Two questions decide almost every discard you will ever make:
How far away am I? and how many tiles would improve me?
In Japanese mahjong these have names — shanten for the first, ukeire for the second — and an enormous technical literature. The American game needs the same two answers but gets almost none of the vocabulary, which is a shame, because the American version is easier.
Shanten: how many tiles away
If your card line needs five specific groups and you have four of them complete plus a pair, you are one tile away. If you have three complete and two half-built, you are further than that, and "further" is worth counting precisely because it is usually worse than it feels.
The practical shortcut is not to compute shanten formally. It is to sort your rack into three piles:
- Done — groups that already match the card line.
- One away — groups missing exactly one tile.
- Not started — groups with nothing useful in them.
If you have more than one group in the not started pile at the midpoint of a hand, you are not going to finish. That is the whole test, and it takes about five seconds.
Ukeire: how many tiles help
Here is where the American game is genuinely simpler than riichi, and also where it catches people out.
In riichi, the number of tiles that improve your hand is a property of the tiles. A hand holding 4-5-6-7 of dots can use a 3 or an 8, and that is true in every game you will ever play.
In the American game, the number of tiles that improve you is a property of the line you are playing. Take a rack holding three 7-cracks and a mixed collection of 2s, 3s and 4s:
- If you are playing a pung-of-7s line, your ukeire is one tile — the fourth 7-crack.
- If you are playing a consecutive-run line, your ukeire might be six or eight tiles — any 1, 2, 4 or 5 that completes a sequence.
- If you are playing a 2468 line, the 7s are worthless and your ukeire is entirely in the even tiles.
Same rack, three completely different counts. This is why the advice to "pick your line early" is not fussy bookkeeping — you cannot count your outs until you know what you are counting toward.
The live-tile correction
Counting outs is only half the work. The other half is asking how many of them are still in the game.
There are four of every suited tile. If you need the fourth 7-crack and you can see two 7-cracks in discards, there is one left, somewhere in the remaining wall. That is a long shot and you should know it is a long shot before you commit another twenty minutes to it.
A working approximation, good enough for the table:
- Four live copies — excellent. Play on.
- Two or three live copies — normal. Play on, but stay honest about your other groups.
- One live copy — you are drawing to a single tile. Only acceptable if everything else in the hand is finished.
- Zero live copies — the hand is dead. You are not allowed to win and should stop feeding the table.
The most common error at intermediate tables is drawing to a tile that is already gone. It is easy to do, because the tile is still sitting on your rack and feels available.
Where jokers change the arithmetic
Jokers break the counting, and you should account for them deliberately rather than accidentally.
A joker turns any one-tile-out into something you already hold. This means:
- A hand with three jokers in it has a much larger effective ukeire than the tiles suggest.
- Conversely, spending your last joker shrinks your outs dramatically. The hand that looked close before the exposure may be nowhere after it.
This is the strongest argument against using jokers early. A joker in your rack is a live out for several different groups at once; a joker on the table is committed to one group and finished. Flexibility has real value, and the card does not price it.
A worked example
Say the line you have chosen needs: a pung of 5-dots, a pung of 9-bams, a kong of East, and a pair of 3-cracks.
Your rack holds: 5-5 of dots, 9-9-9 of bams, East-East-East, 3-3 of cracks.
Done: the 9-bam pung. One away: the 5-dot pung (needs one 5-dot), the East kong (needs one East), the 3-crack pair (already have it — but note, no joker may be used here).
Count your outs. The fourth 5-dot — check the discards, and remember a joker could substitute, since this is a pung. The fourth East — same. The pair of 3-cracks is complete and cannot use a joker.
Now suppose all four Easts are visible on the table. The kong is impossible. Your line is dead, and every 5-dot you were waiting for is irrelevant, because you cannot complete the hand with only part of it.
That is the whole method: sort the rack, count the outs, check they are live, and notice when one of them is impossible. It takes fifteen seconds and it is the difference between a player who finishes hands and a player who nearly finishes them.
Why this is worth learning formally
Because it converts an argument with yourself into arithmetic. "I feel close" is not a plan. "I need two tiles, I can see that both are live, and nobody has exposed more than one group" is a plan — and it is also a fold, if the numbers come out the other way.