Push/Fold Judgment (押し引き)
19.1 The Central Decision of Riichi Mahjong
Push/fold judgment (押し引き, oshi-hiki) is widely regarded by professional players and analysts as the most important skill in competitive riichi mahjong. "Push" (押し, oshi) means continuing to pursue your own hand despite a known threat. "Fold" (引き, hiki) means abandoning your hand to play defense. Every discard after an opponent declares riichi or shows threatening behavior involves this decision.
19.2 Factors in the Push/Fold Decision
The decision is fundamentally a comparison of expected values: the expected gain from pushing (probability of winning × win value) versus the expected loss from pushing (probability of dealing in × deal-in cost). When the expected gain exceeds the expected loss, push. When the expected loss exceeds the expected gain, fold.
Factors Favoring Push
High hand value: The more your hand is worth, the more incentive to push. A hand worth mangan+ justifies more risk than a 1-han hand.
Close to tenpai: If you are already tenpai or 1-shanten with high ukeire, your probability of winning is substantial.
Good waits: Ryanmen with many tiles remaining = higher win probability.
Safe tiles available: If you can push while discarding relatively safe tiles, the risk is reduced.
Placement need: If you are in 4th place and need to move up, the cost of folding (staying in 4th) may exceed the cost of dealing in.
Factors Favoring Fold
Far from tenpai: At 3+ shanten, your probability of winning is very low. The risk of dealing in over multiple discard turns makes pushing almost never justified.
Low hand value: A 1-han hand is rarely worth the risk of dealing into a potential mangan.
Multiple threats: Two or more opponents threatening simultaneously makes safe discard choices much harder.
Good placement to protect: In first place, folding costs you little (you maintain your lead) while dealing in could be catastrophic.
Dangerous tiles needed: If progressing your hand requires discarding tiles in the opponent's danger zone, the risk escalates.
19.3 Simplified Push/Fold Framework
| Your State | Opponent Threat | General Action |
|---|---|---|
| Tenpai, good wait, mangan+ | Single riichi | Push (strong EV advantage) |
| Tenpai, good wait, 1-2 han | Single riichi | Push cautiously (marginal EV) |
| Tenpai, bad wait | Single riichi | Consider fold or partial defense |
| 1-shanten, good shape | Single riichi | Push 1-2 turns, then reassess |
| 2+ shanten | Single riichi | Fold (almost always) |
| Any non-tenpai | Multiple threats | Fold (almost always) |
| First place, safe lead | Any threat | Fold bias (protect placement) |
| Fourth place, final round | Any threat | Push bias (nothing to lose) |
This table is a simplified heuristic. Real push/fold decisions involve many interacting factors and cannot be reduced to a simple lookup. The purpose of this framework is to provide correct directional guidance for common situations. As you gain experience, you will develop more nuanced judgment.
QUIZ — Question 19.1
You are at 3-shanten with a mediocre hand. An opponent declares riichi on turn 7. What should you do?
Answer: B. At 3-shanten, you need a minimum of 3 perfect draws to reach tenpai. With an opponent in riichi, each of those discards carries deal-in risk. The expected value of pushing is extremely negative: low win probability × low hand value vs. real deal-in probability × potentially high cost. Fold immediately and discard safe tiles. Option D is impossible—you cannot declare riichi when not in tenpai.
19.4 Push/Fold by the Numbers — Expected Value Framework
The quantitative push/fold framework, developed in detail in Totsugeki Touhoku's (とつげき東北) 『科学する麻雀』and refined through subsequent Tenhou data analysis, can be expressed as a comparison of expected values:
EV(push) = P(win) × V(win) − P(deal-in) × V(loss)
EV(fold) = 0 (approximately, ignoring noten penalties)
Where P(win) is your probability of winning the hand, V(win) is the expected value of your win, P(deal-in) is the probability of dealing in on each discard, and V(loss) is the expected cost of dealing in. If EV(push) > EV(fold), push. Otherwise, fold.
Practical estimates for these values: P(win) for a tenpai hand with good ryanmen ≈ 40-50%. P(deal-in) per discard against a single riichi ≈ 5-10% depending on how dangerous the tile is. V(win) varies from 1,000 to 12,000+. V(loss) against a typical riichi ≈ 4,000-6,000 average. These numbers, while rough, allow back-of-envelope calculations that guide correct decisions.
19.5 Common Push/Fold Mistakes in Beginner Games
Mistake 1: Pushing at 3+ shanten. At 3-shanten, you need at minimum 3 perfect draws to reach tenpai. Each draw requires discarding a tile, each of which carries deal-in risk. The cumulative probability of dealing in over 3+ discards while the opponent is tenpai is substantial. Meanwhile, your probability of actually winning is very low. This is the most common and most costly beginner mistake — it accounts for the majority of the deal-in rate gap between beginners and intermediate players.
Mistake 2: Folding with a tenpai mangan against a single riichi. If you are tenpai with a mangan hand and a good ryanmen wait, the expected value of pushing is strongly positive against a single riichi opponent. Your win probability is ~40-50%, your win value is 8,000+, and your deal-in risk per tile is manageable. Folding here sacrifices enormous EV out of excessive caution.
Mistake 3: Ignoring placement context. The push/fold calculation changes dramatically based on your placement. A push that is correct in 3rd place may be incorrect in 1st place, because the placement cost of dealing in is much higher when you have a lead to protect. Nagai Takanori's (長井隆典) 『現代麻雀技術論』devotes extensive analysis to placement-adjusted push/fold thresholds.
Source notes: Push/fold theory is the most extensively analyzed topic in modern Japanese mahjong strategy. Quantitative push/fold frameworks have been developed using Tenhou data analysis. Japanese professional commentary regularly focuses on push/fold decisions as key teaching moments. The expected value approach to push/fold is standard in contemporary Japanese mahjong literature.