In this post we'll look at how often players win on each tile, and how that changes based on their discards, early discards, riichi tile, and the dora indicator.
For this, we'll only be looking at hands that declared riichi on turn four or later, and went on to win. This gives us a total of 4,278,292 hands to look at. To start, we'll check the percentage of wins that occurred on each tile.
For the following images, the percentages will be compared to the character tile win rates. To start with, let's look at how the win rates change based on what the dora is.
These percentages are how much larger or smaller the win rate is from the base character tile win rates. For example, when the dora is 1, the 9 has a 71% adjusted win rate. Since 9 is originally 2.79%, that means the win rate of the 9 when the 1 is dora is about 1.98%. A percent less than 100% means the tile has been made safer, while a percent greater than 100% means the tile has been made more dangerous.
The 9 being safer when the 1 is dora can be explained simply: When the 1 is dora, the 9 is the dora indicator, and thus there is one less in play. This means there's one less tile to draw or be discarded, so the rates will naturally be lower. You might want to consider that the base should be around 75%, and thus, the rates of dora indicators higher than that mean it's dangerous.
You can see this pattern all throughout the table. When 3 is dora, 2 is won on less. When 6 is dora, 5 is won on less. When 8 is dora, 7 is won on... more? Huh?
This is due to the dora coming after the indicator. When 8 is dora, the 89 penchan becomes more desirable. Same with when 9 is dora. You can see a similar effect when 2 and 1 are dora. The penchan becomes more desirable, and thus, the win rate on 3 spikes.
Next, let's take a look at how the win rate changes based on what tiles are present in the player's discards.
Also, since the charts are very similar and I want them close together, let's also look at early discards. The first three, to be exact.
We can see the effects of many common defense techniques laid out in this table. The safe tiles below the 2, 3, 4 and above the 6, 7, 8 are sotogawa tiles. The diagonals three spaces to either side of the central diagonal show the suji. We can also see that 4 making 7 suji and 6 making 3 suji are the least impactful of all the suji, another common piece of knowledge due to the existence of penchans.
Just after the suji tile, there's a danger tile. A 4 discard makes the 8 more dangerous, for example. This is ura suji. A 46 kanchan being upgraded to a 67 ryanmen. I'd been told this wasn't statistically significant, but it sure seems to be. It can be seen most clearly around the 5.
How different is the change when we look at tiles after riichi?
None of the adjacent tile safety shown in the early discards is present in the after-riichi discard chart. The largest thing we see is simply the suji tiles, which are a bit more dangerous when the suji is 2, 8, 3, or 7, but the same or safer for the others.
The general >100% trend for non-suji tiles will in part be because, with one suji removed, all the others become a bit more dangerous. One interesting thing is the 3 making the 9 a little bit safer, and the 7 making the 1 a little bit safer. These are two suji jumps, 3 -> 6 -> 9. How mysterious. But, in general, all the tiles after riichi tell you are suji.
Let's check out how the riichi tile affects everything.
This is quite the patchwork of colours. The immediate takeaways are that a riichi on 4 or 6 makes the outer suji (1 or 9) much safer. Comparatively, other sujis are often more dangerous or unaffected. For example, the 4 riichi makes 7 more dangerous, while the 5 riichi doesn't affect the safety of the 2 and 8, essentially making them non-suji.
You can also see matagi suji come into play with some tiles. The 3 riichi makes the 1245 a bit more dangerous, the 5 makes the 3467 slightly more dangerous, etc. Some of the patterns are made safer, strangely.
To top it off, let's take a look at how it changes when a tile is both in the first three discards AND the riichi tile.
Now this is a neat chart. All the middle tiles get at least two tiles of safety on either side. The dangerous corners from the riichi table have been muted, but still retain a slightly heightened sense of danger. The 4->7 and 6->3 sujis are still dangerous.
Another defense technique that comes up now and then is aida yon ken. This is when a player discards two tiles that are four tiles apart. For example, 1 and 6, or 3 and 8. Conventional wisdom is that the inner suji (2-5 for the 1 6 aida yon ken, or 4-7 for the 3 8 aida yon ken) is more dangerous. So, let's take a look.
We can see that the inner suji becomes extremely dangerous. With a 1 and 6 discard, for example, the 1-4, 3-6, and 6-9 suji are prevented. As well, the 4-7 suji (56 ryanmen) becomes less likely, as they've discarded a six, and same for the 5-8 suji (67 ryanmen). This leaves 2-5 as the only really viable suji left in the suit. Meanwhile, the tiles in the middle of the aida yon ken become pretty safe, with their win rates dropping lower than suji tiles.
For a very similar thing, we can look at nakasuji. Nakasuji could be called an aida 5 ken shape, as there are five tiles between them. 1-7, 2-8, and 3-9.
The win rate of nakasuji tiles is lower than the win rate of pre-riichi terminal suji. Interestingly, the tiles around the suji are dangerous, particularly towards the outside.
Someone also wanted me to check the aida 6 ken numbers, so I'll include that chart as well for completion's sake.
All of this data should be taken with a grain of salt, as we're looking at what tiles people
won on, rather than what tiles they were
waiting on. So, the numbers would be a little different if we looked at that, but the analysis would also take a hundred times as long. Still, perhaps later I'll look at all the wait patterns of riichi hands and their win rates.
For a demonstration of the effect this has, let's look at something fairly random: The win rate based on what the ura dora indicator is.
It seems the suji of the ura dora indicator is more dangerous. But, in reality, it's just that the ura indicator removes one of those tiles from the game. Therefore, ryanmen waits involving it have one less tile to win on for it. We can also see all the tiles around the ura indicator getting a bit less likely, as having one tile out makes it harder to form blocks that involve that tile.
If you want to see all the messy raw data, you can find it in
this spreadsheet. Until next time!
No comments:
Post a Comment