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Logical fallacies & Mahjong

Posted: Sun Mar 13, 2016 10:16 pm
by Krabman
Hey! I've lately been reading on logical fallacies and found this:

I think it applies to the thing we're all familiar with, Tenhou ebb & flow. When you're on top of your game, get a great streak of 123 places and you get a feeling you've actually improved significantly & play better but the next thing you know you're on a downward spiral. Eventually, you go back to your average scores which I guess most accurately reflect your skill level.

I'd love to read your thoughts on this. Especially from people who are into statistics and stuff :)

Re: Logical fallacies & Mahjong

Posted: Tue Mar 15, 2016 6:20 am
by DdR_Dan
One thing is that you shouldn't focus on stats other than long term placing too much, because they can be misleading. Something like play in rate doesn't tell you the value of hands you play into and the situation. If you're in a big lead and you play into a cheap hand from someone who's not the dealer, that's usually a good thing. On the other hand, if you play into an avoidable big hand chasing a low value hand, that's usually bad. So two different players could theoretically play in a similar amount, but one tends to play in in situations where it's good and ends up placing well because of it, while one tends to play in in the wrong situations and fares poorly. Other things might vary by play style. For a while I thought I had to call more to do better because my call rate seemed really low compared to the tenhou averages. But, I ended up making 7th dan with a call rate of .276 (for comparison, the average 7th dan player's call rate is .358). Now, I think this low call style is viable on tenhou, and calling at a .35 rate isn't necessary to doing well.

Maybe the hardest part to getting better at mahjong is being able to determine if you are making good decisions, because you can't judge by the result. Sometimes you can make good decisions and get really unlucky, and you can make bad decisions and get really lucky, and anywhere inbetween. Sometimes your play might be a bit below the average for your current rank but you just get dealt a lot of winning hands. Sometimes your play might be as good as the next rank up but you just get dealt unlucky situations or can't draw winning hands. In terms of long term rank, you can play a lot of games and if your skill level isn't changing, eventually you should find the rank that suits you, but that would require a lot of games to determine through outcome alone, and your skill level might vary too. What makes it really hard is that you want to analyze your decisions, and that analysis is going to be based on probabilities that you can't really determine through long term averages. Let's say after 6 discards from each player, someone riichis on 2p. What is the chance that 1p is dangerous? Here are some data you might examine:
  • All riichi's on 2p
  • All riichi's after 6 discards
  • All riichi's on 2p after 6 discards
  • All riichi's on 2p after 6 discards where the riichi player's discards are identical
  • All riichi's on 2p after 6 discards where the riichi player's discards are in identical order including discarded on draw vs from hand
  • All riichi's on 2p with the same visible tiles (tiles in discards or in your hand), and/or same discarded tiles per player, discarded order, etc
  • All riichi's on 2p with a player with the same play style, and/or same visible tiles and discards
  • All riichi's on 2p with the same player, same discards for every player, and your hand is the same
Obviously, when you get to the more specific cases, you won't have sufficient data for regression to the mean to come into effect. How often can you say you've been dealt an identical hand while observing identical discards from every other player while playing against the same players? However, those specific details might hold important information. Maybe it's important that it was 6 discards, or maybe it's important what the specific discards were, or maybe it's important the player played with a specific style, and so on. So, the only way to beat out the lack of repeatable data is through good reasoning. In this specific example, exactly 6 discards probably isn't important, and the amount the hand progressed and what middle tiles the player discarded in order to hold 2p are probably more important. Visible tiles are probably less important unless something notable is visible (multiple tiles near the area of concern or a wall of tiles). Style info such as how quickly does a player discard extra pairs, and how often a player declares riichi on hands that can win without riichi, is important. So, to answer the original question, you have to take all the important information you know and use that to narrow down the situation and come up with a rough guess that doesn't really depend on what was actually true in that one situation.

I guess you could say everything in mahjong is just betting on probabilities, but many of the probabilities are virtually impossible to calculate or generate enough data to determine. Tile efficiency is something you can calculate, but even that has some challenges. The discards other players make tell you something about their hand, for example if someone discards a 1, they're more likely to have a 4 in their hand, so you now have to take into account that someone is more likely to have that 4 in their hand, as well as information for all the other players. The perfect statistics would go from the choice you make to the odds of you ending up 1st/2nd/3rd/4th as a result. You can't calculate that, so you have to break it up into something like: if I declare riichi here and win this hand, what are the chances I get each place? Now, if I riichi here, what are the chances I actually win the hand? Or, if I play in here, what are the chances I get each place, and then what are the chances I play in on this discard?

That's my thoughts on the theory, but in terms of making actual decisions, the two things you should do are probably: 1) think about how your decision will affect your end result (if I discard this dangerous tile here, what are the odds I play in or win or get tenpai, and based on those, what are the odds I get each place?) and 2) try to find and learn from the most important information in every situation. You could say, "Once I discarded a middle tile after 8 discards and played into a damaten mangan, so I don't think it's safe to discard middle tiles after 8 discards." But there's more information to it. Maybe you notice, say, the player had been discarding other middle tiles and then switched out a certain tile from their hand, and you can improve your rule to not discarding middle tiles that haven't been previously discarded and aren't near a player's most recent discard from the hand when their hand looks good. And luck comes into play too. Sometimes you can take a good bet and truly get unlucky, and you have to use your reasoning to be able to say it was luck and not a poor decision. The other side is true too, sometimes you'll take a bad bet, and it won't pay off and you have to realize that it was a bad bet, and not just bad luck. Being able to find that balance, not just calling everything bad luck but not just assuming everything that doesn't work is a bad play either, is really difficult. The same is true on the positive side, not just assuming you're winning because of skill and good decisions but not just writing off your good decisions as good luck either.

I don't know if my thoughts followed your intended topic, but those are my thoughts. :lol:

Re: Logical fallacies & Mahjong

Posted: Tue Mar 15, 2016 8:23 am
by Krabman
Thanks A LOT! You've made some great points there. So regression to the mean would apply in certain vague analyses?

Hindsight bias & outcome bias don't help at all. The other thing is that many people simply prefer to attribute wins to themselves and make losses someone else's fault (self-serving bias, I think) :D

I think you're right about most stats being not all that important!

That's one problem I have - not really knowing which in-game data to focus on. I tend to clutter my mind with pointless observations so that when a critical moment comes I often mess up badly. Thanks a lot for the tips!

Now I'll drift off top a bit - many players I know in Poland study IT or work as programmers and so on... I'm on 'the other side' - I've never been into maths, algorithms, probability, analytical thinking. I get a feeling it's slightly disadvantegous when it comes to Mahjong. Almost all I've learned I found in books, on Mahjong blogs etc. Even stuff like 356 - discard 3 was too much to figure out myself xD Even though I've improved quite a bit over the last couple of years, I don't really discover much on my own. For me it's just like with any other activity - you have the so called naturals and people who have to struggle a bit more. Don't get me wrong - I'm not whining - I keep studying and playing, I'm just curious what your observations are. Do you know any non-scientifically minded strong players? ;p Do all your Mahjong buddies work at IT? :D

Re: Logical fallacies & Mahjong

Posted: Tue Mar 15, 2016 2:48 pm
by Gnom
It's hard to say for sure since we're talking about things that are very difficult to judge and let alone measure, but it feels like some players can reach a respectable level without having a naturally analytical thinking. In my club some players more often than not make what I'd judge to be appropriate, but are unable to explain their choice. If I had to guess, I'd say they do analyze their hand, but not in a rational/conscious way, more in the same way that you'd instinctively know that blue and yellow make green. They're also slower to make progress than other players, which would make sense since they'd rely on non educated guesses through trial and error, and it also feels they reach a practical limit a bit sooner...

Re: Logical fallacies & Mahjong

Posted: Wed Mar 16, 2016 5:33 pm
by Krabman
That's interesting! I think that even if it takes more time, learning everything on your own is more satisfying. Also, I think you naturally incorporate what you've just discovered to your playing whereas stuff that you read (or that someone tells you) needs more time to sink in.

Re: Logical fallacies & Mahjong

Posted: Wed Mar 16, 2016 5:55 pm
by Gnom
It's true that it's fun to discover things by yourself, but it's also a bit slower, and since we don't have an infinite amount of time (yet), that may be a limit to how strong you're gonna get as a player (whereas if you start where other left off, you get a chance to go further!) I think the reason japanese players are generally stronger than westerners is not that they're more clever or have more time to play, but mostly that they have access to a lot of theoretical material. I think it's one of the good points to have a group of players, we can help each others (though sometimes I wish players in my group made more use of that possibility).

Re: Logical fallacies & Mahjong

Posted: Fri Mar 18, 2016 9:45 pm
by Krabman
I hope more and more players will play Mahjong seriously, not just casually - then we will have more clubs in Europe & more active players who like to discuss strategy and share their experience & knowledge with others. I'm really happy that you're so active in that department! :)

Yeah, Japan is a totally different world. After all, Riichi is 'their' game. At the moment, the best source of theory for Europeans is Daina Chiba's book. What he did is just amazing!