What a Bit of Game Theory Can Teach Us by Paul Lederer

Saw this post on the Chicago Mahjong Group https://www.facebook.com/groups/chicagomahjong/ and thought this would be of interest to some — Frenetic

Today I would like to talk about choices and options. Mahjong is a game, and like most games it has options for you to consider and choices that you as the player must make–choices like what to discard, or if you should call or if you should declare riichi.

Now I am not a very experienced Mahjong player, but I am a very experienced game player and what I have learned from basic game theory has let me pretend to know what I am doing in Mahjong to the point where I have people fooled that I’m actually good, and in most games there is one theme that prevails: the player with the most options is highly favored to win. Choices are also what separates a good player from a bad one, as good players make more good choices and bad players make more bad choices. Chess and Go are both zero sum games of open information, and in both games the goal is to remove all options from your opponent. Mahjong is not zero sum, and also it isn’t open information. There is also a decent amount of random chance involved. However, I feel that maximizing your options is key to every good Mahjong player’s strategy(interesting note: Two player zero sum games are more about removing your opponent’s options, while 4 player free for all games are more about maximizing your own options).

A majority of your choices in Mahjong come with how many tiles you have available to discard. At the beginning of the game, each player has 14 tiles that they can discard. It’s a very simple game of looking at your hand and choosing which tiles you should discard to optimize your options in later turns. I won’t get into discard theory, as I’m sure there are vast resources you can look at for that. What I am here to talk about is how options intersect with power. Mahjong offers several ways to trade in your options for power: calling tiles lowers your options in which hands you can make and which tiles you can discard but in exchange speeds up your hand significantly. Declaring riichi completely shuts off your options for discarding but doubles (and sometimes quadruples) the number of points you can score. Dora tiles offer you double points in exchange for cutting off your option to discard them. Unsafe tiles remove your option to discard them in exchange for not losing points. Of these option-removing mechanics, dora and unsafe tiles are not something you get much choice in, but declaring riichi and calling you do. Often times you have to make a choice of when you should do either, and many times it isn’t so clear-cut as to if it’s a good decision or not. Every player is given their resources and each turn is given choices of trading in their resources for some sort of power, and you should evaluate how valuable that power is at the current state of the game.

Often times you will see newer players call at every opportunity they can get, and why shouldn’t they? They get to speed up their hand and gain a supposed advantage! Now the more experienced mahjong player will tell you “hey, that’s wrong you shouldn’t do that,” and when asked why they’ll say something like it lowers your defense or restricts which hands you can make or something to that extent, but that very same player might call tiles in exactly the same game, and when asked why they do this they might give you some reason, and it might make sense or it could be some superstitious nonsense or just instinct, but what should be happening is that player weighs the advantage of being fast vs the ability to hold more options with higher point scoring power, and they decide that the speed trumps options so they trade their “options” resource for the “speed” power.

But why does the experienced player tell the newer player to simply riichi every hand they are in tenpai for? Shouldn’t, by their logic, riichi be a similar offense to calling tiles, as it significantly limits your options—in fact it just removes them entirely to the point where you no longer have any meaningful choices to make in the hand. I still don’t know why this sort of double standard exists, but I assume it’s because players value the “more points” power very highly, and are more willing to exchange their “options” resource to acquire it. Or it could just be that they don’t want the newer player to worry about yaku. My guess is the latter. In a world where everyone knew the yaku when they just start playing, the experienced player would probably have the same sort of hesitation to the “riichi every hand” mindset as they do the “call whenever possible” mindset. I guess the lesson to be learned here is people probably declare riichi way more than they should because nobody told them not to early on, and habits die hard; especially when their impact isn’t incredibly obvious.

Finally, we have the issue of Dora tiles and unsafe tiles. Dora tiles are like that one guy that promises he’ll pay you back if you just lend him $10, and you’re like yeah sure $10 isn’t really that much, but then every day he does the same thing until he owes you $1000 and you have no idea how to get it back. If you don’t see a way to fit a dora tile into your hand, it’s best to ditch it early, but most players will hold onto it until it’s too late and dropping it could mean instant-death from your opponents that have now had time to work that dora into their winning hand. You psychologically removed the option of dropping it until it became a factual block. By holding that dora you make the decision that you are going to make a hand with it, because dropping it when you get to tenpai can lead to an absolute disaster. My guess is players hold onto dora tiles more than they should.

Hopefully this has illuminated a way of looking at the game that you either didn’t know, or didn’t really take time to think about and just kind of went on instinct. My guess is those of you that are better players already apply these concepts but haven’t really verbalized to themselves exactly why these things work, you just know it works and that’s good enough. This kind of results-oriented thinking could be quite toxic to your game play, and you should always have a reason why you make your decisions.

On another note, many times people make wrong choices. They often try to compensate for their wrong choices by playing more aggressively. In poker (and Magic), we call this tilt. Tilt is (for those who haven’t heard of it) when your emotions take over and you play in a sub-optimal or overly aggressive manner. Sometimes you are more verbally aggressive, which is usually just an unpleasant experience for everyone involved and is the more perceivable form of tilt that we are probably all have experienced, but people can tilt without showing physical signs of it. Managing your own tilt is something that can mean the world of difference. Whenever I’m playing I tend to joke around a LOT. This isn’t necessarily because I’m trying to be social or make people laugh, but really because it helps me manage my tilt levels (while also help with tells). By being playful I turn my negative energy around into a more positive place, which helps clear my mind to make better decisions in the future.

I come from the Magic the Gathering world, where there are two kinds of players. Online players, and physical players. Whenever I am paired against an online player, I can immediately tell because they fumble with handling cards and get visibly emotional. They have little experience interacting with opponents or handling the physical materials. Mahjong is a very similar space, only everyone is an online player, so when you go to physical meetups everyone has low experience with the social and physical conditions of mahjong. Here’s a little secret: complaining to your opponents doesn’t do anything but disadvantage you. Often times people complain because they are fishing for sympathy, but if you are complaining then you are physically manifesting your tilt, which signals to others at the table that you are tilting, and your physical reactions fall under heavier scrutiny. Also as your opponent I certainly feel no sympathy to your supposed lack of luck as I am in fact directly benefiting from it. I guess what I’m trying to say is mahjong is a game of luck that we are all affected by equally, pointing out your bad luck does nothing but highlight in your mind how unlucky you are and downplay the times when luck is on your side, and really just puts an exclamation point to your tilt.

7 thoughts on “What a Bit of Game Theory Can Teach Us by Paul Lederer

  1. I will say it outright: DO NOT trust this article. It is apparently written by an unexperienced player who doesn’t understand the game at all.

    (srsly if you read my comment, go back to Magic the Gathering and never write article if you don’t know shit. it is harmful to readers.)

    1. While I do agree that the applications at the end of the article in regards to riichi, calling, and dora are exceedingly contrary to actual leading strategies and data, the general idea that about inspecting options and trade offs seems to be a pretty beneficial line of thought~

    2. Wow! The writer quite clearly stated that they were not an experienced player. I think some real and constructive criticism would be more in order, rather than a “harmful” comment.

  2. Actually, I think the game theory ideas are correct, but the applications aren’t exactly right. You want to maximize your options in many ways: the hands you’re able to go for and the parts of your hand that you can discard (holding onto safe tiles, or holding onto hands that can change). But, when you have a hand that’s one from winning, if you want to keep your option to win, you usually can’t discard any other tiles besides the ones you draw, regardless of if you riichi or not. So because you’d do it anyway, you might as well get extra points when you win.
    But, a related mistake I think people do make is riichi’ing and losing the option to defend. I streamed a hand where I had a perfectly good wait, and could get more value with riichi, and I didn’t riichi, and it was because of the score. It was very roughly like 10000, 15000, 25000 (me), 50000 (dealer). If I riichi, I lose the option to defend when the dealer riichis, and defending is more important to me than getting more points.

    Dora depends on which tile it is a lot. Some dora like non-yakuhai winds will be safer to discard later, while dora that are like a middle 4 tile are hard to discard but easier to use. When you have a dora tile, it’s more useful for you than anyone else because it’s in your hand (and you always have the option to not discard it). Holding the dora only limits your options when you have to discard it because you can’t use it in your winning hand, but it might be dangerous. Earlier on, you don’t necessarily know what your winning hand will be, so holding the dora is often good because you keep the option to use it (and you can’t choose to draw it when you want).

    Options sometimes come into play when building your own hand in interesting ways, like when you have extra pairs. A hand like 337m1236799p2468s might discard 3m because, even though it’s not the most efficient discard in terms of immediate odds to improve, it lets you use more tiles and choose from more tiles and areas to discard later.

    Also, playing around riichi hands feels like keeping options, because you want to keep as many options open as possible for winning while still discarding safely, and you want to see how you can change your hand to use unsafe tiles you might draw.

  3. Hey everyone,

    I wanted to post this up because it had some good points and was from the perspective of a beginning player which might help out some other beginning players in the community. Yes, some of the later points do conflict with leading strategies and data and I hope the author will keep playing riichi mahjong and refine their viewpoint in another post.

    If you take issue with certain points, by all means match labor and write your own article and add your viewpoint. :)

    –F

  4. I have three sets of reactions to this.

    First, let’s talk about some of the mahjong-related points Paul raised. As for Paul’s point on riichi judgement, the “riichi every hand you are in tenpai for” approach actually works well most of the time because riichi is such a powerful tool. I elaborated on some of the theoretical (i.e., deductive) reasons why riichi’ing is often better than not riichi’ing in my book (http://riichi.dynaman.net/), so I won’t repeat them here. In addition to what’s already in the book, there is also ample empirical (i.e., inductive) evidence that indicates riichi’ing generates higher expected utility than not riichi’ing in most instances, on average. The evidence is obtained by analyzing large-scale data from online games. Admittedly, findings from any data analyses are generalizable only to the extent that (1) the sample used in the analysis is representative of the target population about which you want to make inferences, and (2) the “treatment” variable (riichi or not riichi) is randomly assigned to subjects. Now, the assumption (2) is not entirely true with most data analyses and the assumption (1) might also be dubious, as most data analyses are from really high-level games. With these caveats in mind, the current state-of-the-art findings from quantitative studies clearly suggest that riichi’ing is better than not riichi’ing in a wide variety of situations. The chances are that, contrary to what Paul guessed, people declare riichi less than they should.

    As for Paul’s point on “double standard” with respect to calling, I can think of two possibilities as to why Paul thought the advice he’s got looked like double standard. First, it is possible that the experts around Paul are adopting the “do as I say (not as I do)” approach. I’m sorry if that is the case. However, it is also possible that the experts around Paul are trying to teach him the complicated calling judgement criteria as honestly as they can, but that these criteria are a bit beyond the grasp of beginners like himself at the moment. This is also unfortunate, but I think things will become clearer as you get more experience. It’s just that calling judgement is a lot more complicated than riichi judgement.

    Second, I’d like to mention the game theory metaphors Paul used in the post. As someone who uses game theory in his work, I must say Paul’s usage of these terms (e.g., “open information”, “zero sum game”, “maximize options”) is quite non-standard and unorthodox. Mahjong _is_ a zero sum game as long as we understand players’ utilities in terms of points for four players (if we don’t, go and chess can be a non-zero sum game as well). A game theorist would never say a game is an “open information” one (information is either public/private, symmetric/asymmetric, complete/incomplete, or perfect/imperfect. Each of these adjectives has a very specific and well-defined meaning in game theory). There is not a single finding in game theory that I know of to support Paul’s claim that games are about maximizing the options (players are assumed to maximize their expected utility, not their options). These game theory metaphors seem to be rather counterproductive in conveying what he means.

    Third, I’d like to discuss some of the harsh comments posted here. I am perfectly happy to see beginners posting their own perspectives here, as long as they are open to constructive criticisms. If you disagree and would like there to be some sort of gatekeeping so that only “experts” can post, that’s also a reasonable position to take (although, again, I disagree). However, direct your comment to the editor(s) of osamuko, not to the individual posters.

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