Consider the finished game above. Today, we'll be drawing from the pool of discards in order to discuss "safe" tiles.
Safe tiles are basically tiles that have a better chance of NOT dealing into your opponent's hand. In reality, no tile is 100% safe; it's just that relative to other tiles, your opponent will want them less. Of course each game has their own set of safe tiles, but as a general rule of thumb, terminals and honors are considered safe. The point of interest and where we will begin our examination is when East player (Bottom) declares Riichi by discarding 7 Man (Their 12th discard).
Remember that players take turn in a counter-clockwise fashion, so then South player (Right). Their first discard after the declaration of Riichi is 2 Man (South Player's 12th discard). It isn't really 2 Man, due to the taking of discards which influences pool count, but for the sake of practicality, we will assume it is. In this sense, we start with each player's 12th discard.
We now examine each discard up until East player gets Tsumo.
Levels of safety are as listed, from safest to most dangerous:
Absolutely safe
Safe
Not safe
Dangerous
1) 2 Man: This is safe because there are already three 2 Man in the pool; two 2 Man in West player's pool, and the third one as a Dora indicator. Another rule of thumb is that Dora indicators are pseudo-safe tiles, since everyone knows at the beginning of the game (or when someone gets a Kan) what tile there is one less of. I could go on about Dora, but a full post on the subject will be for another day though.
2) 6 Pin: This is not safe, but it isn't dangerous either. Since there is already one 6 Pin in the pool (South), there is a less chance the Riichi player will want it. However, it is quite common that a player in Tenpai will go for a tile that's already out in the pool. Only when there is 2 or 3 that are in the pool does that particular tile become a deterrent.
3) South: This is absolutely safe. Since East player discarded a South tile earlier (8th discard), they cannot win by taking a South tile from another player. This is a rule called Furiten, which basically means that any tile you discard, you can't take from someone to win. You can still draw that tile for a Tsumo however. Granted it may be an absolutely safe discard against East player, the other two players may want it, since it is the Round Wind. But we will only consider the player who declared Riichi.
4) North: No point discussing safe tiles when the Riichi player discards them. They will only be listed for reference.
5) Green Dragon: Absolutely safe; see #3.
6) 3 Sou: Safe, for the same reasoning as #1.
7) 8 Sou: Not safe, see #2.
8) 8 Sou
9) 6 Sou: Dangerous. The pool has no 6 Sou in it, and by probability, that means they are being held by other players. That is indeed the case, since North player takes it for a triplet. Discard #10 would therefore be from North player, but once again for simplicity, I will go in order.
10) 5 Man: Dangerous. See previous explanation.
11) South: Absolutely safe. Rule of Furiten, and that it had already been discarded since the player declared Riichi.
12) White Dragon
13) 1 Pin: Absolutely safe. See #11.
14) 5 Man: Absolutely safe. This was discarded by the same player last turn, and since Riichi player didnt' want it then, they wouldn't want it now.
15) 7 Man: Absolutely safe. This was the tile that was discarded when declaring Riichi; therefore it is also subjected to the rule of Furiten.
16) White Dragon: Absolutely safe. Discarded by Riichi player.
17) 8 Sou: Absolutely safe. Whereas this tile wasn't safe before, since it was discarded and passed by the Riichi player, then it becomes absolutely safe.
18) 6 Pin: Absolutely safe. See previous explanation.
19) 7 Pin
20) 9 Pin: Absolutely safe. Rule of Furiten, and rule of thumb of terminals.
21) 3 Pin: Dangerous. This is the first dangerous tile in a while, and it is so because there is no 3 Pin in any other player's pool. However, it passes.
22) 6 Pin: Absolutely safe, since this is the second time it had been discarded.
23) 5 Sou
24) 1 Man: Safe, due to the rule of thumb of terminals.
25) North: Absolutely safe. Rule of Furiten.
26) 2 Sou: Absolutely safe. Ignoring the double reverse Dora indicators (Which you wouldn't even know about unless Riichi player won), it is safe due to the Rule of Furiten.
27) East: Tsumo
I mentioned before that I'd go in order to simplify things; this left out a few discards which we will go over now. We start with West player's last discard, then discuss the rest of North player's discards.
28) 2 Pin: Safe. Although not visible in the image, North player discarded a 2 Pin early in the game and South player completed a triplet with it. By probability, it is safe, but since it had not been played during the Riichi cycle, nor is it a Furiten tile, it can still be dangerous.
29) 5 Sou: Absolutely safe. Rule of Furiten.
30) 9 Pin: Absolutely safe. Rule of Furiten.
31) 1 Man: Absolutely safe. Was discarded previously (#24).
To sum it all up, just remember 3 things:
1) Rule of Furiten
2) Rule of thumb of terminals and honors
3) Any tile someone else discarded during the Riichi cycle means that you can discard it without worry (At least without worry from the Riichi player).
Remembering these simple things allows you to basically lose less. Once again, I note that no matter how good you are at not dealing into someone's hand, they can always just get lucky and Tsumo.
Things get more complicated when 2 or even 3 players declare Riichi, but it really is the same concept. By having discard pools, it makes Riichi Mahjong the most analytical type of Mahjong, which is why it's my preferred variant.
I end with the original picture, with the hands and melds visible. I'd also like to note that this is my best hand ever (Last one to hold the title was a 13 Orphans hand).
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