Evaluating a hand to see what tiles get to you tenpai helps get through the dangerous “iishanten hell” state in as few turns as possible. While it becomes a rote exercise to look at a hand after drawing a tiles to determine if you can discard into tenpai, knowing the list of tiles in advance can lets you find efficiency leaks that are slowing your game.
Overview
An important realization to help quickly find a complete list of accepted tenpai tiles is that the list of tiles that get you to tenpai is identical to the list of two-tile combinations that complete your hand.
From this, you can separate the suits in a hand and determine what you have, and what you can get from one or two tiles. Then, by combining these possibilities, you get the list of available tiles.
A hand is four sets (shorthand: for this discussion, “set” will mean both “a sequence” and “a triplet”) and a pair. (Alternatively, seven different pairs. Look for five different pairs when you start for this possibility). For each suit, you see what you have already, what you can get from one tiles, and what you can get from two. Then, you can match the lists up:
if a suit, with zero extra tiles, gives you 2 sets,
and another suit, with two extra tiles, gives you 2 sets and a pair,
then those extra tiles are all tenpai acceptance tiles.
if a suit, with one extra tile, gives you 3 sets,
and another suit, with one extra tile, gives you 1 set and a pair,
then those extra tiles are all tenpai acceptance tiles.
and so on.
Method 1 and Examples
Take a hand and make one column for each suit. In each, make a list of what you get with 0, 1, and 2 tiles. s for set, p for pair, Use an x for “leftover tiles”. For example:
| Man: 0: 2s+x 1: 2s+1p 2: 3s | Pin: 0: 1s+1p 1: 2s+x 2: 2s+1p |
As you can see, all three combinations of tile addition add up: 0/2 (2s on one side, 2s + 1p on the other, totaling 4s + 1p: a complete hand), 1/1, 2/0. There are off chances that your combinations won’t match up – too many pairs, too many leftover tiles, not enough sets – so this is a quick check to make sure you don’t do unnecessary work.
Also, do a check to see if there are 5 different pairs, in which case any non-paired tile is a tenpai draw to 7 pairs. (not this time)
So, with the above:
Man tiles:
1 tile adds that add a pair:
(pairing the 7)
2 tile adds that add a set: 
(two of 56789 make the 7 a set, and then if you add a 6, 25 also make a set)
Pin tiles:
1 tile adds that make a pair a set:
(tripling up the 5)
2 tile adds that add a set: 
(two of 12345 make the 3 a set, and then if you add a 4, 58 get back the pair)
also: if a hand has all 4 of a tile, that tile is not a type.
This gives you : 12 types. Now you need to figure out how many actual tiles are available. This is simply 4 times the number of types, -1 for each one already in hand.
In this case, that is 48, minus 257m3558p, 7. 48-7=41. 12 types 41 tiles.
Next example: 
Pin: 0tile:1s+1p+3x 1tile:2s+1p+2x 2tile:3s
Sou: 0tile:1s+2x 1tile:2s 2tile: 2s+x
0/2 doesn’t work, 2/0 doesn’t work, only 1/1.
5 different pairs: 7 pairs chance!
Pin 1tile:34568 7pairs:67
Sou 1tile:25 7pairs:5
Total: 345678p25s, 8 types.
Total tiles: 32- 44556788p5s(9) = 8 types 23 tiles.
Sometimes, nothing will match up. This happens when there are “no pairs available”. Take this example:
| Man: 0: 1s+xx 1: 2s 2: 2s+x | Pin: 0: 2s+xx 1: 3s 2: 3s+x |
Nothing adds up to 4 sets and a pair. So, you need to look at “less optimal tile adding”. For example, discarding out of a set (22256 > 22567):
| Man (alternate): 0: 1p+xxx (22m) 1: 1s+1p+x (ex: 22 567m) 2: 2s+x | Pin (alternate): 0: 2s+xx 1: 2s+1p+x (ex: 22 455667p) 2: 3s+x |
So, the 1/1 setup is where this works if you look at both possibilities on both sides:
1 Man / 1 Pin (alternate) which is 2s / 2s+1p, and 1 Man (alternate) / 1 Pin, which is 1s+1p / 3s. So, all tiles that meet this add 1 tile-on-the-man-side and add 1 tile-on-the-pin-side are tenpai tiles.
on the Man side:
2set: 4 7
1set+1pair: 4 7 5 6
so Man is 4567m.
on the Pin side:
3set: 3
2set+1pair: 2 4 7
so Pin is 2347p.
8 types, 26 tiles.
Method 2 and Examples
This method relies more on memorization than the ability to recognize possible set combinations. In particular, it can be used to quickly knock out the outlier answers. It looks at the remaining tiles of confirmed parts of the hand. First, some terminology, one in particular.
Set: triplet or sequence
Pair: pair
Mentsu: two out of three of a Set
Note that Pair are also a special kind of Mentsu.
That being said, the following confirmed hand setups give the following confirmed waits. First, the list, then the breakdown.
5 Pairs: all singular other hand tiles are a wait
3 Sets + 1 Pair: all other hand tiles, and waits 1 and 2 away from them, are waits*
(* note: tiles are not themselves waits if you have 3 or more of them. Example where they are: 123456789m 99p 4s. 4s can become 234,345,456, or 444. Example where they are not: EEE SS 1233345. looking at it as EEE 123 345 SS 3, you can make 123,234,345 out of the leftover 3, but not 333, because then you’d have too many 3 in your hand. So, instead of that 3 giving you 12345, it just gives you 1245.)
3 Sets + 1 Mentsu: the waits that complete those mentsu, and all other remaining tiles, are waits
2 Sets + 2 Pair + 1 Mentsu: the waits that complete those mentsu, and the tiles in the pairs as well
2 Sets + 1 Pair + 2 Mentsu: the waits that complete those mentsu
5 Pairs:
– 55m 66m 77m 44p 55p, leaving 9m 67p, which are waits.
3 Sets + 1 Pair:
– 567m 567m 567p 44p, leaving 9m 5p. 789m and 34567p are waits.
3 Sets + 1 Mentsu:
– 567m 567m 567p sets, leaving 44p or 45p. 4p and 36p are waits.
2 Sets + 2 Pair + 1 Mentsu:
– 567m 567m 44p 55p 67p, 4p 5p 58p are waits.
2 Sets + 1 Pair + 2 Mentsu:
– 567m 567p 44p 56m 79m, 47m 8m are waits.
Adding it up: 4789m345678p.
5 Pairs:
– 44m 55m 88m 33s 44s, leaving 67m 5s, which are waits.
3 Sets + 1 Pair:
– none
3 Sets + 1 Mentsu:
– none
2 Sets + 2 Pair + 1 Mentsu:
– 567m 345s 44m 88m 34s, 4m 8m 25s are waits. Alternatively,
– 678m 345s 44m 55m 34s, 4m 5m 25s are waits.
2 Sets + 1 Pair + 2 Mentsu:
– 567m 345s 88p 45m 34s, 36m 25s are waits.
Adding it up: 345678m235s.
Personal Choice
Personally, I have found the fastest method for myself is to:
- Check for the Method 2 5 Pairs,
- Check for the Method 2 3 Sets + 1 Pair method,
- then do Method 1 knowing I don’t have to “check” for things already found
But do what works for you.