1-shanten: the step where hands are won

Nearly every hand you win passes through 1-shanten, one useful tile from tenpai. From the same 14 tiles, one cut can leave 20 tenpai tiles that all end two-sided, and another 12 that mostly end on a pair wait. The difference is one discard.

Each tenpai tile is worth about 1% a draw

Iishanten (一向聴) means one useful tile from tenpai, the count from the shanten lesson. Your acceptance, from Tile acceptance, is exactly the tiles that make you tenpai, and every other draw leaves you at 1-shanten.

So each tile on the list is a straight chance at tenpai. Take 136 tiles and remove your 13, the dora indicator, and the discards. Once each player has discarded five or six tiles, about 100 are hidden from you. If none of your tenpai tiles are visible, each one is about a 1% chance on every draw.

Tenpai tiles	On your next draw	Within your next six draws
12	12%	55%
16	16%	66%
20	20%	75%

Six draws is a third of the 18 or so a hand gives you, as How a hand is played counted. Over those six draws, every 4 tiles of acceptance add about 10 percentage points. The wait you reach matters too, and that's the second number to count.

The spare-tile shape and the complete shape

The everyday 1-shanten holds two sets, a head, two partial sets, and one spare tile. The examples below keep 234m, the 99m head, and 34678s fixed. Only the pinzu change.

Two sets (234m and 678s), the 99m head, two ryanmen (two-sided shapes) in ryanmen and ryanmen, and one tile with no job: the 1p, a loose (isolated) tile. That's the spare. In the five-block method a spare was the extra tile of a compound shape; at 1-shanten the word covers whichever 13th tile has no job, loose or not. The 5p, 8p, 2s, and 5s make you tenpai: 16 tiles. Each fills one ryanmen and leaves the other as your wait, so all 16 end two-sided. The spare adds none of them.

Now draw a 6p. It's a shape draw: no tenpai, but it changes your count.

Cut	What you keep	Tenpai tiles	Good shape
	Two ryanmen and two pairs	20	20
	Two ryanmen, the head, and the 1p	16	16
	One ryanmen, two pairs, and the 1p	12	4

Cut the 1p. The pair plus ryanmen is a ryanmen sharing a tile with a pair, from Shapes worth keeping, and with the 99m you hold two pairs.

• 5p or 8p finishes the pinzu. Cut the extra 6p and wait on the 2s and 5s.
• 2s or 5s finishes the souzu. Cut a 6p and wait on the 5p and 8p, with the 99m as your head.
• 6p makes 666p. Cut the 7p and wait on the 2s and 5s.
• 9m makes 999m, and the 66p becomes your head. Cut the 7p, same wait.

That's 20 tiles, every one two-sided. Japanese players call this kanzen iishanten (完全イーシャンテン), the complete 1-shanten: two ryanmen and two pairs, with one pair sharing a tile with a ryanmen so it all fits in 13. When the 2s or 5s comes first, you could also cut the 7p and wait on both pairs, a shanpon (pair wait). Take the ryanmen: 8 tiles against 4, as Mahjong waits counted.

The tidy 6p cut throws away the 4 tiles the second pair brought: two 6p and two 9m. The 7p cut keeps both pairs but breaks the 67p ryanmen, and 8 of its 12 tiles, the 2s and 5s, leave you on a shanpon. The hand analyzer prints these counts for any hand.

Count the draws that end two-sided

The hand analyzer and the efficiency trainer print this second number at 1-shanten, in a column called Good shape. It counts the tenpai tiles that let you wait on two or more kinds with five or more copies outside your hand. A ryanmen passes with 8, and so do the wider waits. A kanchan (middle), penchan (edge), or tanki (single wait) waits on one kind, and a shanpon holds at most 4, so they don't.

The gap at the table is wide. In Tenhou's top room (Houou), a riichi declared on turn 8 wins 52% to 57% of the time on a two-sided wait, and 33% to 36% on a one-sided wait on a 4, 5, or 6. Turns count from zero there, so turn 8 is your ninth discard. The wait win rates post has the full table.

Here's the same frame with a ryankan (two kanchans sharing a tile), the ryankan from Shapes worth keeping, and an 8p drawn this turn.

Cut the 8p, the 3p, or the 5p and you keep 16 tiles. The tile count can't split them. The second number can.

• Cut the 8p and keep the ryankan. The 4p and 6p fill it and leave the 34s as your wait. But when the 2s or 5s comes first, half your tenpai tiles, you cut one end of the 357p and wait on a kanchan. 8 of 16 are good shape.
• Cut the 3p or the 5p. The 78p takes the 6p and 9p, and whichever block fills, the other is a ryanmen. 16 of 16.

So count tiles first, then good shape. When cuts tie on tiles, take the one with more good-shape draws. When they come close, a wide good-shape gap can outweigh a tile or two. Headless and floating-tile 1-shanten weighs that trade.

Keep a spare that can still build

In the spare-tile shape, one tile adds nothing to today's count, so choose it for what it does on the draws that miss. The spare matters when a partial set is weak.

The kanchan and the 34s take 12 tiles, and only the four 8p leave a two-sided wait. The 4p adds nothing today, and a 1p in its place would keep the same 12. The shape draws split them: a 3p or a 5p lands beside the 4p and makes a second ryanmen. Cut the 7p or the 9p and you hold 16 tiles, all good shape. With the 1p as your spare, a 3p only makes a kanchan and a 5p a ryankan.

So with a weak partial set, keep the spare that can grow into a ryanmen: a middle tile over a terminal or an honor, the order from What to discard first. With two ryanmen, the spare can be the tile that's safest to throw later. That's when safety comes free. Until someone declares riichi or makes their second call, a 1-shanten with good shape or some value doesn't give up a tenpai tile to keep a safe one. Defense before the riichi covers which spares stay safe.

Practice

Say both numbers before you tap.

In the efficiency trainer, every cut tied for widest counts as right, so break those ties on good shape yourself.