Wait efficiency: ryanmen, kanchan and penchan compared

1. Count the tiles before anything else

The first question about a wait is not shape, it is count. Each number tile appears four times, so the nominal size of a wait can simply be counted: ryanmen 23 waits on 1 and 4, four copies each, eight tiles nominal; kanchan 46 waits on 5, four tiles; penchan 12 waits on 3 and 89 waits on 7, four tiles each as well; tanki holds one copy in hand, so only three remain.

The nominal figure is a ceiling. The real count subtracts two things: the copies in your own hand, and the copies already visible on the table — discards, calls and the dora indicator. Hold two 4s yourself and the 23 ryanmen drops from eight tiles to six; see two more 4s on the table and it is down to four, the same as a kanchan.

So the first move is always subtraction. Comparing shapes on nominal numbers is the most common mid-game error, and middle tiles suffer most: 3 through 7 take part in more ryanmen and kanchan shapes, so they are held by other players more often than terminals, and the real remainder usually sits below the nominal one.

2. Where the three shapes really differ

Beyond the count, the shapes differ structurally, and this part does not change with the table.

A ryanmen is the only shape with two ways to win: 23 waits on 1 and on 4, and either one completes the hand. It also preserves the conditions for pinfu — four sequences, a non-value pair and a two-sided wait. So a ryanmen is not only eight tiles against four, it is also one extra yaku.

A kanchan has one way to win but two ways to improve: 46 plus 3 becomes the 34 ryanmen, plus 7 becomes 67, and plus 5 completes it outright. A kanchan is a shape that is poor now and can still get better.

A penchan also has one way to win, but only one improvement: 12 plus 3 completes, while plus 4 merely turns it into the 24 kanchan, no better than before. A penchan always contains a terminal, and that tile has almost no use other than as a pair or a triplet, so a penchan rarely rescues itself by drawing.

In one line: a ryanmen is already good, a kanchan can become good, a penchan can only wait for the one tile.

3. Turn count: why the gap changes value

How many times you draw in a hand is fixed. From 136 tiles, 52 go to the deal and 14 form the dead wall, leaving 70 in the live wall; split four ways that is 17.5 draws each. The first six draws are the early game, turns 9 to 12 are the middle, and after that every draw decides the hand.

A ryanmen hits roughly twice as often per draw as a kanchan, and that ratio does not change with the turn. What changes is how many draws remain, and therefore what the difference is worth. Early on, eight against four means a dozen more chances to cash the gap in; by turn 13 only four or five remain, and the gap is compressed.

There is a second late-game effect: your opponents are in tenpai too. Winning then depends less on your own draws and more on ron, and a closed wait is roned less often, because opponents can read what you are waiting for from your discards and hold the tile back.

The conclusion is not that you should take a closed wait late. It is that early on, eight tiles is worth giving up four for; late on, four tiles is not worth breaking an eight-tile shape you already have.

4. Four waits on one skeleton

Set out 234m 678m 345p with a pair, then change the last two tiles. Run through a tile-efficiency engine and the results are: 23s waits on 1s and 4s, eight nominal; 78s waits on 6s and 9s, eight nominal; 68s waits on 7s, four nominal; 12s waits on 3s, four nominal.

All four are tenpai. There is no right or wrong in efficiency terms, only a factor of two in tile count. At the table that factor is amplified by riichi: with the same stick on the table, an eight-tile wait wins about twice as often as a four-tile one.

The same logic applies one step earlier. Take 234m 678m 46p 78s, a pair of white dragons and a lone east. Discard the east and the hand accepts 5p, 6s and 9s — three kinds, twelve nominal tiles. Swap 78s for 12s and it accepts only 5p and 3s, eight nominal; swap in 68s and it accepts 5p and 7s, also eight. One shanten either way, but the choice between a two-sided and a closed shape is a four-tile difference, and over ten turns that is the hand.

5. Four common mistakes

First, assuming more wait types means a better wait. A shanpon waits on two tiles with two copies each, four in total — the same as a single kanchan wait — and while it can add value by drawing a triplet, it cannot claim pinfu.

Second, counting only your own hand. Without subtracting what is visible you are using a ceiling as if it were an actual figure, and middle tiles are where this hurts most.

Third, ignoring value. A ryanmen keeps pinfu, a closed wait cannot, so the eight-to-four gap also carries a yaku.

Fourth, delaying for improvement indefinitely. Improvement is only worth something while draws remain. Going back from tenpai to one shanten to look for a prettier shape trades a certain draw for a possible one, and that trade is rarely good.

6. Priority checklist

1. Count the real tiles: four minus your own copies, minus what is visible.

2. When counts are close, rank the shape: ryanmen, then kanchan, then penchan, then tanki.

3. Check the value: can you keep pinfu, tanyao or riichi?

4. Check the improvement: a kanchan improves from either side, a penchan from one.

5. Check the turn: early favours tile count, late favours certainty.

6. If you are already in tenpai and the gap is two tiles or less, do not step back to one shanten.