Guide - Floating Tile Order

Initial discard order is something that comes up in nearly every hand. So, there's good value in improving it. I won't personally be putting a strong focus on it until month 4, but I've been reading about it in books and taking notes, so I'll post this now in case other people want to use it.

Fundamentals

First, let's look at the basic tile discard order. Most Mahjong players who have tried to learn at all will know some variation of this. I'm sure if you're one of the few people still reading this blog in 2025/2026 you also already know it.

4/6 > 3/7 > 5 > 2/8 > Seat Wind > Dragon > Round Wind > 1/9 > Guest Wind > Useless Tiles

And some explanation in case any of that sounds weird:

• 4/6 is best because they connect to red fives as a ryanmen. All their connected shapes also end up fitting tanyao
• If the red five is visible and tanyao isn't a consideration, you can cut them before 3/7
• 3/7 > 5 because ryanmen involving 3/7 have higher win rates
• Yakuhai > 1/9 because being able to call is strong and 1/9 typically only make bad shapes, so losing the bad shape ukeire tends to be worth it
• Exception: If the rest of your hand is pinfu, you'd rather pair a terminal or guest wind than a yakuhai, so the yakuhai can go first
• Exception: If your hand is very good, you can cut yakuhai first to try to discard them before others can pair theirs and call it
• Dragon order is minor enough to not matter; guest winds get cut counter clockwise by default
• You keep your own wind longest because nobody else can use it, and you cut the round wind earlier than dragons because it's worth two han for somebody else when it's not also your own wind
• Useless tiles are, for example, the other two suits in a flush hand

If you somehow haven't already heard that order or close to it, you should probably adopt it, it's not much effort at all.

When you have 6 blocks, you cut the weakest block and leave the strongest 5.

When you have 5 blocks, you cut the floating tiles connected to the strongest blocks. Eg, between 446 and 445, you cut the 4 from the 445 if you have a pair elsewhere. Five block theory is explained everywhere so I won't go into depth here.

When you have 4 or fewer blocks, that's when the value of floating tiles is highest. Then, you need some way to distinguish between which e.g. 3 is better. That will be the focus of this. The above alone already gets you 80% of the way there. Let's try to raise that from 80% to 90%. Mahjong is a game about small advantages building up over hundreds or thousands of games, after all.

Comparing Floating Tiles

For all of these, imagine the shapes presented are your only tiles in that suit, and that your hand is 2-shanten with 4 blocks and a pair elsewhere. Thus, you need to make one more block.

Something like this hand. What 3/7 to cut?

Now, let's look at some rules for comparing floating tiles. The bold parts are the important things to remember, and the rest is explanatory or quite minor in comparison.

The closer it is to a completed shape, the better it is than an isolated floater. (3456 > 3567 > 3678 > 3)

• Distance 0: 3456 has lots of ryanmen transformations (2457 for ryanmen, 18 for kanchan)
• Distance 1: 3567 can become sanmenchan (24 for good wait, 158 for kanchan)
• Distance 2: 3678 has one less kanchan option (24 for ryanmen, 15 for kanchan) but drawing 5 gives 35678 which can then become ryanmen on 2679
• Distance 3: In the case of a 2/8, 2678 drawing 4 then 5 gives a sanmenchan instead of a ryanmen, giving value over a normal 2/8.
• Isolated: 3 is straightforward (24 for ryanmen, 15 for kanchan). But, after drawing 5, it has fewer upgrades than the 3678 shape (only 26 for ryanmen).
• It's practically identical to a 3 in 3789, but is one tile better after drawing 5 then 6 (56789 is using one seven already). Then again, 356789 is getting close to ittsuu (pure straight). This is minor enough to just stick to the rule rather than complicating it further.

Among the zero distance cases, there's 3345 (aryanmen), 3445 (nakabukure / bulging shape), and 3456 (yonrenkei / nobetan). The difference between 3445 and 3456 can vary depending on the hand, but usually both are better than 3345. They all get worse on the edge. 1223 is worse than 2234, 1234 is barely better than an isolated tile.

The closer it is to a taatsu, the worse it is than an isolated floater. (3 > 378 > 367 > 356) Note that 357 does not have floating tiles, that's a block. Similarly, when a tile overlaps an incomplete shape, like 233 or 335, it's generally viewed as one block rather than a floating tile, but you may want to e.g. cut a 2 from a 223 to keep a floating 3 in some cases.

Imagine drawing 4:

• 3: 34 gives a new block
• 378: 3478 is two blocks (same as above in this case)
• 367: 3467 is two blocks with overlap on the 5, so 4 less ukeire
• 356: 3456 is still one block. Lots of ryanmen transformations but no immediate progress on the block forming front

Now instead imagine drawing 5:

• 3: 35 is a block
• 378: 3578 is the same block
• 367: 3567 is as described above, no immediate progress
• 356: 3556 is a shape everyone hates

Then imagine drawing 6 with all of those:

• 3: 356, discard 3, get ryanmen
• 378: 35678, this completes the ryanmen, so the draw is not related to this floating 3 (in other words, the 78's direct ukeire is overlapping with the 35's upgrade ukeire. The ukeire here and above is the same, but above has four more tiles that can widen the hand. Thus, 3 > 378)
• 367: 35667, discard 3, get better floating tile
• 356: 35566, ew...

Even very far apart ones follow this. Eg, 2 > 278. Imagine drawing 4, cutting elsewhere: 24 vs 2478. Then imagine drawing 5, cutting 2: 45 vs 4578. The latter has overlap, so it's a worse outcome.

So, with these two things, another shape being included in that suit anywhere in the hand affects the tile's worth. Floating tiles in suits that have completed shapes are better than isolated ones which are better than ones in suits that have incomplete shapes.

When equal distance, close to good shape is better than bad shape.

• Distance 0: 233 > 335. Imagine drawing 4, 2334 is better than 3345.
• Distance 1: 356 > 355. Imagine drawing 4, 3456 is better than 3455.
• Distance 2: 367 > 368. Imagine drawing 5, 3567 is better than 3568.
• Distance 3: 378 > 379. Imagine drawing 5, 3578 is better than 3579.

For floaters in the same suit, connected by suji is bad, connected by a gap of 3 is good. (15 > 1 > 14; 37 > 3 > 36)

• Suji gap: Anything within the gap will also make a shape with the other side. With 14, drawing 2 or 3 will make a shape with the 4 even if the 1 isn't there.
• Gap of 3: Allows for ryankans to be made (15 draw 3 -> 135), which are good shapes.

To be overly specific, ryankan acceptance is better than being two away from a completed shape (2456 > 26 > 2567 > 2678), and suji overlap is only better than connecting to a two-gap bad shape or one-gap good shape (any other 2 > 25 > 257 / 255 > 245). These specific comparisons won't come up often, so just remembering the general rules will be good enough.

With all three suji tiles, cut an outer one for max good shape ukeire (258 -> cut 2 or 8, -4 ukeire, but three ryanmen chances vs two. 147 -> obviously cut 1)

Now, if the floating tile is a dora, or can give you things like ittsuu (pure straight) or sanshoku, its value will also rise. The comparison between potential value vs hand speed will be a case-by-case sort of thing, depending on the options, the point situation, etc.

Everything here also assumes you already have a pair. You can generally just pick up a pair along the way, but some shapes do get stronger when you need one. For example, the normally very bad 245 becomes better, with 3 giving a nobetan and 25 giving a pair+shape.

And, with all of this, the visible tiles will change the value of each shape. That's why this is only going from 80% to 90%.

Let's take another look at our random example hand.

In the example hand, our candidates are 3m37p7s. 3m is very close to a completed shape, so it is a strong floating tile. 7s is part of a good block and keeps us at two pairs, so we'd like to leave it unless we have a good reason. 37p could make a ryankan with a 5p draw, but they are the weakest overall, so one should go. Between 3p and 7p, 7p could be part of a distant 678 sanshoku (draw 6p cut 3m draw 8m cut 5m draw 6s cut 7s tsumo 8p), so we'll cut 3p. Looking at the efficiency trainer's explorer section for a quick sanity check:

• 7s: 66 ukeire, average of 17 1-shanten ukeire
• 37p: 60 ukeire, average of 23 1-shanten ukeire
• 3m: 53 ukeire, average of 22 1-shanten ukeire

Alright, that was a lot of information. Just focus on the bolded parts.