Sankantsu

Sankantsu is 2 han, open or closed. You hold three quads: three sets of four identical tiles, each one declared as a kan.

The Japanese is 三槓子. This site's glossary lists it as Three Kans, and the EMA 2016 rules call it Three Kongs.

Every kind of kan counts

The yaku asks for three kans and nothing else. Any mix of the three kinds works:

• A closed kan: you hold all four tiles and declare it on your turn.
• An added kan: you add the fourth tile to a pon you called earlier.
• An open kan: you hold three and call the fourth off a discard.

Four identical tiles you never declare aren't a quad. They sit in your hand as a triplet and a spare tile, and they don't count toward the three.

A closed kan keeps your hand closed. An open kan or an added kan opens it, the same as a pon. Sankantsu keeps its 2 han either way. Riichi, menzen tsumo, and the other closed-only yaku don't.

The glossary entry is the short form: three quads in one hand.

Why the fu climb

A quad scores four times the fu of the same triplet. The EMA 2016 minipoint table, which Tenhou and Mahjong Soul share:

• Open quad of simples: 8 fu. Closed quad of simples: 16.
• Open quad of terminals or honors: 16 fu. Closed quad of terminals or honors: 32.

Three open quads of simples already add 24 fu to the base 20. Make two of them closed and one of them terminals, and the quads add 48. A sankantsu hand never scores at 30 fu, so its 2 han pay more than most. The scoring guide counts fu line by line.

Three kinds of kan, one yaku

You called three kans:

• A closed kan of 3 man, . At the table, two of its tiles lie face down.
• An open kan on a discarded 9 pin, .
• An added kan of 5 sou, , built on a pon.

These four tiles are still in your hand.

The hand waits on or , from both sides. The 9 pin rule out tanyao. The run rules out toitoi. Sankantsu is the only yaku: 2 han.

The fu on a ron are the base 20, plus 16 for the closed quad of simples, plus 16 for the open quad of terminals, plus 8 for the open quad of simples. The open kans make the hand open, so the ron adds nothing. That's 60 fu. At 2 han 60 fu, a non-dealer collects 3,900. The dealer collects 5,800.

A tsumo adds 2 fu, and 62 rounds up to 70. The hand is open, so menzen tsumo doesn't apply and the han stay at 2. At 2 han 70 fu, a non-dealer collects 1,200 from each other non-dealer and 2,300 from the dealer. A dealer collects 2,300 from each player.

The same 2 han at 30 fu would pay 2,000 on a non-dealer ron. The quads nearly double it.

The replacement tile and kan dora

Every kan gives you a replacement tile from the dead wall. Win on it and you add rinshan kaihou, 1 han, and the win counts as a tsumo.

Say the third kan in the hand above was the added 5 sou, and the replacement tile is . That's sankantsu and rinshan kaihou: 3 han 70 fu, which is paid as a mangan. A non-dealer collects 2,000 from each other non-dealer and 4,000 from the dealer. A dealer collects 4,000 from each player.

Every kan also turns one more dora indicator, and the new dora counts for the whole table. A closed kan turns it right away. On Tenhou and Mahjong Soul an open or added kan turns it after the discard. Three kans mean three extra indicators, and a quad that matches one is four dora. The dora guide has the timing for each rule set.

Toitoi and sanankou ride along

Three quads leave one set and a pair. Make that set a triplet and you have toitoi. Make the quads closed and you're close to sanankou.

You called a closed kan of 2 man, , and a closed kan of 6 pin, . Both lie with two tiles face down. You also called an open kan on a discarded 9 sou, . These four tiles are still in your hand.

The hand waits on or , a wait on two pairs.

By ron, the triplet the discard finishes counts as open. Two concealed sets aren't sanankou, so the hand is sankantsu and toitoi: 4 han. The fu are 20, plus 16 for each closed quad of simples, plus 16 for the open quad of terminals, plus 2 for the open triplet. That's 70 fu, and 4 han 70 fu is paid as a mangan. A non-dealer collects 8,000. The dealer collects 12,000.

Draw the tile yourself and the new triplet is concealed. Two closed quads and a concealed triplet are three concealed sets, so sanankou joins: sankantsu, toitoi, and sanankou make 6 han. The open kan still rules out menzen tsumo. The fu are 20, plus 2 for the tsumo, plus 48 for the quads, plus 4 for the concealed triplet: 74, rounded to 80. 6 han is a haneman. A non-dealer collects 3,000 from each other non-dealer and 6,000 from the dealer. A dealer collects 6,000 from each player.

Those payments have no dora, no honba, and no riichi sticks. Count the kan dora in a real game: this hand turned three extra indicators.

The fourth kan

Four quads in one hand are suukantsu, a yakuman. A sankantsu tenpai is one kan away from it.

Four kans at the table can also end the hand with no winner. Tenhou and Mahjong Soul both list 四槓散了, the four-kan abortive draw, among their abortive draws. The EMA 2016 rules don't use abortive draws. Their section 3.3.10 lets play go on after a fourth kong and bans any further kong.

Tenhou, Mahjong Soul, and EMA 2016

Tenhou's rules list 三槓子 at 2 han with no mark for a closed hand. Among the yaku a closed kan after riichi can add, they name 三槓子. The abortive draws go on the dealer: すべて連荘.

Mahjong Soul's Japanese FAQ defines 三槓子 as a win with three quads. Its ranked rules list 四槓散了 among the abortive draws, keep the dealer, and pay no nagashi mangan after it.

The EMA 2016 rules file Three Kongs with the 2 fan yaku: "Hand with three kongs."

Common mistakes

• Counting only closed kans. Open and added kans count the same.
• Counting four tiles you never declared. A quad has to be called as a kan.
• Scoring the hand at 30 fu. Three quads add at least 24 fu.
• Adding menzen tsumo after an open kan. The hand is open.
• Missing sanankou on a tsumo. Two closed kans and a drawn triplet are three concealed sets.
• Forgetting the kan dora. Each kan turns one more indicator.

What sits with it

Toitoi when the fourth set is a triplet. Sanankou when three sets stay concealed. Rinshan kaihou on the replacement tile. Yakuhai when a quad is dragons, your seat wind, or the round wind. Riichi only when every kan is closed.