Speed or value: when a yaku is worth slowing down

One cut keeps 16 tiles. Another keeps 12 and gives every win tanyao (all simples). Two counts settle it: the tiles each cut keeps and what each version pays. Sometimes the han is worth its tiles. Sometimes it means breaking a good shape for a han the hand has half the time anyway.

A hand is worth its price times its chance

What a hand earns you is its price times how often it wins. On paper, a hand that wins half as often at twice the price earns the same, and you can count both numbers at the table.

The speed side is tile acceptance: the tiles that move your hand forward. On every draw, a 1-shanten hand that takes 16 tiles has four chances to reach tenpai for every three that a hand taking 12 has. The hand analyzer counts any hand for you.

The value side is the price from What a hand pays. Count the han the hand will have when it wins, then read the table. Below mangan, one more han about doubles the price.

The tile count tells you how soon you reach tenpai, and a later tenpai wins less often. In the site's data from Tenhou's top room (Houou), a two-sided riichi waiting on a 1 and a 4 wins 79% of the time when declared at turn 2 and 47% at turn 11, about 3.6 percentage points less for each turn (riichi wait win rates). Turns count from zero there, so turn 2 is your third discard. Price times chance also leaves out what a hand you don't win costs: another player can win it, sometimes off your discard, while your win ends the hand. So when the two sides come out close, take the faster hand.

Speed first: riichi and dora add value for free

A closed hand rarely needs a yaku you have to build. Riichi gives any closed tenpai a yaku and a han. A win on your own draw adds menzen tsumo, and a riichi winner counts the ura dora too. Tenhou and Mahjong Soul also play with three red fives, one per suit, each a dora by itself, on top of the dora the indicator shows. None of that asks your hand to change shape.

A winning riichi pays well. In the same Houou data, a non-dealer riichi declared at turn 8 that won by ron collected 5,869 points on average, ippatsu included (What folding costs). That counts every kind of riichi hand, but it's well above what riichi, pinfu, and tanyao pay by ron: 3,900.

So build the fastest shape and let the value come to you. Yaku and dora still break ties: when two cuts are equal on tiles and shape, keep the one with value. A kanchan and a kanchan are both kanchans (middle waits) of the outer kind: each waits on 4 tiles and grows into a ryanmen (two-sided shape) with 4 more (Ryanmen, kanchan, penchan). But a 13m finishes with a 1 in it, so drop it and tanyao stays possible. When a red five and a plain tile do the same job, keep the red five. Pinfu and tanyao and Playing the dora come back to both.

Put the trade in numbers

The real choices start when value costs tiles. You're 1-shanten with no dora in the hand, and you draw a second 2p.

Throw the 2p back and nothing changes. The 11m stay your head, the 246p takes the 3p or the 5p, and the 34s takes the 2s or the 5s: 16 tiles. Or keep the 2p and cut a 1m. The 22p become your head, the 46p a kanchan, and the other 1m goes by the time you reach tenpai: 12 tiles. Once it's gone, every tile is a 2 to 8, so every win has tanyao.

	Cut the 2p	Cut a 1m
Tiles that make tenpai	16	12
Of those, draws that end on a two-sided wait	8	4
Your head	11m	22p
Win on a kanchan	1,300: riichi	2,600: riichi, tanyao
Win on a two-sided wait	2,000: riichi, pinfu	3,900: riichi, pinfu, tanyao

Pinfu needs a closed hand of four sequences, a pair that isn't a value tile, and a two-sided wait (What is a yaku?), so a kanchan finish loses it and counts 40 fu (Fu without counting).

The 1m cut gives up the 3p, which only the 246p could use: 4 tiles of 16, a quarter. It costs shape too: the 3p was one of the draws that end on a two-sided wait, so the tanyao hand lands on the kanchan with 8 of its 12 tiles. It still wins the trade, because its worst finish, 2,600, pays more than the fast hand's best, 2,000. Keep the 2p and cut a 1m. The hand analyzer lists both cuts, plus the 6p, which also keeps 16 tiles without tanyao, and the score calculator checks the prices.

My rule of thumb comes from price times chance, with the tile count standing in for chance. Give up a quarter of your tiles for a han that doubles every win and you keep 3/4 × 2 = 1.5 times what the fast hand earns: take it. Give up half and you get 1/2 × 2 = 1, a tie on paper, and a tie goes to speed. Between the two, let the rest of the hand decide: a riichi-only hand needs the han more than one that already holds two dora.

Before you pay, ask how much of that value you'd get anyway. The first practice problem below costs the same 4 tiles and buys almost nothing.

One more han: where it pays and where it doesn't

Here's what the last han added at each step.

Han	30 fu	40 fu
1	1,000	1,300
2	2,000 (+1,000)	2,600 (+1,300)
3	3,900 (+1,900)	5,200 (+2,600)
4	7,700 (+3,800)	8,000 (+2,800)
5	8,000 (+300)	8,000 (+0)
6	12,000 (+4,000)	12,000 (+4,000)
7	12,000 (+0)	12,000 (+0)

At 30 fu, each han up to the fourth roughly doubles the hand. Then the doubling stops at mangan (Every mahjong hand has two invisible han shows why), so the fifth adds 300 or nothing, the sixth 4,000, and the seventh nothing.

That table is ron only, and half or more of a two-sided riichi's wins come by tsumo: 50% to 58% in the same data. Menzen tsumo, ura dora, and ippatsu stack on the han you built. Riichi, pinfu, and two dora is 7,700 by ron, and one more han makes it 8,000. By tsumo it's already a mangan, and the extra han makes it a haneman, 12,000. Split the wins half and half and the han lifts the average from 7,850 to 10,000, about a quarter more. A riichi-only hand doubles with one han, whichever way it wins. Spend your tiles on the cheap hands.

As dealer, lean toward speed

A dealer's win buys more than its points. A dealer who wins keeps the deal (How a game works), so even a 1,500-point win comes with another hand at dealer stakes. And while your hand is slow, a tsumo by another player costs you double, as What a hand pays showed: 4,000 of a mangan instead of 2,000.

The 1.5 times payment doesn't tilt the trade, since it scales both sides: riichi and pinfu pay the dealer 2,900, and tanyao makes it 5,800. A non-dealer gives a close trade to speed. As dealer, my rule of thumb is to take the value cut only when it wins clearly, like the 1m cut above.

Practice

You're not the dealer in these, and riichi is the plan for each hand. Count the tiles each cut keeps, then price the wins.