Luck in Games

Luck plays prominently in human thinking and thus, in religion.  But before getting into that, I would like to ask readers to help me with something I have wondered about for ages:  Is it possible to order mind games in terms of the amount of luck vs. skill in the game?  We all have intuitive ideas about which games are luckier than others, but does anyone know of disciplined attempts to rank games by luck?

Below I have quickly and casually attempted to make an  ordered list of a few games — the most skilled are on top and the most lucky on the bottom.   Have I left out your favorite game–where should I put it? Are any games over/under-rated — why?  Do you think this a pointless venture?

  1. WéiQí
  2. Chess, XiangQi, Shogi
  3. Mahjong , Bridge
  4. Poker
  5. Reversi, Pente, Connect Four
  6. Checkers
  7. Backgammon
  8. Scrabble
  9. Solitaire
  10. Stratego
  11. Yatzee
  12. Monopoly
  13. Dominoes
  14. Tic-Tac-Toe
  15. Coin Flip

Challenges in the this ordering include:

  • Many different kinds of skills: spatial, memory, reasoning …
  • Effort vs. Natural skill: Some skills come natural to some people and take no effort.
  • Several sorts of luck (perhaps).

I think a one-dimensional spectrum is totally inadequate so I am looking for suggestions before going off on my own.  Any ideas, arguments, or questions?   For instance, though I made WéiQí as number one in skill, I sometime doubt this status.  But when I tell WéiQí enthusiasts that I suspect even WéiQí has luck, my skepticism is met with violent objections.

Anyway, let me know your thoughts about luck in games.

This post on wiki mentions the complexity of comparing abstract strategy games.


Filed under Philosophy & Religion

21 responses to “Luck in Games

  1. Temaskian

    What about Xbox games like Battlefield 2? 😀

    I would say it ranks somewhere after chess? It does require some thinking and skills, then after that, luck.

    Luck is also created, as in, you have to get out there to get some. You don’t get no luck by hiding in a corner with your rifle. 😀 (For B2)

  2. Ian

    It is possible to exactly order them in terms of the randomness, yes. Although you’d get a different order to yours. Tic-Tac-Toe, for example, has no randomness.

    You seem to have two dimensions here. The skill (which we could measure with something like the total game tree size) and the luck. Where I assume ‘luck’ is a combination of both randomness (you don’t know what dice rolls are upcoming in Backgammon, say), and imperfect information (your opponents have a definite set of cards in bridge, but you don’t know what they are). They are different, because the latter is subject to deduction, which itself can be skilful.

    On this scale, WeiQi is the most skilful and least lucky of popular and traditional abstract strategy games (ASGs).

    But in terms of the skill part, it would be a little minnow compared to something like Starcraft 2, which has orders of magnitude greater branching factor. Starcraft 2 isn’t random (in PvP mode), but has imperfect information. It also involves both mental skill and physical skill, because unlike Go or Chess, implementing one’s moves also takes skill.

    The thing about the WeiQi bias is not about its inherent skilfulness, but about the amount of study that has gone into it. Those classic ASGs have been studied far, far deeper than Starcraft 2 or even modern ASGs with similar branching and information characteristics. If you put a couple of thousand years of study into the deep mechanics of Starcraft 2, you’d get massive understanding of the character of the game-tree too.

    So your metric is more cultural than empirical, because if you do make empirical judgements, your list will be populated mostly with the vast numbers of games that have been invented in the last 100 years.

    See BoardGameGeek if you want to go down that rabbit hole.

  3. Ed

    I know nothing about modern games played on phones, computers or big screen TV’s. I like Bridge, Chess and Cribbage in that order. There is another game called Pente that is OK… I also like the game of ranking games… :-}

  4. This is an interesting topic. I do like Ian’s definition of luck, but I don’t think it should necessarily include imperfect information — dealing with imperfect information is a statistical skill in a lot of these games, and it can therefore be controlled in a way that randomness can’t. I think I’m open to being convinced otherwise, though 🙂

    It’s funny how game enthusiasts are averse to the luck aspect of a given game, because I think luck (or randomness) in all its aspects makes skill all the more important. Take Mahjong, for example. I’ve actually got some pretty golden fingers when it comes to grabbing tiles, which some would call luck. But, because I’m a gormless idiot, I can never turn those tiles into a winning hand. (Seriously. My friends can’t stand it. They’ll peek at my hand over my shoulders and slap themselves in disbelief every time I make an inane play.)

    On the other hand, we’ve got another friend who’s really quite skilled at the game, and the difference between when he’s letting someone win and when he’s playing for hard cash is palpable. It doesn’t matter what someone else has got in their hands, and it doesn’t matter which tiles Lady Luck decides to put in his own — if he wants to, and if he wants to badly…. he’s going to win.

    His skill comes into play when strategizing how to circumvent the “good luck” (beneficial randomness?) of others or his own bad luck. That’s what makes a good player. And I think good players should embrace this aspect of the game instead of denying the existence of luck or randomness, ’cause it makes their mad skillz all the more impressive.

  5. Ian

    Zach, one interesting statistical thing you can do is to look at the range of outcomes for players with a particular ELO (i.e. skill level). Even in games with a lot of randomness, like Backgammon, the range is relatively small. Obviously it is much smaller in non-random games like Chess.

    Or in other words, if one player is a little better than another in chess, then they’ll win almost all of the matches. In the same situation with Backgammon they will win only a small majority.

    This is an empirical measure of randomness. I’d suggest your Mahjong playing friend is far enough ahead of you that it more than compensates for the randomness. Put him against a *slightly* inferior player, and chances are luck will be deciding most of the games.

    But like any probabilistic system, even tiny differences in probability are significant if you just do enough trials.

  6. Once upon a time I read a book. The book had non-human beings. Whether they were Angles, or Jinn, or Aliens invisible to the human eye was never made clear.
    What was made clear was they liked to play tricks on humans and even manipulte human history.
    A way to do both was to use what today would be classified as nano technology to change the order of the cards in a deck after they had been shuffled to change the outcome of a card game. In the past this might have resulted in one man having new wealth or another becoming destitute. Perhaps the ownership of a slave changed hands.
    I wonder if these beings are still up to thier old tricks how they might try to influence world history today by influencing the outcome of a card game.
    A funny thing happened to me in the fall of 2007. I had told this story to some people. The very next time that I played cards it was a game of UNO a few days latter. In that game I had to draw 4 cards, OK I can no longer remember if it was the first time that I had to draw four cards or not, I picked up four draw two cards. I seriously had to wonder if I was being sent a message based on the timing of this incident. Well of course if it was a message one could argue over what the message would be. To me it is obvious, we are here and we are watching you. Of course someone could say, no if you would have gotten 4 wild cards that would have been the message but since you only got four draw twos there is either no message or it is a totally different message.
    Of course the sceintific types will accuse me of a flaw in logic by saying that I recognized a pattern and gave it meaning when a pattern has no inherant meaning. Like seeing Jesus in an oil stain on the driveway or seeing the devil in the cloud rising from the World Trade Center.
    Of course if some scientist got the idea of trying to document these beings using nano technology to manipulate a card game with hidden cameras or some such thing the other wordly beings would always be three or four or five steps ahead of them.
    If there were other worldy beings and they wanted to send us a message we surely could only guess what that message might be. The scientific types would of course assume that they would either land and tell us in Chinese or Hindi what the message is or that they would telepathically communicate the message in every persons mother tonge, or they would send a radio message addressed to earths inhabitants. Yet many scientists lack something. Of course they would say what ever it is that they lack is not needed. To have it would have been a hinderance anyways.
    I can not say how such beings might send us a message or if we would notice when they do. They could even manipulate a Lottery. It is an institution that many people have direct access to. I do not know if the lottery drawing is held on TV in the US but it is held on TV in Germany. A lot of effort goes in to making sure that the results are random. But what would happen if a some point some people started to say that there was a pattern? Would it be possible to say if was a pattern or only the illusion of a pattern. What if the pattern had possible political significance? Should it be ignored because it does not meet our scientific pre consieved notions of what patterns to pay attention to and what patterns to ignore?

    Anyways I think that one possible message that would do mankind a lot of good if it were recieved by the right people would be something really really simple,
    “We are here and you are being watched.” Such a message does not explicitly spell out anything at all. Do you think that some people might infer something from it however and possibly change their behavior in some ways?

  7. @ Temaskian
    I need to learn more Video games some day. I like the concept of “making luck” that you use. How true in life too.

    @ Ian
    Those are helpful categories, and some I had thought of. I am going to try and sketch up a diagram capturing some of this. Thank you kindly for your contribution.

    BTW, I had to look up “Elo” — thanks, I did not know that system. I know that in WeiQi though there is ranking based on stones handicaps, there is great debate on the best system to determine those rankings — all very mathematical, of course. One would intuitively hope that such one clear ranking method would emerge as mathematically necessary, but it hasn’t. So I guess this just points to the problem with intuitions or the fact that mathematicians don’t care about this area. Do you have thoughts on that?
    Thanks too for the Board Game Geek link — I will show it to my son. I like keeping games between face-to-face people when possible.

    @ Zachery
    I agree, adjusting for luck is a skill in itself. But as you say, some are more averse to it than others — I am very averse to it. I wonder if it points to some defect in my personality or mind? 🙂
    But the luck element does allow people to take the game less seriously and thus, win or lose, the game can take on more of a social element between players.

    BTW, I had to look up your British use of the word “gormless” — cool word, but then you are in the word profession! But looking at the definition, isn’t “gormless idiot” redundant? –Not that I’d expect more from one so gormless 🙂

    @ Ed
    I too don’t play video games — but I sort of wish I did just so I could understand this more. I probably will jump into them in the near future as my son gets older, but for now, we don’t allow them in the house and time with computer games are limited severely — whereas time with computer graphic design, WeiQi, simulation games and a few others are allowed (but even those times are limited). But as the kids get older, I must loosen those up and make room for independence and responsibility. I just don’t want to allow brain damage too early. 🙂

    I added “Pente” to the list. I only knew it under its original Japanese name “Gomoku Narabe” (“5-stone aligning”) and had to look it up. I wager that the game was probably invented by someone who didn’t want to struggle with WeiQi and so just made up the quick rule of getting 5 in a row. I use to play it with my son until he could play WeiQi. It actually required more energy than I expected — I had to try real hard to lose!

  8. Ed

    @ Sabio…. That comment was interesting… I didn’t know about the Pente/WeiQi connection. Pente is fine, but not that challenging, as you explained.

  9. I would rank the ones you listed pretty much the same as you have.

    I personally wouldn’t put Xbox games in the same ranking, since those are more like basketball or soccer. They rely mainly on training your physical reflexes. Does it make sense to rank sports like soccer and basketball to see which requires more “skill”? Probably not. It’s only when there is *some* element of chance that it becomes interesting to rank by how much skill is required. In that sense, I think weiqi is very close to basketball. The more skilled player will win, period.

    While bridge is often claimed to require a higher intelligence than weiqi, I would put it lower on the scale. But I’m not positive about this. Games where bluffing plays a large role are interesting to rank.

    Very interesting topic; I definitely want to think about it more. I think it’s an important topic.

  10. @ JS Allen
    I am glad you find it interesting. The topic has implications in many areas to me, but I thought I’d keep it focused on something as neutral as a simple game, to begin with.

    The next post makes more clear my direction — input from readers helped me focus my thoughts (as always)!

  11. @Ian – I didn’t know about the Elo rating system either. That’s fascinating. But then again, all you mathy types take all the fun out of conjecture, superstition, and telling tall tales about the Mahjong Madman who no one could beat.

    @Sabio – Listen here, you: gormlessness implies a lack of gorm, and idiots are idiots. And the cadence of that sentence would’ve been a bit gorked had I used one and not the other. Above all, I am a poet, and sound to me trumps meaning when it comes down to it.

    Nevertheless, I’ll accept your call of redundancy, and raise you a shellful of “anyone lived in a pretty how town (with up so floating many bells down).”

    /crack-induced ramble 🙂

  12. … did I just ruin that conversation? >_<

  13. @ Zachary,
    Nope, just working on the follow-up post on Games (II). But my wife thought your comment was weird. I told her you were being funny. She read the comment out of context. It made me smile!

  14. TheDuke285

    What about card games like YuGiOh!, MTG, CardFight Vanguard etc

  15. Go for it, Duke — start a blog and tell us about them!

  16. Just ran into this posting. Actually, your question makes a lot of sense, mathematically. But it is a hard one for several reasons: (1) one has to define the game in a precise mathematical language; (2) one has to define the notion of randomness to use (you call it luck, but there is no such thing as luck); (3) one has to use a precise notion of complexity.

    Games are like algorithms which may involve more than one agent. They are randomized algorithms in that the next state depends on the current one (e.g., the current configuration of backgammon), the players’ decisions AND the outcome of dice.

    Such a question needs a lot of work and depends, besides one’s mathematical abilities, on one’s knowledge of all these games (and more). At the minimum, one could try to come up with a theory combining randomness and deterministic complexity of a game. It’s a lot of work. (Who pays the bills?)

  17. I agree, takis, thanks for reading. I wonder if you got to my cute graph in part II.

    Oh, and there is “luck” — just depends on how you define it, eh?

  18. As a side remark, I have my own concept of “perceived luck” in games of chance, but have not thought about it seriously. There is something called “null recurrence” in probability theory which roughly means that if you play a game of chance giving you a reward (or a loss) each time, and consider the number of times you need to play until you, say, double your money then this number is certainly random, and, quite frequently a finite number. However, it may have an infinite mathematical expectation, meaning that if you average this random number over many many games you obtain an infinite number. This is a very real phenomenon. When this happens, players observe long stretches of consecutive winnings (perceived luck) and others consecutive losses (bad luck). In fact, it is my opinion that the presence of this property in a mathematical model of the game (a model may never be exact and infinity may be replaced by a large number in practice) leads to what we call “superstition” and eventual “addiction”. It is my opinion that behind these behaviors lie simple mathematical formulas such as
    1 + (1/2) + (1/3) + (1/4) + (1/5) + … = infinity.
    My notes on the subject of simple models of random evolutions contain a definition of null recurrence, although I do not expect anyone without background of 2 years of college mathematics to understand them.

  19. No, I haven’t read part II yet…
    And, yes, everything depends on the definition.
    For example, James Clerk Maxwell was very lucky to have been born in a rich family and so not worry about anything and therefore have a lot of time to think. He developed the final formulation of electromagnetism, upon which Einstein’s theory of relativity was based. But he was lucky to be wealthy. He died young though. So he wasn’t that lucky.
    Others can influence one’s luck. For example, there are scientists who became “famous” because they sexually pursued a certain scientist better than them and got married to them.

  20. R Vogel

    Poker is an interesting entry at number 4. I would think that it would be far more dependent on luck in the turning of the cards then some of the other. I wonder how you are thinking about it differently than I?

  21. @Takis: Looks like your question was answered in the next post.

    @Vogel: See my next post, and see if that answers your question.

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