--- title: "Mahjong Shanten Calculator: What to Discard | Mahjong Lore" description: "Enter 13 or 14 mahjong tiles to see shanten, the best discard and how many unseen tiles improve each choice. Covers seven pairs and thirteen orphans." url: https://mahjonglore.me/mahjong-shanten-calculator/ --- Tile efficiency # Mahjong shanten calculator: what to discard **Shanten is the number of tiles a hand still needs before it is tenpai**, one tile from winning. Enter 14 tiles to see, for every possible discard, the shanten that is left and how many unseen tiles would improve it (ukeire). Enter 13 to see exactly what you are waiting for. Normal hands, seven pairs and thirteen orphans are all counted. ## What shanten means A hand that can win with one more tile is *tenpai*. Shanten counts the steps before that: a **1-shanten** hand needs one useful draw to become tenpai, a 2-shanten hand needs two, and so on. A complete winning hand is written as −1. Every step means drawing a tile you need and discarding one you do not, so a lower shanten is always closer to winning, whatever the hand is worth. Three shapes can win, and the calculator counts each one: - **Sets and a pair**: four sets (sequences, triplets or quads) and a pair, the shape almost every hand uses. - **Seven pairs**: seven different pairs; in riichi two identical pairs do not count as two (EMA Riichi Rules 2025, 4.2.2). - **Thirteen orphans**: one of each terminal and honour plus one more of any of them. The overall shanten is the lowest of the three. Seven pairs is never more than 6-shanten for 13 tiles, so no hand is ever worse than 6-shanten, even when sets and a pair would need eight steps. ## How to choose a discard With 14 tiles, list every different discard and look at two numbers: the shanten that is left, and how many tiles would improve it next turn (*ukeire*, "accepting tiles"). Throw the tile that keeps the shanten lowest; among those, the one that leaves the most tiles that help. The calculator sorts the table that way. **The example above:** 2-3 characters, 5-6-7 characters, 3-4-4-6 circles, 5-7-9 bamboo and a pair of east winds. It is 2-shanten. Most discards keep it 2-shanten, but they are not equal. Throwing the 6 circles leaves 28 tiles that help in 8 kinds: the 1 or 4 characters for 2-3, the 2, 4 or 5 circles around 3-4-4, the 6 or 8 bamboo for 5-7-9, and the third east wind. Throwing the 3 circles instead leaves 24, and throwing one of the east winds breaks the pair and makes the hand 3-shanten. Count tiles that are gone. The calculator starts from four of each tile and subtracts the ones in your hand. Add discards, dora indicators and other players' called sets under *Seen elsewhere* and the counts drop to what can still be drawn. A wait on tiles that are all visible still counts as tenpai under the EMA rules (3.3.8), but it can never win. ## How this calculator counts Many tools use a quick formula: 8 minus twice the number of complete sets, minus partial sets, minus one for a pair. It is right for most hands but goes wrong when a hand holds all four copies of a tile. Take 1-9 of characters with four 1 circles: the formula calls it tenpai on a fifth 1 circles, which does not exist. As the EMA rulebook puts it, a hand cannot wait on a fifth copy (3.3.8). This calculator works out the fewest tiles the hand is missing from any complete hand that can really be built, never more than four of a tile, so that hand is correctly 1-shanten, and almost any draw makes it tenpai. The tile counts can be checked against well-known shapes: the nine-sided wait 1-1-1-2-3-4-5-6-7-8-9-9-9 of one suit is tenpai on all nine tiles of its suit, 23 copies in all, and the thirteen-sided thirteen orphans wait is tenpai on 13 kinds, 39 copies. ## What shanten does not tell you - **Value.** Fastest is not always best. In riichi a hand needs a yaku to win, so a slower route to all simples or a dragon triplet can beat the widest one. Score the finished hand with the [riichi score calculator](https://mahjonglore.me/). - **Wait quality.** Ukeire counts how many tiles improve the hand, not whether the tenpai you reach waits on one tile or eight. - **Safety.** When another player declares riichi, the tile that keeps your hand fastest may be the one that deals into theirs. How likely you are to draw one of those 28 tiles in the next few turns is a card-draw probability question; [Dice Parlor](https://diceparlor.me/) works out draw odds like that. ## Questions about shanten **What does 1-shanten mean in mahjong?** The hand is one useful draw away from tenpai: after drawing one of the right tiles and discarding another, it will be waiting to win. Tenpai itself is 0-shanten. **What is ukeire?** Ukeire ("accepting tiles") is the number of tiles that would lower your shanten if you drew them, counting the copies still unseen. It is the usual way to compare discards that leave the same shanten. **What is the highest shanten a hand can have?** Six, for a 13-tile hand. Sets and a pair can be as bad as 8-shanten and thirteen orphans as bad as 13, but seven pairs never needs more than six steps, so the overall shanten is at most 6. **Does the calculator know about discards and dora indicators?** Only if you add them. Mark them as seen elsewhere and they are taken off the count of tiles left. Your own called sets are taken off automatically. **Why does a hand with four of a tile show 1-shanten when another tool says tenpai?** Because there is no fifth copy to wait on. Shortcut formulas can count a pair or single tile as waiting for a tile you already hold four of; this calculator only counts hands that can really be completed. ## Sources 1. European Mahjong Association, [Riichi Rules for Japanese Mahjong, 2025 edition](https://mahjong.dk/hubfs/Mahjong%20documents/Riichi/Riichi_Rulebook_2025_v1.1.pdf) (version 1.1, August 2025): 3.2 Winning hand, 3.3.8 Tenpai and noten, 4.2 yaku (seven pairs, thirteen orphans). Copy hosted by Mahjong Danmark; [the EMA's original file, archived](https://web.archive.org/web/20251223001014/http://mahjong-europe.org/portal/images/docs/Riichi-rules-2025-EN.pdf). 2. World Riichi Championship, [WRC Rules 2025](https://www.worldriichi.org/wrc-rules) (version 20250526): winning hand shapes and yakuman definitions. Shanten and tile counts are worked out mathematically by this page; the rulebooks define the winning shapes they are measured against. Checked on 5 November 2026.