Statistical Intuition
30.1 Why Statistics Matter
Riichi mahjong is a game of probability. Every decision involves estimating likelihoods: the probability of drawing a specific tile, the probability that a discard is safe, the probability that an opponent is tenpai. While you cannot calculate exact probabilities at the table, internalizing key statistical benchmarks helps you make better intuitive decisions.
30.2 Key Statistics
| Statistic | Approx. Value | Significance |
|---|---|---|
| Draw chance for specific tile (4 unseen, ~70 wall) | ~5-6% per draw | Basis for tenpai completion estimates |
| Average tenpai rate | ~35-40% | Not reaching tenpai is normal |
| Average win rate | ~20-25% | Win roughly 1 in 4-5 hands |
| Target deal-in rate (strong player) | ~10-12% | Lower = better defensive play |
| Riichi win rate | ~45-50% | Riichi does not guarantee winning |
| Ura dora average pickup | ~0.5-0.7 han | Significant boost to riichi EV |
| Ippatsu rate | ~15-20% | Unreliable but meaningful bonus |
| Suji safety | ~85-90% | NOT 100% safe |
30.3 Expected Value Thinking
Every decision has an expected value (期待値, kitaichi) = (probability of good outcome × benefit) - (probability of bad outcome × cost). Positive EV decisions are correct even when they sometimes fail. Training yourself to evaluate decisions by EV rather than outcome is the statistical foundation of strong play. A correct fold against riichi that turned out to be safe is still correct. A reckless push that happened to win is still reckless.
30.4 Tile Counting
Keeping track of how many copies of key tiles remain unseen is a practical statistical skill. If you need 5p to win and you can see two copies in discards and one in your own hand, only one remains—your tenpai has very low acceptance. Conversely, if all four copies of your wait tile are unaccounted for, your wait is strong. On online platforms, visible tile counting (discards + your hand + open melds) should become automatic.
QUIZ — Question 30.1
You are tenpai waiting on 3m. You can see one 3m in discards and none in open melds. How many unseen copies remain?
Answer: B. There are 4 copies of every tile. One is visible in discards. You do not hold any (you are waiting for it). No open melds show it. So 4 - 1 = 3 copies are unseen (in the wall or opponents' hands). Your acceptance is 3 tiles.
30.5 Key Probabilities Every Player Should Know
Beyond the benchmarks listed in Section 30.2, the following probabilities are useful for in-game estimation. These numbers come from the mathematical analysis in 『科学する麻雀』(Scientific Mahjong) by Totsugeki Touhoku (とつげき東北) and from subsequent Tenhou data verification:
Probability of drawing a specific tile per draw: If N copies remain unseen among approximately T unseen tiles, the probability is N/T per draw. With 70 tiles in the wall at the start and 4 copies of a tile, this is ~5.7%. As the wall shrinks and copies are seen, this changes dynamically.
Probability of completing tenpai within K draws: For a ryanmen wait with 8 unseen acceptance tiles and approximately 50 remaining wall tiles, the probability of completing within 10 draws is approximately 1 − (42/50 × 41/49 × ... ) ≈ 80%. For a tanki with 3 acceptance and 50 wall, within 10 draws: approximately 45%. These numbers explain the dramatic win-rate difference between ryanmen and tanki.
Probability that a random opponent is tenpai: On any given turn in the mid-game (turns 8-12), the probability that a specific non-riichi opponent is in tenpai (dama) is estimated at roughly 10-15% in typical play. This "background threat" is why some caution is warranted even when no opponent has declared riichi.
Source notes: Statistics based on large-sample Tenhou data analysis. Key benchmarks consistent with Japanese analytical sources.