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Chess vs. checkers

Mark Palko writes:

Chess derives most of its complexity through differentiated pieces; with checkers the complexity comes from the interaction between pieces. The result is a series of elegant graph problems where the viable paths change with each move of your opponent. To draw an analogy with chess, imagine if moving your knight could allow your opponent’s bishop to move like a rook. Add to that the potential for traps and manipulation that come with forced capture and you have one of the most remarkable games of all time. . . .

It’s not unusual to hear masters of both chess and checkers (draughts) to admit that they prefer the latter. So why does chess get all the respect? Why do you never see a criminal mastermind or a Bond villain playing in a checkers tournament?

Part of the problem is that we learn the game as children so we tend to think of it as a children’s game. We focus on how simple the rules are and miss how much complexity and subtlety you can get out of those rules.

As a person who prefers chess to checkers, I have a slightly different story. To me, checkers is much more boring to play than chess. All checkers games look the same, but each chess game it its own story. I expect this is true at the top levels too, but the distinction is definitely there for casual players. I can play chess (at my low level) without having to think too hard most of the time and still enjoy participating, making plans, attacking and defending. I feel involved at any level of effort. In contrast, when I play a casual game of checkers, it just seems to me that the pieces are moving by themselves and the whole game seems pretty random.

I’m not saying this is true of everyone–I’m sure Palko is right that checkers can have a lot going for it if you come at it with the right attitude–but I doubt my experiences are unique, either. My argument in favor of chess is not a naive “Chess has more possibilities” (if that were the attraction, we’d all be playing 12x12x12 three-dimensional chess by now) but that the moderate complexity of chess allows for a huge variety of interesting positions that are intricately related to each other.

Overall, I think Palko’s argument about elegant simplicity applies much better to Go than to checkers.

But what happens next?

I wonder what will happen when (if?) chess is fully solved, so that we know (for example) that with optimal play the game will end in a draw. Or, if they ever make that rules change so that a stalemate is a loss, maybe they’ll prove that White can force a win. In a way this shouldn’t change the feel of a casual game of chess, but I wonder.

27 Comments

  1. conchis says:

    Overall, I think Palko's argument about elegant simplicity applies much better to Go than to checkers.

    Funny, that's exactly what I was thinking while reading the piece too.

  2. Ken Williams says:

    Regarding your comment – "all checkers games look the same, but each chess game it its own story" – that's a red flag that you probably just don't understand it very well. Consider an (overly-simplistic but often useful) analogy from music: people who prefer classical music often say that they find rock music "boring because it all sounds the same". People who prefer rock music often say the exact same thing about classical music. The reality is that both are complex and expressive, but if you don't understand their nuances, you won't get much out of it.

    I usually prefer this "just don't understand it well yet" interpretation to the idea that everything's just a matter of taste and that's the end of the story.

    Though I'm no good at either checkers or chess. =)

  3. Andrew Gelman says:

    Ken:

    Sure, I'm only giving my impressions. But it's believed by many (not just me) that chess is more interesting than checkers! Palko is the one making the counterintuitive claim otherwise.

    "Everything's just a matter of taste" should be the beginning, not the end, of the discussion. The next step, which Palko and I are exploring, is what aspects of taste are relevant to these games.

  4. Manoel Galdino says:

    Just curious: DO you prefer chess or go? I prefer chess, but nowadays I play go much more.

  5. Jeremy Miles says:

    Like conchis, I was thinking about go as well whilst reading.

    I pretty much agree with this – a game of checkers is completely unmemorable to me when I've finished it, but I can tell you what happened in a game of chess. When I play go, I feel like there's a story and it's written in another language. I'm dreadful at go, I always lose abysmally, and I've no idea what is happening or why. (When I lose at chess, at least I have some understanding of why).

  6. Paul says:

    The biggest difference I see between chess and checkers is not piece differentiation, but the locality of influence in checkers. Moving a single piece in chess can change the dynamics of all the regions of the board. Checkers, on the other hand, requires that influence be maintained by an actual chain of pieces: Thus chess is much more about managing control of the board as a whole, and checkers is more about building powerful structures and winning localized skirmishes. Go is similar to Chess in this regard as well: Battles seem to me to be dictated by the distant structures that the battle will eventually grow to collide with. I suspect that contributes to the perception of intellectuality in chess: you can perform passably in checkers with a very myopic view, but not so in chess/go.

    As others have said, narrative may have a lot to do with chess's popularity. Checkers endgames all look more or less the same (ditto Risk, which should lend itself strongly to narrative but somehow doesn't). But a chess game where you infiltrate the enemy ranks and checkmate without many pieces exchanged, versus a game where you slowly push a defensive line forward, versus crushing a wing and invading that side of the board all feature different narrative arcs.

  7. Mark Palko says:

    Counterintuitive, but not that uncommon. Some game historian (I think it was David Parlett) observed that most masters of both games tend to think more highly of checkers. Poe certainly agreed and when the great chess master Emanuel Lasker invented his own game he chose to make it a checkers variant.

    (when I talk about checkers I mean the version with forced captures and long jumps [a.k.a. Spanish checkers])

    Still, even with all those people behind me, I'm not prepared to claim that checkers is the superior game, only that it's an interesting one with cool mathematical and strategic properties. We tend to miss these properties because the game is so simple and familiar and because we think of it as a child's game to be played reactively rather than strategically.

  8. Mark Palko says:

    Paul,

    As far as I can tell, most people who are serious about the game prefer long jumps which changes this dynamic quite a bit.

  9. Mark Palko says:

    conchis,

    I left out Go because I was introducing checkers variants but in terms of elegant simplicity, it is certainly the ideal.

    And it's one of the games where good human players can still consistently beat computers.

  10. Paul says:

    Which would certainly explain a lot of the disconnect between popular perception and expert perception: they're not even talking about the same game. Long jumps add long range interactions, moving checkers towards the go/chess category. I can certainly believe that if we all grew up playing long jump checkers we'd see it as a deeper game. As it is, I get the impression that a lot of casual family play doesn't even include the "you have to jump an opponent if you can" rule.

  11. matthew says:

    even if chess were 'solved' i don't think it'd suffer from robotic human play, since i doubt anyone outside of the grandmasters would ever always play games of mutual best-responding.

  12. Bill Mill says:

    > The big difference is the number of positions possible in each game: 1020 for checkers and 1040 for chess. To get some idea of this, if a computer could solve checkers completely in one nanosecond (a single cycle of a 1 GHz computer), it would take this computer 3000 years to solve chess.

    So, assuming this is true, and chess has roughly 20 orders of magnitude positions than checkers, we can do a back-of-the-envelope calculation to guess when we can solve chess.

    1) Checkers was solved completely by Chinook in 2007. Let's give a conservative estimate that it took one year of 2007 computer time to solve; it was actually more like 7 (http://www.sciencedaily.com/releases/2007/07/070719143517.htm)

    Thus, we can say that one compute-year in 2007 is worth about 10^20 positions.

    2) Let's assume Moore's law holds, and computing power doubles every two years

    3) log2(10^20) ~= 66 implies that we'll have enough computing power in 66 doublings, or 132 years, to solve chess in one 2139-year of compute time.

  13. Wayne says:

    Go. At 19×19, it's much more strategic than either 8×8 game. It has an amazing handicap system that allows players up to 9 levels apart to play an even game and teach/learn. It is aesthetically pleasing by design, and aesthetics enter into the play as well.

    Chess is cramped and has that damned Zugzwang, while Go has multiple levels of tactics and strategy and it's always in your interest to move right up until both players decide they don't need to move, when the game is over. In Go, the fighting usually starts in the corners, spreads out to the sides, and then spills over into the center, where the previous fights — even lost positions — may suddenly spring back to life.

    Plus you have all of the cool Zen-like concepts, like playing away from where you intend to attack before you attack, and keeping your positions "light" rather than allowing them to become heavy.

  14. J.J. Hayes says:

    I say instead of pitting one against the other combine them into a new game which is just like chess except that when one piece "attacks" another it does not automatically take that piece, but the players must play a game of checkers (or Go- maybe the attacker chooses) to determine which of the pieces wins the particular encounter upon the chess board. A king could even get out of checkmate by defeating the checking piece at checkers or Go.

    How would one solve this game?

  15. Mark Palko says:

    I suspect there has been a steady dumbing-down of the game with things like mandatory capture falling away. I do know that there used to be a penalty called 'huffing' where a player lost the piece that failed to take the capture.

  16. What is the evidence that "it's not unusual to hear masters of both chess and checkers (draughts) to admit that they prefer the latter"? I have known quite a few chess masters, and I've never heard of one who preferred checkers.

  17. zbicyclist says:

    Palko: "a steady dumbing-down of the game with things like mandatory capture falling away"

    I don't think these rules are new. As a kid in the 1950s, we always had to clarify whether we were playing with mandatory capture or not.

    Is it the case that the game is simpler/harder with/without mandatory capture? This isn't obvious to me.

  18. Mark Palko says:

    I was thinking in terms of the past 100 – 150 years.

    As for the difficulty level, mandatory capture give a big advantage to players who are thinking a move or two ahead. It alo makes certain traps and strategies possible.I suspect that makes it more a game of position than points. We could debate whether that makes the game simpler or more difficult but I'm inclined toward the latter.

  19. Mark Palko says:

    I'm believe that I got that from David Parlett's "Oxford History of Board Games." We also have Poe's "The Murders in the Rue Morgue" quote and the indirect evidence from Lasker's interest in the game.

  20. Mark Palko says:

    In case you're wondering "I'm believe" is what you get when you start with "I'm pretty sure" and don't check your rewrite.

  21. Mark Palko says:

    Add Irving Chernev to the list

  22. Chessmaster says:

    I would love to see what fraction of a random sample of chess masters think checkers is a superior game (I would guess that less than 5% would say that). Meanwhile, this scene from Season 1 of The Wire settles the chess vs. checkers debate rather definitively:

    http://www.youtube.com/watch?v=S1HUlTKvDUI

  23. PoliSci Chess Fiend says:

    I know no one who plays chess competitively, but prefers checkers. That's just silly. It's like saying that a lot of political scientists really think more highly of sociology than their own discipline. Sociology? Really? Checkers? Really?

    Anyone who says that chess derives its complexity from "differentiated pieces" and not the interaction between the admittedly different pieces is having troubles remembering how knights move and cannot actually play chess. Checkers may have a magical morphing property to it that chess does not, I have no idea knowing nothing about checkers, but the beauty of chess very much comes from the interaction between the pieces. I just got home from playing in a chess tournament and the most beautiful position I had all day was one in which my opponent and I had the same amount of material left, but my pieces were all working together in a well-coordinated mating net and his pieces looked like they were sitting unused on the unorganized shelf that was his back rank.

    I like what you said about a chess game having a narrative. Each game does have its own feel, almost its own music. Some games are tactical battle royals and others are quiet positional struggles. And good players know when to change the music: e.g. Game 4 of last year's world championships, which was an incredible game because in the space of two moves (2.Ng4! Rad8 23.Nxh6+!!), Anand took a game that had been all all about fighting for a small positional advantage on the queenside and turned it into a game that ended in a sudden and unexpected kingside fireworks show.

    Finally, chess will not be formally solved anytime soon. Its game tree complexity is greater than the number of atoms in the known universe. Anecdotally, the stronger the player the more likely they are to think that chess is theoretically a draw, but this has little impact on how the game is played. What is important, however, is the impact of computers on the opening game. The earliest theoretical novelty (an opening move that has never been played before in top level tournament play) in last year's world championship match was white's tenth move. I lost just as many games as I won today and in some of those games my first fifteen moves were played rapidly from memory. For the casual player, and by casual I mean below the master level, this is less important because your opponents suffer from the same problem and your time would be better spent focusing on improving your endgame than memorizing more opening lines. But at the very highest levels, opening preparation/memorization is only going to get more and more ridiculous. Forget your correct 20th move and you're screwed. Heavily researched, highly tactical openings like the dragon are already like this for players of all levels (the recommended line in my computer's opening book is 30 moves long, again that's 30 moves for each player!). More positional lines are less life and death, but they too have extremely long (though not as well researched) lines that at the very top level are extremely important to winning. At some point you have to question the wisdom of playing a game that will become more and more based on the ability to memorize rather than the ability to actually play the game for yourself. The answer to the problem? Fischer Random effectively does away with any opening line memorization but without that opening preparation the game is a lot more clunky, a lot less beautiful. Perhaps more importantly, we've all invested in the imperial system and will damn anyone who tries to make us go metric.

  24. nnyhav says:

    Pet peeve #1: comparing number of possible chess positions to number of atoms in universe conflates configuration with counting and belies a lack of understanding of combinatorics.

    Pet peeve #2: handicapping in chess (and go) is social not intrinsic: odds games in chess were common in 19th century, and in these times time handicaps are bread-and-butter to speed-chess hustlers (many GMs at Open tourneys make more from that between rounds than from prize funds).

    Pet peeve #3: solving chess is not equivalent to exhausting the game tree (think meta, cf 4-color theorem); not soon, but sooner than you think (cf progress on endgame databases).

  25. Wayne says:

    @nnyhav

    I can agree on pet peeve's #1 and #3, but I think #2 is wrong. Chess has only ad hoc handicapping: it's arbitrary, and may change the game entirely (i.e. you have no bishop of a certain color).

    Go, on the other hand, has handicapping built-in for up to a 9-level rating difference. The handicap system has been tested over centuries and there are good heuristics for setting and modifying handicaps. In addition, giving a handicap doesn't modify the game at the tactical level and only modifies the stronger player's strategy to be a bit riskier and to keep more options open, complicating the game for the weaker player.

    Go is a more subtle game in play and also in scoring, and that enables a structured handicapping system that Chess simply cannot have.

  26. Andrew Gelman says:

    Wayne:

    Chess has continuous handicapping via the clock.

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