Chess can be a Game of Luck


Can chess be a game of luck?

Let us consider the following two scenarios:

A) We have a chess tournament where each of forty chess players pay 50 dollars entrance fee and the winner takes the prize which is 80% of the the total entrance fees.

 B)  We have a chess tournament where each of forty chess players pay 20,000 dollars entrance fee and the winner takes the prize which is 80% of the the total entrance fees.

Before dealing with these two rather realistic scenarios let us consider the following more hypothetical situations.

C) Suppose that chess players have a quality measure that allows us to determine the probability that any one player will beat the other. Two players play and bet. The strong player bets 10 dollars  and the waek player bets according to the probability he will win. (So the expected gain of both player is zero.)

D)  Suppose again that chess players have a quality measure that allows us to determine the probability that any one players will beat the other. Two players play and bet. The strong player bets 100,000 dollars and the weak player bets according to the probability he will wins. (Again, the expected gain of both players is zero.)

When we analyze scenarios C and D the first question to ask is “What is the game?” In my opinion we need to consider the entire setting, so the “game” consists of both the chess itself and the betting around it. In cases C and D the betting aspects of the game are completely separated from the chess itself. We can suppose that the higher the stakes are, the higher the ingredient of luck of the combined game. It is reasonable to assume that version C) is mainly a game of skill and version D) is mainly a game of luck.

Now what about the following scenarios: 

E) Two players play chess and bet 5 dollars.chessnyc

Here the main ingredient is skill; the bet only adds a little spice to the game.

F) Two players play chess and bet 100,000 dollars. 

 Well, to the extent that such a game takes place at all, I would expect that the luck factor will be dominant. (Note that scenario F is not equivalent to the scenario where two players play, the winner gets 300,000 dollars and the loser gets 100,000 dollars.)

Let us go back to the original scenarios A) and B). Here too, I would consider the ingredients of luck and skill to be strongly dependant on the stakes. The setting of scenario A) can be quite compatible with a game of skill where the prizes give some extra incentives to participants (and rewards for the organizers), while in scenario B) it stands to reason that the luck/gambling factor will be dominant.  

One critique against my opinion is: What about tennis tournaments where professional tennis players are playing on large amounts of prize money? Are professional tennis tournaments  games of luck? There is one major difference between this example and examples A and B above. In tennis tournaments there are very large prizes but the expected gain for a player is positive, all (or at least most) players can make a living by participating. This changes entirely the incentives. This is also the case for various high level professional chess tournaments.

For mathematicians there are a few things that sound strange in this analysis. The luck ingredient is not invariant under multiplying the stakes by a constant, and it is not invariant under giving (or taking) a fixed sum of money to the participants before the game starts. However, these aspects are crucial when we try to analyze the incentives and motives of players and, in my opinion,  it is a mistake to ignore them.   

So my answer is: yes, chess can be a game of luck.

Now, what about poker?

This post was triggered by a discussion with a young brilliant probabilist (and an amateur poker player) in Sweden who gave an expert opinion regarding poker in Swedish appeals court. It turned out that there were similar cases in Israel as well. I am not sufficiently informed about current poker disputes to offer any opinion about current cases, but let me tell you about a case from fifty years ago.

About fifty years ago, the police raided a poker club in Jerusalem, arrested the operators, and proceeded to prosecute them for running an illegal gambling operation. Israel law defines gambling as participation in what is primarily a game of luck; i.e., where the element of skill is absent or inconsequential.  At the request of the defense, Bob Aumann,  young game theorist at the time, gave an expert opinion that poker is primarily a game of skill. Aumann gave a detailed explanation, and cited, among others, John von Neumann, Oskar Morgenstern, and John Nash. The basic point is that even when your hand is very good, if you bid accordingly you won’t win much more than the ante, because the other players will catch on and fold; and the other side of the coin is that if you have a poor hand, you can still make a lot of money by skillful bluffing.  To Aumann’s surprise, the judge’s verdict was that poker clubs are illegal; he explained by writing: “In these clubs people lose their monthly wages, leaving their families with nothing to live on.” A few weeks later, Aumann met the judge at a party (Jerusalem was then a small town, and perhaps still is).  He asked the judge how he could make his ruling after hearing Aumann’s detailed explanation that poker is a game of skill. The judge listened to what Aumann said and replied: “But you see, these clubs cause people to lose everything, leaving their families destitute.”

For years Aumann regarded this case as an example of Israeli judicial activism, where judges ignore the law, ruling by their own personal conception of what is right and what is wrong.

I respectfully disagree.

The issue is what “the game” is. Is it just the pure abstract game, be it chess or poker, or is it the entire setting. The judge was correct to consider the entire setting. The judge did not base his argument on an abstract mathematical modeling of the entire setting but rather on the consequences. If such clubs indeed cause people to lose everything leaving their families destitute we must conclude that the overall setting makes this activity mainly a gambling activity and that this game is mainly a game of luck (in the same way playing the roulette is).

The law is vague and open to different interpretations and, in any case,  I am not a legal expert, but from the point of view of game theory (and economics) I think the judge was correct!

We always need to have a large rather than a narrow interpretation of what “the game” is.

Some more discussion can be found in lesswrong

Update: Here is a related post over freaconomics. Stephen Dubner bring a simple argument why poker is primarily a game of skill: It is possible to intentionally lose a poker game. One comentator sais: “one could also intentionally lose at blackjack (continue drawing cards) but it is still primarily a game of chance.” Another commentator asserts: “Poker, as played in brick & mortar casinos and online is not a zero-sum game because of the rake (the miniscule percentage that the house takes from every pot). Therefore, for the average poker player, poker is a losing proposition. (In fact, around 8% of online players are long-term winners. We know this because we can datamine the billions of hands that have been played online and compute such statistics with a high level of confidence).” And here is a post from “new scientist“.

Update: Here (from the comments section) is my proposal for a definition of the term ” A game which is primarily a game of luck”.

A game of luck is a betting game where the short terms outcomes depend on luck and the participants bet in spite of being able to rationally conclude that their expected returns are negative.

A betting game is primarily a game of luck if this definition applies to most bets in the game.


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38 thoughts on “Chess can be a Game of Luck

  1. JeffE

    I don’t understand your argument at all. Sure, scenarios A and B will have different psychological effects. Is that difference what you call “luck”? This seems very different from the usual definition. (Scenarios C and D beg the question by assuming that the probability of winning exists!)

    If poker (including the entire setting) is primarily a game of luck, how could there be successful professional poker players? (In contrast, there are no professional roulette players.)

    Your argument seems to imply that there is no such thing as a game of skill that involves large sums of money. Consider the following game: I bet you $100,000 that you will not win the best paper award at the next FOCS. (If that example seems too farcical, feel free to replace “$100,000″ with “tenure”.) Is it illegal for you to accept this wager in Israel? Or does accepting this wager make it illegal for Israelis to submit papers to FOCS?

  2. John Sidles

    Gil, an early reference on this subject is Mark Twain’s hilarious (and mathematically accurate) essay of 1867, title “Science vs Luck” … the full text is available on Google Books and through Project Gutenberg, and is well worth reading.

    Eccliastes 1:9 (KJV) “The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun.”

  3. JGWeissman

    “For mathematicians there are a few things that sound strange in this analysis. The luck ingredient is not invariant under multiplying the stakes by a constant, and it is not invariant under giving (or taking) a fixed sum of money to the participants before the game starts. However, these aspects are crucial when we try to analyze the incentives and motives of players and, in my opinion, it is a mistake to ignore them.”

    You seem to have forgotten to write the part of the article that actually analyzes the effects of the bets on the incentives and motives, and explain how you arrive at your conclusion that this can transform a game of skill into a game of luck.

  4. GreedyAlgorithm

    This argument seems to presume some definition or idea of “luck” with which I am not acquainted. At all. The closest I can come to having this post make any semblance of sense is to reinterpret your $10 vs $100,000 chess example to say you actually MEANT to have each game include repeated plays, with the goal of eventually winning >= $100,000 from the other person, or something like that.

    Maybe you have some coherent definition of “luck” in mind? I can’t figure it out.

  5. Bill Jarvis

    We ran a few tournaments where the score was adjusted to account for player rating difference. (In chess the rating system worked such that a 200 rating difference implied the stronger player would win a 4 game match 3-1.)

    The experiment was discontinued when it was discovered that the strongest player had to work very hard indeed to win and could easily be streeted by someone who “got lucky” – imagine someone knocking over a player 400 points stronger (or even holding them to a draw).

    This happen in the second tournament.

    Gil’s argument is correct.

  6. Gil Kalai Post author

    Dear All, thanks for the interesting remarks.

    I agree with greedyalgorithm that a major difficulty is to define a “game of luck,” and another difficulty is to measure the part of skill in a game which combines skill and luck.

    I even have problem in regarding the roulette as a game of luck: If you play the roulette over time you are going to lose. So a skillful player (unless he owns the roulette) simply does not play. We can regard the game as having many unskillful players giving their money to a single skillful player. (OK, they get something in return which is the excitement of gambling.)

    Anyway, let us take for granted that roulette is a game of luck (and perhaps return to define it some other time).

    Now I can see the rationale of a judge in the 50 years old case who said: If it is the case that 80% (or 95%) of poker players in the clubs simply lose money (sometimes their entire family savings) in return of gambling excitement than my verdict is that this game, as played in these clubs, is primarily a game of luck. This is a reasonable and legitimate ruling that also prevailed. (But I do not see that the stance of Aumann and other mathematicians who measure the skill ingredient by some other methods as illegitimate.)

    JeffE wrote: “If poker (including the entire setting) is primarily a game of luck, how could there be successful professional poker players? (In contrast, there are no professional roulette players.)”

    Interesting point! Actually it may well be the case that in professional poker tournaments the skill ingredients is high. (And I am not sure it is a negative-expectation game.) Professional players can exploit even a small ingredient of skill in the game, so the game need not be primarily a game of skill.

    Interestingly, the fact that professional players emerge can also be the outcome of pure games of luck. Imagine a game of dice were after a player wins once he get better odds next time (or he can toss a biased dice according to his earlier performances.)

    Jeff also wrote:

    “Your argument seems to imply that there is no such thing as a game of skill that involves large sums of money.”

    Yes, when the expected gains are negative and the stakes are high I would expect that the element of skill diminishes.

    JGW is correct that I did not describe mechanisms that makes a high stakes negative expectation game primarily a game of luck. For example, if players are playing even-bets chess games then a major effort of the players will be to choose opponents with lower or equal skill level. This will push the betting to be primarily between players of equal skills with roughly the same probability to win. (Scenarios C and D are not entirely hypothetical. We cannot know the probabilities in questions (or even properly define them) but sometimes we can well estimates them.)

    In a negative expectation game when the skills are pretty much known weaker players have no incentive to play (other than the joy of gambling) and this pushes the situation to “criticality” where winning becomes primarily a matter of luck.

    Another related mechanism driving the luck ingredients up was described by Bill. This is the case in tournaments where the bets (or score) is adjusted according to the player’s rating.

    And thanks John for the interesting link to Mark Twain!

  7. shmuel

    Gil, I think a version of your argument can be as follows (I hope I’m not muddying waters):

    Let U be my utility function that I will assume is a function from states of the universe to the real numbers.

    When I win against Kasparov, my utility goes up enormously (and Kasparov’s goes down enormously, perhaps). When I lose $10000, I lose U(Current situation) – U(Current – $10,000 & seeming to be a worse chess player than Kasparov).

    This is very possibly a positive expectation value for me, a wealthy American mathematician who dreams of just possibly succeeding in Chess.

    There are also scenarios by which Kasparov could have a positive utility by playing chess against me.

    We can both have positive expectations precisely because Chess is not just the game on the board.

    Moreover, this fits in with Judge’s view of the issue of Poker.

    But I haven’t yet thought through how exactly the size of the stakes affect the extent to which it’s a game of luck (although it seems clear that assumptions of rationality and selection bias should help).

  8. Gil Kalai Post author

    Dear Shmuel,
    Indeed modeling the situation by taking the players utilities may explain why we do not have invariance to scaling the bets and to “translations” (changing the the entrance fee). One obvious effect of high stakes is that factors like “enjoying the game” “improving the skills” etc. become negligible.

  9. miroslodki

    If i might be allowed to venture a few words

    an understanding of this philosophical problem rests (as Gil noted) on the definition of skill versus luck and some arbitrary line that demarcates situations where both factors co-exist. That said, the factor of winnings is extraneous since winnings are arbitrary – it could be money, pride, social standing…

    handicapping is not relevant since it is an artificial condition – if the handicapping is too lax – skill prevails, too stringent – and luck rules

    there is a chance this comment answers your question
    is it skill or chance or simply the “inevitable?” result of random typing of a million monkeys on a million typewriters over a million eons…

  10. Gil Kalai Post author

    Another comment regarding Shmuel’s points. Concerning poker, indeed the very naive point of view is that poker is a game of luck since when playing a single round the dominant factor for winning or losing is the quality of your cards. A more careful analysis indeed shows that over time skillful players have a great advantage as described by Aumann testimony (or Mark Twain’s story).

    However, this analysis is also naive since when the game is played repeatedly there are also other effects. For example, over time, (rational) players will be able to estimate their own skills according to their performence and stop playing if they are losing. Or in other settings players will be able to learn also other players’ skill and choose partners of similar skills to their own. These matters are now completely standard in economics and game theory. They are referred to as “learning in games” in game theory, and they are closely related to the notion of “rational expectations” in economics. (They were not standard fifty years ago.)

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  12. Johan Richter

    In game theory terms we can explain the presence of luck in chess by observing that people in fact play mixed strategies, which in turn probably can be explained by limitations of computational resources.

  13. Gil Kalai Post author

    The definition I propose is:

    A game of luck is a betting game where participants bet in spite of being able to rationally conclude that their expected returns are negative.

    A betting game is primarily a game of luck if this definition applies to most bets in the game.

    (Alternatively, you can consider most participants rather than most bets.)

  14. Gil Kalai Post author

    This is a good point. I would not consider insurance as being under the scope of “a betting game”. Oterwise, you can consider it to be a game of luck both according to my proposal and also according to the more standard/naive interpretation.

    (In a betting game the outcomes are random variables which (apart from the betting) are not related to the participants’ needs/utility.)

  15. David Speyer

    “A game of luck is a betting game where participants bet in spite of being able to rationally conclude that their expected returns are negative.”

    That seems very unrelated to the ordinary meaning of “luck”. I think most people would say that a game is a game of luck when the outcome is primarily determined by random factors. So the children’s game Candyland, although not usually played for money, is a game of luck.

    I actually thought you were going to make a different argument. I thought you would say that only extremely well matched players would agree to play each other for a $100,000 stake, and therefore it was primarily luck that would decide the game. As it is, I just don’t understand the way you are using the word “luck”.

  16. Gil Kalai Post author

    Dear David,

    I did make the other argument you mentioned (of participants selections) and the definition I propose is based, in part, on this argument.

    The problem is this: When we have games with some element of skill then, of course, played over time the skill factor becomes dominant. This is the crux of the naive argument regarding poker that goes back to Mark Twain story.

    There are various problems with this naive argument. But essentially it applies whenever there is an element of skill. For example, consider Black Jack (21) and suppose that in each round a fresh deck of cards is used. There is a huge difference between skillfull players and unskillfull players. But no player can win over time. So I think we will regard it as a game of luck although the sentence “primarily determined by random factors” does not really applies. Overtime, the outcomes are primarily determined by the skills.

    Take even the roullete, what do you mean when you say that it is a game of luck? Played over time, there is no luck at all, and the outcomes depend on one factor: a skillfull player is a player who don’t play (or the owner of the roullete); an unskillful player is a player who plays.

    The gambling phenomena is that people keep playing the roulette in spite of the sure fact that they will be loosing over time. This is really what we mean by saying that the roullete is a game of luck. This applies to black jack as well.

    So if we return to the poker clubes in Aumann’s story: when the expected gains are negative, over time, either there will be an effect of participants selection and all players will be of the same level and will have negative expectation to win, or there will be a large number of unskillful players that can rationally deduce that they are unskillful and that will continue to play for the same reason that people are playing the roullete. In this case, most players in the game will be the same type of players in a game of luck as the roullete or ’21’ are.

    There is an ordinary meaning of what “a game of luck” is. But there is no ordinary meaning to what a “betting game which is primarily a game of luck” is. And I think that the above proposal, judged over examples, makes most sense.

    (update: 7/20) Anyway, Let me try to improve the proposal:

    A game of luck is a betting game where the short terms outcomes depend on luck and the participants bet in spite of being able to rationally conclude that their expected returns are negative.

    A betting game is primarily a game of luck if this definition applies to most bets in the game.

  17. miroslodki

    A game of luck is a betting game where the short terms outcomes depend on luck and the participants bet in spite of being able to rationally conclude that their expected returns are negative.

    A betting game is primarily a game of luck if this definition applies to most bets in the game.

    I don’t think you can use the short-term to demarcate anything especially skill vs luck since the true underlying nature of whatever system can only be revealed with enough observations, not just with one person but with many different people. |Consequently if outcomes are random across subjects – there can be no claim of skill. Wagering is only a way of monetizing the activity and that means the odds are by design in favor of the house.

    So in the end the outcome (winner/loser) of the game of chess between two players is a matter of skill, the betting (from the house’s perspective is a matter of policy – it will make money on the betting however the game is won/lost as fulfilled by the role of the betting line

  18. Gil Kalai Post author

    There were interesting discussions on this matter in various forums and let me quote one participant, Yaacov Bergman:

    The Misnah disqualifies dice gamblers from giving testimony in court. The rationale given is that they are not participating in building the world. In fact, the NET TOTAL contribution of their activity to the building of the world is negative; not in expectation, but non-randomly negative.

    This might be the rationale for the modern law against playing chance games (not because the expectation is negative to one side and positive to the other side).

    Therefore: poker – out, stock market – in; because playing it helps build the world, albeit capitalistically.

    See the attached file (in Hebrew), copied from

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  20. Yan

    Hi, Gil. I have two main points:

    I) I’m extremely confused about the main legalistic/moralistic point you seemed to have tried to make:

    The structure of your point seems to be this: There’s some definition of a “game of luck” -> the judge made a claim that poker is a game of luck, and you agreed with him, proposing a definition that might not even be the one that *the judge used.* I feel for your argument to make sense, either:
    a) you have to use the definition that the judge used (which is probably the “common conception” of a “luck” that most of the other commentators seem to share, which is one different from yours, or:
    b) you have to concede that the judge made a judgment not using your definition, in which case you need a separate argument showing why your definition shows games of luck are “bad,” justifying the decision.

    II) I think the poignant-sounding defense of the blackjack example in the Freakonomics blog is not quite sound.

    My definition is this: “skill” means that you can alter the outcome of the game in a highly nontrivial way (and I suspect this is what most people think and this is why Dubner made his example).

    In this light, I believe blackjack *is* a game of skill, just one where you cannot make your gains positive. I like this definition better since it *does* scale in all the ways you admitted mathematicians want them to be, even with a linear bonus.

    Here’s a thought experiment: consider the following two cases, with the assumption that the setup (factoring in the shoe, “tips” if you consider them part of the game, etc.) is one where the best blackjack players have an expected return of $45 for every $50 they bet, and the worst have an expected return of $5 for every $50 they bet. By your definition this would be a game of chance since you can’t “win.” However, suppose we have a generous casino that gives you $20 each time you bet $50. Now the best players are expecting $65 and the worst $25. But here by your definition this suddenly becomes a game of skill! Of course by mine it was and always is a game of skill. I feel this is a more mathematically clean definition.


  21. hyperpat

    Mr. Jarvis earlier wrote about an experiment where players were handicapped via the expectation value implied by their current chess rating, indicating that this format does not work as the ‘luck’ element becomes dominant in the final outcome. The problem with this scenario is that ratings measure past performance, not current playing strength. It is well known that newer and weaker players improve more rapidly than stronger ones, which gives a strong bias towards towards these weaker players, as they are more likely to have significantly improved their current playing strength by the time of the tournament (I know this from very personal experience!).

    In addition, the variability of playing strength is higher for the weaker players (the standard deviation of performance ratings of Class E players is much higher than that of masters). Chess is normally a case of who makes the fewest errors – while the weaker player, over the long term, will make more errors than the stronger one, in any one game he may make many fewer errors than normal, resulting in a win, whereas if he makes more than normal, his result is the same as expected – he loses.

    Both of these factors make handicapping a tournament via expected results impractical and strongly detrimental to the most skilled players in the tournament. However, this does not thereby make chess a game of ‘luck’, where outcomes are strictly determined by random factors, as very obviously the player’s skill level has a strong bearing on his final result, and this is also just a true in the game of blackjack, where the skilled player over the long term will always do much better than the unskilled player (note that the skilled player may still end up losing, but he won’t losing as much as the unskilled player).

    I find the argument that changing the stakes changes the nature of the game from one of mainly skill to one of mainly luck inadequate unless factors outside of the game are considered: psychological mind-set, consequences of losing (such as going bankrupt), etc. The game itself remains a game of mainly skill, only the social outcome (the consequences) change.

  22. Gil Kalai Post author

    Dear Yan,

    A general remark, the sentiment “I feel this is a more mathematically clean definition” is a great line. It is certainly a sentiment that should drive us, and it leads to many successes of mathematics. But it also a sentiment that can, at times fails us.

    In my definition Black Jack in your first realistic scenario is a game of luck. In the long run the player is doomed to lose and the motivation for playing comes from an irrational belief that he can win or from a love of gambling. I think from the point of view of the written law and also from the point of view of the intention of the law, blackjack is a game of luck.

    In any case, a person that agrees that blackjack (in your first scenario) is a game of luck, has good reasons also to regard poker in the case we discussed as a game of luck too.

    I do not know what to say about your second unrealistic scenario. Certainly you made an interesting point.

    Regarding the judge’s decision. I think my definition is a way to “rationalize” his decision, and to legitemize his own line of thought and overall conclusion.

  23. yanzhang

    Dear Gil:

    I think we’re getting somewhere, so let’s start fixing parameters.

    I feel the definition you are intuiting is person-specific: i.e. it seems with your definition it only makes sense to say: “FOR person X, game Y is a game of luck” than to say “Game Y is a game of luck,” because part of your definition DEPENDS on “the player” (who is even isolated as a single person in your sentence “… the player is doomed to lose…”). However, I think the purpose of my thought experiment is to show that clearly this is dependent on X. In my second scenario, this negative sentiment clearly only applies to the “bad” player (who loses $25 per game in expectation), whereas the “good” player is winning the game in expectation. I think the fact that this difference exists is why most people would consider blackjack a game of skill.

    Thus, I cannot agree with you that your definition applies to poker, even though I would concede that *given your definition,* “normal blackjack” is a game of luck. “Good” players will win over the long run and “bad” players will lose over the long run, because “bad” players consistently make the same betting mistakes and psychological mistakes that “good” players can consistently profit from. Thus, a reasonable compromise we can make with your definition is that the game is a “game of luck” for the “bad” players, whereas it doesn’t really make sense to say the whole game is a “game of luck” since the good players consistently win. Your words “In the long run the player is doomed to lose and the motivation for playing comes from an irrational belief that he can win or from a love of gambling” do not apply to them.


  24. Gil Kalai

    Dear Yan,

    Right! My definition or interpretation of the law starts with the assertion what does it mean that for person X the game is a game of luck. Blackjack where every player is doomed to lose is a game of luck for every player X even if skill-differences make the rate of losing different.

    I regard a game as primarily a game of luck if this definition applies to most players X of the game (or most bets of the game).

    My analysis of a given scenario takes into account what we can expect over time: if when we analyze the situation we realize that at the end the setting will lead to all players or even most players being “doomed to lose and their motivation for playing comes from an irrational belief that he can win or from a love of gambling,” then I think it is very reasonable to regard the situation as a game of luck. (As defined by current laws.)

    Now you offer a scenario that in some society some philantropic organization (or perhaps the government) regards blackjack or poker as a valuable human activity and puts money so that the expected gains will become positive, so people will have incentives to play skillfully and win.
    I agree with you that in such a scenario it will be difficult to regard this activity as a game of luck.

  25. yanzhang

    Okay. I agree now everything works out given your definitions.

    I guess the main confusion for me (and other people) is that why you chose those definitions in the first place, since they don’t scale well and they seem to be properties of ordered pairs (Game, Player) as opposed to just (Game), which is somewhat implied by statements like “Game X can be a game of luck.” However, modulo the choice of your definition, I think we agree and I have learned something here.


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  27. Win@Chess

    Yes, luck is involved, no doubt. It’s like poker. Strategies are always useful. Unfortunately you can have the best tricks in the world but if luck is not on your side you have no chance.

  28. Jonathan

    I don’t see your point – you seem to be directly associating betting with luck and that’s not always the case. If you’re saying that the more money I bet the more that luck is involved vs. skill that’s a pretty bad and false statement. I do not doubt that fact that if I was playing against someone for a high amount of money it would very much be a determining factor but not as luck, as chance. See chance is the likelihood that an event will occur and luck is a modifier of chance – it’s something that the player has NO CONTROL over. If there’s that much money at stake I’ll want to play much more seriously and double check my thinking before making a move – this increases my chances at winning, but does not BOOST luck in any way shape or form. Now this is not to say that something lucky will not happen like say the experienced player making a blunder – there is always a minuscule chance that an outcome like that could happen, and that chance may be better in my favor say that the player is more arrogant but what is the money changing? The CHANCE that the person will make a blunder. Even if this chance factor is modified, it wouldn’t be modified to the point where the odds are in my favor vs his, factors like these will most likely not be in my favor and it will be up to LUCK whether that happens – it’s something that I can’t control.

  29. Gil Kalai Post author

    Dear Jonathan,

    consider the following effect: When the bets are higher every player will try to play only against players which are not better than him; this will lead to games between players with the same level of skill; and this will increase the element of luck!

  30. Chess Coach

    A very clever argument here, but I don’t think changing incentives and the psychology of the palyer constitutes as luck.

    Great post though, did have my head turning :-)

  31. Natalie Port

    This is my ahead just the same from time to time i visit here. I create so innumerable enchanting effects in your blog primarily its discussion. From the tons of comments on your articles, I judge I am not the only individual having all the gratification here! maintenance up the tolerable work.


    of course, there is a component of “luck” involved. Depending on how one defines luck. In that: if the randomness and unpredictability – PLUS -“the shaking -trembling hands” problem as witnessed in the “game-theory” – could or would – induce – an element of asymmetric mind-thoughts, leading to “irrational response” -> in other words randomness without knowing that the player is being random, could in turn, confuse the opponent and make chess – a game-of-poker :

    if so, and when so -> and if -labeling such behavior = surprise = luck
    then yes..
    Chess= a game-of-chance + game-of-skill+a game of nerves-and-steel,

    i look at it this way:

    [a] CHESS IS NOT A PARAMETRIC game, when only the ranked ordering of preferences + the computational power + ability = decides the winner or mate.

    [b] Chess = a strategic game – > wherein the other player { opponent} has paayoffs: PAYOoF’S that not only depend on knowledge – of the rules, and the ability to compute; but also, depend on knowing, but more importantly, anticipating, the payoffs AND the moves of the other party -> and vice-versa.

    [c] a + b – is non-deterministic -> if it were, then chess would not have been a strategic game: it would indeed have become a mathematical algorithm – and then IF one assumed – EQUAL computational power, THEN -> the game would have landed in a “draw” – a prisoner’s dilemma. will happen..

    ps: i am not arguing that chess is luck. On the contrary, chess involves intensive knowledge and computation . sorta like, you take the KIDUM – psychometric test in isarel or it entrance exam in india or GMAT OR GRE – the same person, on different times, { assuming the intelligence doesnt change) – does not score the same -> even on a relative scale { relative scale, among – a group of participants, to reduce , the sampling issue)

    sister of KATRINA-KAIF
    via olga-and-katrina-kaif


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