Why a Mahjong primer?#
If you work in game AI you know Go, chess, poker, and maybe Hanabi. Chinese Standard Mahjong (国标麻将) is less familiar to Western researchers but is a wonderful testbed: it is a four-player, imperfect-information, stochastic, sequential game with a sparse and oddly shaped reward. This post teaches just enough of the game to understand why it is hard for RL, with no prior Mahjong knowledge assumed. It is the companion primer to our build notes for the IJCAI 2026 Mahjong AI Competition.
1. Tiles and the goal#
There are 34 tile types, 4 copies each → 136 tiles. Three number “suits” run 1–9:
- W (characters / 万), B (dots / 饼), T (bamboo / 条)
plus honor tiles (4 winds, 3 dragons) that have no numeric order.
Each player holds 13 tiles. On your turn you draw a 14th and discard one, going around the table. A winning hand is 4 sets + 1 pair, where a set is either:
- a triplet — three identical tiles, e.g. \(\text{W2 W2 W2}\); or
- a sequence — three consecutive in one suit, e.g. \(\text{T4 T5 T6}\)
- (a kong — four identical — is a special set that grants an extra draw)
So a complete hand has \(4 \times 3 + 2 = 14\) tiles. Example:
$$ \underbrace{\text{W2 W3 W4}}_{\text{seq}}\;\; \underbrace{\text{B5 B6 B7}}_{\text{seq}}\;\; \underbrace{\text{T1 T1 T1}}_{\text{triplet}}\;\; \underbrace{\text{T7 T8 T9}}_{\text{seq}}\;\; \underbrace{\text{J1 J1}}_{\text{pair}} $$2. Claiming other players’ discards#
You don’t only draw from the wall — you can claim a tile someone discards to finish a set:
- Peng (碰): you hold two of a tile; claim a third anyone discards → exposed triplet.
- Chi (吃): claim a discard to complete a sequence — but only from the player to your left.
- Gang (杠): make a four-of-a-kind (kong).
Claiming reveals that set face-up and jumps you straight to discarding. Claims are how you speed up — and, as we’ll see, how you commit to a plan.
3. Shanten: distance to “ready”#
A natural progress metric is shanten (上听数): the minimum number of tile swaps until your hand is ready (one tile away from completion). Shanten 0 is tenpai (ready); higher is further away. A rough lower bound used in practice is
$$ \text{shanten} \approx 8 - 2 m - \max(1,\, t + p) $$where \(m\) is completed sets, \(t\) partial sets, \(p\) pairs. Minimizing shanten greedily — “always take the move that gets me closest to ready” — is the obvious baseline policy.
And it is exactly the trap. Here is why.
4. The twist that defines the game: the 8-fan floor#
In Chinese Standard Mahjong, a complete 4-sets-+-pair hand is not automatically a win. It must also score at least 8 fan (番). Fan are points awarded for patterns, from a table of 81. If you declare a win worth fewer than 8 fan, it is an illegal move with a heavy penalty.
So there are really two objectives, and they conflict:
- Be ready (low shanten).
- Be worth ≥ 8 fan when you get there.
A plain hand of mixed sequences scores ~0–4 fan — complete but unwinnable. The points live in structured hands you must commit to early:
| Pattern | Description | Fan |
|---|---|---|
| 清一色 (full flush) | all tiles in one suit | 24 |
| 组合龙 (knitted straight) | 1-4-7 / 2-5-8 / 3-6-9 across the three suits | 12 |
| 混一色 (half flush) | one suit + honors only | 6 |
| 碰碰和 (all triplets) | every set is a triplet | 6 |
Reaching the 8-fan floor almost always means sacrificing speed for value — passing a tempting claim that would make you “ready” cheaply, in order to chase a hand that is actually worth winning.
The reward, stated cleanly#
Let \(f\) be fan above the floor. A self-drawn win pays the winner \(3(8+f)\) and each opponent \(-(8+f)\); a win on a discard pays the winner \(24+f\), the discarder \(-(8+f)\), and the other two \(-8\). An illegal action pays \(-30\) to the offender and \(+10\) to each of the others. So the reward is sparse (most hands end in a draw worth 0), highly asymmetric, and dominated by a legality cliff — getting the 8-fan rule wrong costs more than most wins earn.
5. Why a naive bot draws every single game#
Picture a shanten-minimizing bot. You hold \(\text{W2 W2}\) and an opponent discards \(\text{W2}\). Peng-ing instantly forms a triplet and lowers shanten, so the greedy bot takes it. But if your other tiles are a three-suit jumble, you have now rushed to ready on a hand worth maybe 2 fan. You are one tile from a “win” you can never legally declare. You sit there discarding until the wall is exhausted, and the game ends 0–0–0–0.
This is not hypothetical — it is exactly what our first bots did: clean, legal, fast play, and a draw in ~75% of games, with the best hand anyone reached worth only 4 fan. The bug was not in the code; it was in the objective. A shanten-only rule is fan-blind: it optimizes distance and ignores value, so it never deliberately builds 清一色 or 碰碰和 — the only hands that clear the 8-fan bar.
The fix mirrors what a human expert does: don’t peng that W2. Keep collecting one suit, or peng only tiles that build all-triplets. Trade speed for value, because a fast sub-8-fan hand is worthless.
6. Why this makes Mahjong a good RL problem#
The 8-fan floor turns Mahjong into a genuinely strategic planning problem rather than a greedy-completion race:
- Long-horizon credit assignment: the decision that wins the game (committing to a suit) happens dozens of moves before the payoff.
- Value vs. speed trade-off: the optimal policy routinely declines locally-greedy moves.
- Imperfect information + opponents: you infer others’ hands from discards, and a careless discard can hand an opponent a big win (放铳 / dealing in).
- A legality cliff: the action space must be masked and win-declarations verified, or a single mistake erases a match.
It is precisely because “getting ready” and “being able to win” are different goals that hand-written heuristics plateau and learning — imitation from strong players, then self-play — becomes necessary. A policy trained on millions of expert decisions implicitly encodes the fan economy: it claims the tiles experts claim and passes the ones they pass, because it learned what good play looks like, not just what is closest to ready.
7. Takeaways#
- A Mahjong win = 4 sets + 1 pair and ≥ 8 fan. The second condition is the whole game.
- Shanten measures speed-to-ready; fan measures value. Optimizing only the first is the classic beginner (and beginner-bot) mistake — it draws every game.
- High value comes from committing early to structured hands (清一色, 碰碰和, 混一色, 组合龙).
- This speed-vs-value tension, plus imperfect information and a legality cliff, is what makes Chinese Standard Mahjong a rich reinforcement-learning benchmark — and why data-driven policies beat hand-crafted rules.
Next in this series: how we turned those ideas into a bot — feature design, supervised learning on 98k expert games, and the move from a fan-blind heuristic to a model-driven policy.