Analysis - Starting Seat Placement Bias

This week, we're going to look at how the starting seat affects the ending placement of that player. Are people right to dislike certain starting seats? Should tournaments shuffle players in a way that each player plays on each seat the same number of times? Let's find out.

Different players having different win rates is a common thing in many games, usually favouring the player who goes first. Some games, like Chess, make no attempt to remedy this. Others, like Go and many card games, give the disadvantaged player a little bonus to offset it. Surely this is present in Mahjong too, but to what extent, and what positions?

Let's check the Houou replays. We've got 1,242,729 ari ari Hanchan games to look through. We'll check what placement each starting seat got in each game. Keep in mind that an even average placement would be 2.5. What seat is the best to start in?

Well, this is a bit amusing. North has the highest chance to come in first place, but also the highest chance to come in last place! North will be the last dealer, so they have the final chance to make a comeback with dealer repeats, but also are the easiest to overtake due to the dealer payment. Still, they come first more often than fourth, and have the best average placement of any seat.

West has the lowest chance of coming in first, and the worst average placement. The superstitions are true. East manages to have a positive average placement thanks in part to it having the lowest fourth rate, while South is so close to going totally even.

West and North have over a two percent difference in their first place ratios. Though, overall, the average placement is pretty close to even for all the seats, with none going more than .01 more or less than even.

So, how about in Tonpu? There are only four rounds in Tonpu, so will that make the difference even more drastic, or less drastic? We have 450,728 ari ari Tonpu fast games to look at.

Amazing, in Tonpu, North is the only seat that has a better than even average placement! That's incredible, and the difference between North and West's first places is nearing four percent. East has taken over South's role as the close-to-even seat, and South inherits East's fourth place avoidance.

I'd imagine the reason why North is so powerful in Tonpu is that there's less time to fall far behind. Combined with the lower average hand value in Tonpu, the distance you need to close to come in first in East 4 will be shorter on average than a Hanchan South 4.

Unfortunately, it seems a bit trickier to calculate the Sanma numbers. The order of players seems to have some randomness to it, so I'd have to look into altering the script for it. Maybe I'll update this with a Sanma table later. I found an old screenshot where I was only looking at the 2019 Houou games, and the first place ratio was 36.52% West, 31.97% East, and 31.52% South, just to give you a rough idea in lieu of a full analysis.

Online, these numbers don't matter much. You end up playing so many games that your number of games in each seat will even out. In a short tournament, where there are only a handful of hanchans, maybe it's important enough to ensure each player plays each seat the same number of times, if possible. Perhaps finals tables could be seeded so the player with the highest score going into it is placed in the seat they prefer. Things to think about, anyway.

The values are likely different in tournament settings. In a lot of tournaments, there are time limits on hanchans, so you might not be able to reach South 4, which would remove North's advantage. Also, if agariyame is disabled, you have to keep playing and risking your position even if you win a hand and get first. Though, you also get the chance to raise more points, which can be important. I don't think we could get enough data to look at the stats from tournaments, especially with the wild skill differences usually present in tournaments, but it's fun to theorycraft.

These tables along with the raw data are available in this spreadsheet. You can find the code used to generate the tables on GitHub. Until next time!