Analysis - Hanchan vs Tonpu vs Sanma

This analysis will look at some of the differences between the primary game modes. hanchan (East-South games), tonpu (East-only games), and sanma (Three-player games).

First, the sample size. In my dataset, there are 13,049,280 rounds of hanchan, 2,529,327 rounds of tonpu fast, and 4,054,278 rounds of sanma. The sanma games are all hanchan games. Overall, there are slightly more sanma hanchan games played than tonpu games, which is also interesting.

Let's start by looking at the end results of games, similar to what we did in the very first analysis.

The tsumo rates are about the same between tonpu and hanchan, but the ron rate is higher, suggesting a higher deal-in rate. Tonpu also reaches an exhaustive draw less often, but more often than sanma. Despite the lower amount of tiles in the wall, hands being easier to build in sanma offset it. Of course, four wind, four riichi, and triple ron abortive draws are not possible in sanma.

Interestingly, sanma has a much higher abortive draw rate, with many kyuushu kyuuhai called. In the I told you not to go for kokushi article, it mentions that you can go for kokushi with eight tiles in sanma. So, you would think if you had the chance for a draw, you would just go for the kokushi, since that's at least nine. Maybe I'll have to do an analysis on kokushi in sanma later to verify this.

The tsumo rate is understandably higher in sanma. You get two chances to ron per one chance to tsumo, compared to three chances to ron per one chance to tsumo in four player.

Let's compare the call rates next. Tonpu is often cited as being a lawless wasteland full of Mankeys that call at every opportunity, so let's see how much higher the call rate is. We'll also look at it by round, so we can see if a tonpu game has any correlation with a certain part of hanchan games.

Overall, it's a bit under 5% higher. The call rate in the east rounds of a tonpu game is higher than the call rate of the South 4 round of a hanchan game. In the South round of a hanchan, players will be ahead or behind. People with comfy leads over the people below them have an incentive to not call, and maintain their leads. But, in tonpu, people start off even, so everyone has a reason to win quickly. That's my theory for why the call rate is higher.

It's interesting that the call rate in the South round of tonpu is higher than the call rate in the West round of a hanchan. I would have expected these to be fairly similar, but maybe the tonpu players are just more call happy in general from the format.

For sanma, the call rate stays fairly even throughout the main rounds. Since there's no chii, the call rate is lower in general, and it's harder to find opportunities to call. Maybe this, combined with the higher value hands, makes it so the reasons and chances to call are fairly constant? I'm not sure. It does go up in the West round.

Sort of the opposite of call rate, there's riichi rate. How often do people riichi in each game type? Again, we'll sort by round.

The tonpu riichi numbers actually line up fairly well with the hanchan numbers if you ignore the East round of the hanchan stats. Sanma is sitting higher up than all of them. The lower number of tiles makes it easier to get the tiles you need, and thus, makes it easier to reach tenpai and call riichi. Also, with tenpai speed being compared between three players instead of four, there's less competition. If we take the 24.43%, multiply it by 3, and divide by 4, we get 18.32%, which is still higher than the other modes.

The remaining primary stat is deal-in rate, so let's check it out.

I think the explanation for these numbers, with regards to hanchan and tonpu, is the same as the explanation for the call rate. Plus, having a higher call rate will mean the players have less defense. For sanma, with only three players, there's one less other player to deal in for you, or reveal safe tiles for you, so the deal-in rate is understandably higher.

A stat that isn't shown normally on Tenhou, but is in Majsoul, is your average hand value. All those calls in tonpu should lower the average hand value, and we can look at just how inflated the sanma scores are.

The tonpu scores aren't that much lower. Around 10% on average. The sanma scores are much higher, nearly mangan on average. All those nuki dora, more useful dora tiles, and missing suit really help out.

There's one more thing I want to look at. The yaku distribution for each round. These tables are pretty big, so click the image to make them larger if you don't have a magnifying glass handy. A green cell means that yaku rose in placement compared to the previous round, while a red cell means it fell in placement.

It's red five mahjong, so akadora claims its rightful place as the most important way of gaining han. We already saw the riichi rate steadily declining in a previous table, so riichi falling as the round goes on shouldn't come as a surprise. Honitsu and Sanshoku Doujun switching places in South 4 is interesting, perhaps due to a hesitance to go after hands that are seen as slow in the final round. Itsu and Toitoi switching places also indicates this. You can see the percentages of each in the spreadsheet linked at the end of the post, but it's a bit hard to read.

Anyway, let's compare this to tonpu.

The higher call rate means menzen tsumo is lower in the rankings. Other than that, it's actually pretty similar. East 3 matches up with South 3 in the Hanchan table, aside from iipeikou, and South 4 in hanchan and East 4 in tonpu are identical. The percentages of each are within 0.5% of each other.

Finally, sanma. The removal of most of the character tiles make this a much different ruleset, so it's unlikely to be comparable to the others, but it might have interesting data regardless.

Honitsu rises only one place, but the percentages show it's more drastic than it looks. In hanchan, honitsu has around a 1.65% rate, while in sanma, it's around 2.65%. Pinfu also falls quite a bit. I suspect the lower number of tiles leads to a lot more clumping, and you can kind of see that with iipeikou's rise in position, and sanankou beating out chanta.

Rinshan being on the chart is also amusing, which is of course largely in part due to the kita calls. Aka dora also falls, partly because there's one fewer, and partly because the normal dora is more likely to be useful in your hand with fewer tiles.

Well, that was a lot of data. Hopefully it was as interesting to you as it was to me! You can see all the data, and some more stuff, in this spreadsheet. You can find the code on Github. See you next time!