related hands

Seven Rob One 8 tai Hold seven flowers and rob the eighth when someone draws it, for 8 tai: who pays and how it differs from Eight Flowers. Flower Set 2 tai All four seasons or all four plants for 2 tai: how it stacks with your own flower, and why there's at most one. Own Seat Flower 1 tai Each flower that matches your seat wind is 1 tai: a flower chart, and why any flower rules out Ping Hu.