Statistics

I told you not to go for Kokushi

umaikeiki

— 5 min read
I told you not to go for Kokushi

We’ve all been there: you’re dealt a hand with a lot of yaochuu tiles — ones, nines, and characters — and you find yourself asking, “Do I go for the stupid thing?”

Despite being one of the most common yakuman, Kokushi Musou still boasts a wide arsenal of ways to betray you. Those last few tiles never seem to come; your discards give away your strategy; you have no real defense; and if the other players discard all four of a tile you need, you can’t easily switch to something else.

So when do you go for it? An advanced player might say that you can do it when you start with 11 different yaochuu tiles, but if you’re playing a 3-player game on Tenhou, you can do it with 8. Aside from that, are there any situations in which it’s worth being more aggressive? Are there any strategic uses for the forced redeal (kyuushukyuuhai)? In this post, I will look at the strategies employed by players when they had the chance to go for Kokushi. What choice did they make? Were they successful? What situational information influences the decision to be more or less aggressive?

As usual, this data comes from querying the  Tenhou statistics database maintained by bps. For this post, I looked at just over 9000 hands, each of which started with 9 or more distinct yaochuu tiles. All results came from 4-player games in the Houou lobby.

First off, let’s identify the strategies you can use when dealt a lot of yaochuu tiles:

  1. Redeal the hand (kyuushukyuuhai)
  2. Go for yakuman
  3. Try to make some other hand

Now let’s look at what choices people made when dealt 9, 10, 11, or 12 different yaochuu tiles:

Starting YaochuuRedealsKokushi AttemptsOther Attempts
982.02%4.72%13.26%
1044.16%31.59%24.25%
1110.67%64%25.33%
120%66.67%33.33%
Let’s see the success rate. Did they get their Kokushi?
Starting YaochuuKokushi GetsOther Agari
95.5%13.26%
1013.55%1.96%
1135.42%0%
1250%0%
A note on that 12-tile case: I only found 3 games in which that happened. That means there’s not enough data to make any meaningful analysis of that situation. Of course, 12 tiles is already 1 shanten if not tenpai for yakuman — you’d have to be crazy not to go for it! As for the “other” attempts — they include the cases in which they originally were trying for Kokushi but had to bail (either to defend or because Kokushi became impossible). As you can see, bailing from a Kokushi attempt doesn’t offer much hope of making any other hands.

What about speed? How many turns does it take to complete your Kokushi?

Starting YaochuuAverage Turns to KokushiStd Dev
911.253.46
1010.233.44
119.184.11
1240
This doesn’t seem too helpful, particularly in light of the success rate highlighted above. I wouldn’t go saying you can turn 9 tiles into Kokushi in just 11 turns when only 5.5% of attempts to do so actually succeeded. Maybe instead we should look at how many turns elapsed between getting each new tile.
Progress to KokushiAverage Turns since Previous TileStd Dev
10th tile4.32.47
11th tile4.912.93
12th tile4.072.96
13th tile2.242.26
This is slightly better since it takes into consideration all the attempts, including the ones that failed. Expect it to take 2-6 turns to get each new tile. Of course, if you have a pair, getting the 13th tile is much easier, since you can Ron it off someone else rather than waiting to draw it yourself.

We can assume from this data that it makes sense to go for Kokushi when you start with at least 11 of the tiles needed. A success rate of 1 in 3 is phenomenal for a 4-player game. Anything less than 11 and you might as well force a redeal. Or should you? Even a 10% chance of success could be worth the tremendous Yakuman payout. We can see that people did sometimes try for Kokushi even when dealt only 9 or 10 of the tiles they needed. Since this is the houou table, we can assume that any silly “limit maker” or other showy playstyles don’t come into play here. There must have been some situational factors that made these players decide the risk was worth the reward. If we take a look at these factors, maybe we can identify if there is a consensus on when to be aggressive and when to play it safe.

One obvious factor would be placement by score. Here’s the frequency of forced redeals separated by place:

Score PlacementRyuukyoku with 9 tilesRyuukyoku with 10 tiles
1st84.52%51.52%
2nd84.14%49.61%
3rd84.27%43.54%
4th73.18%32.29%
We can clearly see a strong preference to avoid last place here. The desperation to get out of last is so powerful that some players are even trying to make Kokushi with a “bad” starting hand.

How about early vs. late game? Here’s the frequency of forced redeals separated by phase:

Phase of gameRyuukyoku with 9 tilesRyuukyoku with 10 tiles
Early83.75%39.69%
Early Mid82.38%42.32%
Late Mid82.20%44.79%
Late79.29%50.94%
This unveils some interesting information. The placement chart showed something like “desperation” at play, but this seems to show more of a calculated gamble, and highlights the difference between a 9-tile and a 10-tile start. This chart tells me that going for Kokushi with only 9 tiles is a “bad” move, but trying with 10 tiles could be called “edgy”. While your chance of agari is maybe half what it would be for a typical hand, the payout is four times or more! In addition, when you take a gamble in the first round and fail, you have the whole game to recover. If you take a gamble in the final round, however, there is no recovery should you fail.

What about seat? Does being Oya make players more or less likely to try for Kokushi? Here’s the frequency of forced redeals separated by seat:

SeatRyuukyoku with 9 tilesRyuukyoku with 10 tiles
East90.36%62%
South81.8%43.74%
West79.24%35.7%
North76.57%34.94%
This shows a huge preference to avoid risk when Oya. This makes sense: as dealer, you don’t want to invest too heavily in a slow and risky hand. The chance of someone else getting a tsumo can be pretty high when you are waiting for the last few tiles, and you stand to lose more points as dealer. I think that most players would prefer to make fast and cheap hands during their dealer turn. Interestingly enough, people are more likely to take the risk and go for Kokushi when they are North, moreso than when they are South or West.

So, to recap:

  • Go for Kokushi when you start with 11 or more tiles. The odds are actually better than your odds with a typical starting hand.
  • Go for Kokushi with 10 tiles only when the points are important in the long run — for example, in a tournament where points carry over from each game.
  • Don’t attempt Kokushi if you only have 9 tiles.
  • Players who are in a position to take risks will often go for Kokushi with “bad” hands.

Finally, feel free to post any interpretations you might have for the data shared here. I’m sure there are quite a few strategic angles that I’ve overlooked. I also haven’t covered defense. Maybe that will be a future article?

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