Pairs: two is right, three is one too many

Three pairs feel like three chances at a set. Count them, though, and the third pair is the weakest block in your hand: it adds 2 tiles to your acceptance, while the kanchan (middle shape) you'd break to keep it adds 4. A closed hand wants two pairs. When a third arrives, one of them should go.

A pair does two jobs

A pair, or toitsu (対子), is two identical tiles, like pair. It can be your head, the one pair every standard hand needs. Or it can be a partial set waiting on its third copy, with 2 tiles left to finish it. The partial-sets lesson ranked it the narrowest partial set for that reason.

With one pair, you get one job. Once your hand has its five blocks (four sets or partial sets, plus the head), the third copy of that pair makes a set and leaves you with no head. You're no closer to tenpai, so that draw isn't acceptance.

A hand with no pair is less trouble than it looks, because the head often turns up on the way.

It has three sets, the 78m and 23s ryanmen (two-sided shapes), and no pair, yet it's already 1-shanten and accepts 28 tiles. Sixteen finish a ryanmen, and the other 12 pair a ryanmen tile, any 7m, 8m, 2s, or 3s, to give you your head. Headless and floating-tile 1-shanten shows the waits each kind leaves, later in the course. Sets are the hard part. Don't break a set or a ryanmen early to build a head.

Two pairs work as a team

Add a second pair and both start to count. Either one can become a set, because the other is there to be the head. Each brings 2 tiles, so together they bring 4, as many as a kanchan or a penchan (edge shape). If both are still pairs at tenpai, you win on either one: a shanpon (pair wait), the 4-tile wait from Mahjong waits.

You've drawn your 14th tile and must cut one. The hand holds six blocks, one more than it can use: two sets (234p and 678s), the 55m and 33s pairs, the kanchan kanchan, and the penchan penchan. Add up what finishes each partial set: four 3m, four 8p, two 5m, and two 3s, 12 tiles in all. Every cut takes something off that 12.

• Break the penchan: 8 tiles. Four 8p for the kanchan, plus two 5m and two 3s for the pairs.
• Break the kanchan: 8 tiles. Four 3m for the penchan, plus the same two pairs.
• Break a pair: 8 tiles. Four 3m and four 8p, and nothing from the pair you kept.

Breaking one of two pairs costs 4 tiles, not 2. The pair you broke loses its own 2, and the pair you kept can't become a set any more, because it's your head now.

When the count ties, shape decides, as Tile acceptance showed. Every partial set here but the penchan can grow. A 6p lets the 79p become the ryanmen 67p. A 4m or a 6m next to the 55m makes pair plus ryanmen or pair plus ryanmen, a pair sharing a tile with a two-sided shape, which Shapes worth keeping covers. No single draw turns the 12m two-sided. So cut the 1m and keep both pairs. If a 4m comes next, cut the 2m: the hand then accepts 16 tiles, twice the 8 you have now.

A third pair is the cheapest block to break

Two sets (234m and 678p), three pairs (88m, 22p, and 99s), and the kanchan kanchan. Six blocks again, so one has to go. Together the partial sets take 10 tiles: four 5s and 2 for each pair.

• Break a pair, say the 99s: the other two still work as a team. The 5s (4), the 8m (2), and the 2p (2) make 8 tiles. That cut costs 2.
• Break the kanchan: the three pairs bring 2 tiles each, 6 in all. That cut costs 4.

The third pair adds only 2 tiles, because the other two already cover the head.

The block you break	Example	What it costs
One of three pairs	pair	2 tiles
One of two pairs	pair	4 tiles
A kanchan or a penchan	kanchan penchan	4 tiles
A ryanmen	ryanmen	8 tiles
Your only pair	pair	A step of shanten

A pair joined to other tiles, like the 455m above, is a bigger shape and counts differently.

Which pair to let go

With nothing visible, a cut from any of the three pairs keeps the same count. At the table, two things split them, in this order.

1. Value. A pair of dragons, your seat wind, or the round wind is a yakuhai pair: while a copy is left, its third copy is a set and a yaku, and you can pon it from any player, which the yakuhai lesson covers. A pair of dora is 2 han even as your head. Keep both kinds. The exception is a pinfu-shaped hand, where every partial set is two-sided: a yakuhai head rules out pinfu, so keep the guest-wind or number pair as your head, as Pinfu and tanyao shows. Tanyao (all simples) counts too: when a 1, 9, or guest wind pair is all that keeps your hand off it, break that pair. In the three-pair hand, 23488m22678p4699s, every tile but the 99s is a 2 to 8.
2. Copies left. A pair with one copy in the discards has 1 tile left, not 2. In that same hand, say both other 9s already sit in the discards. The 99s can still be your head, but it can never become a set. Break it and you keep 8 tiles. Break the 88m or the 22p instead and the dead 99s adds nothing: 6. Here both rules point at the 99s.

When value and copies tie too, two small pulls cancel out. A middle pair can grow into a shape like 455m on the way to tenpai. A 1, 9, or honor pair makes the easier pair wait once you're there, because folding players throw those tiles, as Riichi wait win rates shows. Any pair is fine.

When extra pairs earn their place

Everything so far assumes a closed hand built as four sets and a pair. Two things change the count.

Calling. Before tenpai, a closed hand turns a pair into a set only with your own draw. Once you're willing to call, any other player's discard can do it, by pon. That makes pairs faster, so a hand that plans to call can keep three pairs over a kanchan or penchan: pon one and you're back to two. A called hand still needs a yaku, as the yaku lesson showed, and When to call weighs what a call costs.

Four or five pairs. Seven pairs (chiitoitsu) wins with seven different pairs in a closed hand, for 2 han. The shanten lesson counted that route as 6 minus your pairs, so four pairs put you 2-shanten on it and five put you 1-shanten. Seven pairs or toitoi covers which route to take once the pairs pile up.