Mahjong Hand Reads: Irime Case 1
Opponent Call timings:
Chii 2s => cut south
Chii 2p (tsumogiri) => cut second 7p
I had a pretty interesting South 4 push / fold decision recently, with the potential for an even more interesting set of reads. I'm going to start by analyzing the dealinrate of 7p (at the time it was pushed) and 1m, and then make a conclusion on the discard choice.
Incentives
Let's start by analyzing the all last incentives.
Our competitor declares riichi from 1st place, temporarily dropping to 2nd place from the riichi stick cost. They declare riichi into two pretty threatening 1 call hands, suggesting that they have no yaku and a good wait.
The dealer has called for a seeming honitsu hand in the dora suit, with a lot of suit overflow. The green dragon is live, and the red dragon and east are once cut. They cut 7p into the ippatsu turn risking last place, likely indicating tenpai with a valuable hand. With so many tiles in their suit cleared, the only remaining ryanmen is 14s. The dealer could also at any time start folding to try and avoid last, especially near exhaustive draw. Even with mangan, they don’t have a huge chance of hitting 2nd or 1st.
Last place calls a ryanmen before the riichi stick is put in. They need 4500pts to escape last, suggesting they have 4 han, or 3 han with direct ron and tsumo outs. After the riichi stick comes in, last place can now win any 3 han hand. It’s possible that they have skipped ron on a tile from 1st or 2nd place which would have confirmed 4th before the riichi stick. They’ve cut many middle tiles, and are likely tenpai or 1-shanten.
Irime
https://mahjong-ny.com/features/terminology/
I first heard about the term “irime” reading Riichi Mahjong Strategy by Nemata. Irime refers to the tile that is drawn when a player goes from 1-shanten to tenpai. By performing an analysis on what kind of 1-shanten hands could possibly cut the last tedashi (tile from within their hand) into tenpai, we can better estimate how dangerous different tiles are.
For example, let’s say that a player has this hand, and get fed a 3m chii. They would call the 3m and cut 5m, waiting on 47s. The 3m would be the irime tile, and the 5m would be the last tedashi. From the perspective from another player, if we assume the 3 call player is tenpai with a pair, their 1-shanten shape would be pair + 455m + some other shape. With reading, we are unable to gain any information about their other shape, because the 3m irime and 5m tedashi cannot give any information about the other shape. However, if they chii 47s cut 5m, that 5m could have come from a variety of complex 1-shanten shapes, such as 455m, 556m, 135m, 579m, 335m, 577m. We get more information when the irime tile is in a different suit than the last tedashi.
Here is a chart that analyzes the dealinrate of tiles that are matagi, or 1 or 2 tiles away from the last tedashi, assuming that the player is tenpai.
The top 3 lines are chii with 1/2/3 calls, and cutting a tile that’s not part of call.
For example, on turn 12, if someone calls 56s and cuts 5m, and we know they are tenpai, the combined dealinrate of 36m and 47m are around 55%. Let’s say that 36m passes against their pond - the dealinrate of 47m has gone up drastically, since we just ruled out ~27.5% of the original dealinrate.
The black line is matagi dealin to riichi, and is around half the chii examples. This makes sense because without the chii which reveals the shape that the call completed, it’s roughly a 50-50 between which of the 1-shanten shapes completed when the player declares riichi. For example, if someone declares riichi cutting 5m, we might be able to say that 36m and 47m dealin 55% of the time if we know that they drew 7s to complete 56s. But it’s also possible that their 1-shanten hand was 455m 34s, and they drew 6m, completing the shape around the riichi tile.
So tiles near the riichi tile aren’t necessarily extremely dangerous, because the irime tile could have completed the shape with the riichi tile. For open hands, when the last chii informs us that the irime tile and the tedashi tile are far away from each other, tiles close to the tedashi tile are around 2 times more dangerous compared to if someone declared riichi cutting the same tedashi tile.
However, there are special cases where we can make reads based on an opponent’s discards, and eliminating 1-shanten possibilities can make some tiles much more dangerous than the corresponding lines on that chart.
- 5p was kept as a safe tile
- 5p was kept as a floating tile
- 1335p cut 3p, cut 5p on tenpai
- Ankou headless 555p + 2 unrelated shapes
- 556p, 566p, the classic matagi cases
- 579p
We can rule out case 1 because the safe haku was rejected in favor of 5p.
We can rule out case 2 because the player would choose 5s floater or choose a safe tile over furiten 5p. 5678p would probably declare riichi cutting the safer 8p instead of 5p.
We can rule out case 3 because we see every 3p.
We can rule out case 4 because we see 3 5p.
Case 5 is still possible. There are 4 combos of 556p, and 6 combos of 566p.
Case 6 is unlikely because we see 3 7p and 2 9p. There are 2 combos of 579p.
So let’s naively assign probabilities to the cases defined in Case 5/6 based on the combo counts.
556p 4/12 = 33%, 566p 6/12 = 50%, 579p 2/12 = 16%.
Let’s assume that the opponent’s 1-shanten is (shape with 5p) + pair + XY. In the following sections, we will use various assumptions to estimate 7p dealinrate. Feel free to follow the combo counting, or just read the highlighted conclusions.
7p Matagi Dealin Estimate
Let’s try to estimate the dealinrate of 7p at the turn of the riichi (before the dealer pushed it and it passed).
We’ll start with fewer assumptions and add more information to refine our read.
If we see 5p riichi, what is the chance that the opponent is waiting on 7p? For simplicity, let’s say XY is a ryanmen 50% of the time and a kanchan 50% of the time.
Case 1: XY kanchan, weighted 50%
1a: 556p
- 1/3 * 4/16 XY fills first = 1/12 5p cut, 7p wait (4 uke on XY, 12 uke on 556p + pair)
- 1/3 * 8/16 47p fills first = 2/12 5p cut, XY final wait
1b: 566p
- 1/2 * 4/16 shanpon fills first = 1/8 5p cut, XY final wait
1c: 579p
- 1/6 * 4/12 XY fills first = 1/18 5p cut, 8p wait
- 1/6 * 4/12 8p draw = 1/18 5p cut, XY final wait
Total: (1/12 + 2/12 + 1/8 + 1/18 + 1/18) / 2 = 24.3% Case 1
Case 2: XY ryanmen, weighted 50%
1a: 556p
- 1/3 * 8/20 XY fills first = 2/15 5p cut, 7p wait
- 1/3 * 8/20 47p fills first = 2/15 5p cut, XY final wait
1b: 566p
- 1/2 * 4/20 shanpon fills first = 1/10 5p cut, XY final wait
1c: 579p
- 1/6 * 8/16 XY fills first = 2/24 5p cut, 8p wait
- 1/6 * 4/16 8p draw = 1/24 5p cut, XY final wait
Total: (2/15 + 2/15 + 1/10 + 2/24 + 1/24) / 2 = 24.6% Case 2
Summary: conditional dealins given 5p riichi + 1-shanten assumptions
7p dealin: ½ * (1/12 + 2/15) / (489/1000) = 22.2% dealinrate
8p dealin: ½ * (1/18 + 2/24) / (489/1000) = 14.2% dealinrate
XY kanchan dealin: ½ * (2/12 + 1/8 + 1/18) / (489/1000) = 35.5% dealinrate
XY ryanmen dealin: ½ * (2/15 + 1/10 + 1/24) / (489/1000) = 28.1% dealinrate
Sanity Check: all conditional probabilities add up to ~100. Note that XY covers a wide range of possible kanchans / ryanmens, so the numbers are higher than the dealin rates of the average musuji.
Irime + Ankou Suji
At the time of the riichi, we see 2 7p, and 3 4p. Ankou suji tiles / suji to 3 visible tiles raise dealinrate by ~2% for the average turn 9 riichi. This 2% dealinrate increase comes from a lowered irime chance. If the player is less likely to have drawn 47p into tenpai, it is more likely than usual that they completed the other shape in their 1-shanten, and are on 47p wait.
But when combined with a limited set of possible 1-shanten shapes from pond reading, we can explore if the ankou suji effect could be higher than 2% in specific cases.
Let’s repeat the above analysis, but see what happens when we remove 4 tiles from the 47p ryanmen. I’m not going to remove 5 tiles, because this would certainly overestimate the effect, since other tiles could be missing from the XY kanchan/ryanmen or the shanpon pair. I'll use 4 as a compromise.
Case 1: XY kanchan, weighted 50%
1a: 556p
- 1/3 * 4/12 XY fills first = 1/9 5p cut, 7p wait (4 uke on XY, 8 uke on 556p + pair)
- 1/3 * 4/12 47p fills first = 1/9 5p cut, XY final wait
1b: 566p
- 1/2 * 4/12 shanpon fills first = 1/6 5p cut, XY final wait
1c: 579p
- 1/6 * 4/12 XY fills first = 1/18 5p cut, 8p wait
- 1/6 * 4/12 8p draw = 1/18 5p cut, XY final wait
Total: (1/9 + 1/9 + 1/6 + 1/18 + 1/18) / 2 = 25% Case 1
Case 2: XY ryanmen, weighted 50%
1a: 556p
- 1/3 * 8/16 XY fills first = 1/6 5p cut, 7p wait
- 1/3 * 4/16 47p fills first = 1/12 5p cut, XY final wait
1b: 566p
- 1/2 * 4/16 shanpon fills first = 1/8 5p cut, XY final wait
1c: 579p
- 1/6 * 8/16 XY fills first = 1/12 5p cut, 8p wait
- 1/6 * 4/16 8p draw = 1/24 5p cut, XY final wait
Total: (1/6 + 1/12 + 1/8 + 1/12 + 1/24) / 2 = 25% Case 2
Summary: conditional dealins given 5p riichi + 1-shanten assumptions
7p dealin: ½ * (1/9 + 1/6) / (1/2) = 27.7% dealinrate
8p dealin: ½ * (1/18 + 1/12) / (1/2) = 13.9% dealinrate
XY kanchan dealin: ½ * (1/9 + 1/6 + 1/18) / (1/2) = 33.3% dealinrate
XY ryanmen dealin: ½ * (1/12 + 1/8 + 1/24) / (1/2) = 25.0% dealinrate
1st Place Ryanmen Riichi Assumption
What if we repeat the original analysis without the ankou suji effect, but add the condition that the opponent would not riichi a non ryanmen wait? In addition, let’s assume that they would dama any pinfu hands. Roughly 40% of hands that win include riichi, and 20% include pinfu (https://tenhou.net/sc/prof.html). Let’s assume that these hands completely overlap (they don’t because of dama), and that 10% of riichi hands have no pinfu + bad shape, and 10% of riichi hands have no pinfu + good shape. So for the shanpon draw, we will weigh it as normal since it is guaranteed to not have pinfu, but for all other ryanmen final waits, we will weigh them by a relative 50%.
Case 1: XY kanchan, weighted 50%
1a: 556p (weighted 50% for dama pinfu chance)
- 1/3 * 4/16 XY fills first = 1/12 5p cut, 7p wait (4 uke on XY, 12 uke on 556p + pair)
- 47p fills first => not ryanmen wait
1b: 566p
- not ryanmen wait
1c: 579p
- not ryanmen wait
Total: (1/24) / 2 = 2.1% Case 1
Case 2: XY ryanmen, weighted 50%
1a: 556p (weighted 50% for dama pinfu chance)
- 1/3 * 8/20 XY fills first = 2/15 5p cut, 7p wait
- 1/3 * 8/20 47p fills first = 2/15 5p cut, XY final wait
1b: 566p
- 1/2 * 4/20 shanpon fills first = 1/10 5p cut, XY final wait
1c: 579p (weighted 50% for dama pinfu chance)
- 1/6 * 8/16 XY fills first = 2/24 5p cut, 8p wait
- 1/6 * 4/16 8p draw = 1/24 5p cut, XY final wait
Total: (1/15 + 1/15 + 1/10 + 1/48) / 2 = 12.7% Case 2
Summary: conditional dealins given 5p riichi + 1-shanten assumptions
7p dealin: ½ * (1/24 + 1/15) / (148/1000) = 36.6% dealinrate
XY ryanmen dealin: ½ * (1/15 + 1/10 + 1/48) / (148/1000) = 63.3% dealinrate
8p dealin: 0%
XY kanchan dealin: 0%
Reverse Matagi
So depending on the assumptions, we’re estimating 7p dealin at 27.7% - 36.6% dealin rate. If we combined the ankou suji and 1st place riichi reads, this number could go up even more, though the 1st place only riichi’s good wait assumption may not be true, so I’m ok with using 36.6% as a reasonable upper bound.
Let’s move on to estimating the dealin rate of 1m, under the assumption that 7p has not passed yet.
Let’s start by counting the most plausible ryanmen deal ins: 47p, 14s, 69s, 14m, 25m, 47m, 58m. I ruled out red 5 sotogawa ryanmens and 69p (if 56p and 78p are both in hand, 7p draw into tenpai is not possible b/c 3 7p are in pond, and 4p draw is furiten). So there are 6 ryanmens not counting 47p. Let’s divide the XY ryanmen dealin% number from the above analyses, since we can rule out 1m bad shapes (1m is twice cut, ruling out shanpon).
1-shanten assumption: 4.6%
Ankou Suji + 1-shanten assumption: 4.2%
1m ryanmen dealin, 1st place riichi + 1-shanten assumption: 10.6%
The first 2 numbers seem to suggest a low estimate of 1m dealinrate. This is a result of the high matagi dealin rates and the 50% kanchan assumption. I think the truth is probably closer to the 100% good wait assumption.
Cleared Matagi
Now let’s investigate a different effect. Now that the really high dealin rate 7p from shimocha passed, what is the dealinrate of 1m? Let’s use the 1st place riichi + 1-shanten assumptions here.
7p has not passed, 1st place riichi + 1-shanten assumption: 10.6%
1m ryanmen dealin, 7p passes, same assumptions => 100 / 6 = 16.67%
Cleared Musuji
What if a different live suji clears- how does 1m and 7p dealinrates scale? Let’s say 2m passes.
7p dealin: ½ * (1/24 + 1/15) / (148/1000) = 36.6% dealinrate
1m ryanmen dealin: 63.3% / 5 = 12.66%
Bot Decisions + Revealing Hands
Analysis - Win:Dealin Requirement
We have a 1-shanten ryanmen + ryankan shape, and can push 1m, fold with 2p, or half push a tile like 8m. When analyzing all last decisions, I like to think about the win:dealin ratio which would make pushing good. I discussed this concept in a previous blog post.
Let’s try to estimate our average placement based on the incentives above.
Let’s start with the outcomes. If the riichi player wins, our average placement is 2nd.
If the dealer wins, we get 1st if the game ends (ron on last), an advantaged repeat if the dealer wins off of the riichi player, and a slight 100 pt advantage over the riichi player if they tsumo. This is a weighted average of ~1, 1.1, and ~1.4, let’s set our avg placement to around 1.2.
If 4th place wins, we get 1st.
So if we fold, our average placement is some weighted average of 2, 1.2, and 1, depending on the probability that each player wins. But we concluded that the riichi player probably has a good wait, meaning the weight on 2 should be pretty high, and that 4th place might not be tenpai, meaning the weight on 1 is lower. The dealer is probably not on the last ryanmen wait, and if we give a 2s pair to last place to satisfy our value read, it becomes even less likely. They could also decide to fold their hand at any point, drastically lowering our expected placement if we fold.
It’s very hard to weigh the winrates of these 3 players, and it’s not practical to do these calculations in a game, so let me just say that the Naga UI’s estimate is around 1.60. I think this number is pretty reasonable, because our competitor winning their probable good wait riichi seems like the most likely outcome. This would correspond to a required win:dealin ratio of 2:3.
If we assume the dealer folds out (which they probably should), the chance of the riichi player winning or exhaustive draw gets much higher, possibly making our average placement around 1.8 or worse, as we have to bet on last place winning. This would correspond to a very low required win:dealin ratio of 1:4. We can take a lot of risk in a desperate scenario.
Pushing a 10% dealin tile with a bad shape tenpai has a win:dealin ratio of around 1:1, and full pushing this 1-shanten might be around 10% winrate to 30% dealinrate, through pushing has added benefits of exhaustive draw chance and the ability to push and then fold on a worse tile (the option can only improve our w:d ratio when compared to full pushing).
So in conclusion, if we assume that 1m is a 10% dealin tile, I would say that the decision depends on if we think the dealer will keep pushing, suggesting fold if the dealer keeps pushing and push if the dealer folds. It’s possible that the dealer should start folding in row 3, assuming they are a rational player, though their ippatsu turn push might indicate that they’ll keep pushing. I personally buy this second assumption, meaning fold is probably better. If we use the information that the very dangerous 7p passed, we can estimate 1m dealinrate to ~16.6%, making fold even stronger.
If you manually recalulate the akochan EV estimate setting 1m and 8m dealinrate to 16.67%, these options actually become worse than folding the hand. For example, 1m dealinrate becomes: 58.9 * .8333 + 45 * .1667 = 56.58 pt EV, worse than folding with 6m (56.84 pt EV). (akochan is using 7 dan tenhou rates, so 1st is 90 pt EV, 2nd is 45 pt EV)
Takeaways
In summary, our opponent’s delayed block cut (3p => safe tiles => 5p) and the all last situation gave us a large amount of information that let us make reads on their 1-shanten hand shape.
Under certain assumptions, we concluded that the riichi tile matagi 7p was between 27.7 - 36.6% dealinrate. We used information from the opponent’s pond to rule out possible shapes involving the 5p riichi tile. We layered on 2 additional reads - ankou suji and higher ryanmen wait chance. These additional reads synergistically made 7p more dangerous. The combination of ankou suji and riichi tile matagi increased 7p dealinrate by 5.5%, more than the 2% average that we might find in a chart.
We observed what happens to other dangerous tiles when a very dangerous tile passes. Under the ryanmen wait assumption, 1m was ~10% dealinrate before 7p passed, and 16.6% dealinrate after 7p passed. When a really dangerous tile passes, the dealinrate of every other tile has to increase, so that the sum of all remaining tiles adds to 100%.
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