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Some of you must have an idea of the answer to this one.

Suppose I play EJ in chess—I think his rating is something like 2300 and mine is maybe, I dunno, 1400? Anyway, we play, and my only goal is for the games to last as many moves as possible, and EJ’s goal is to checkmate me in the minimal number of moves. Say I have to pay him $1000 * (50 – X), where X is the length of the game. (We can safely assume that he’ll win.)

So, here’s my question: What will X be? How long will I last, if my only goal is to last, and his only goal is to bring it to an end in as few moves as possible? 30, maybe? And what if you swap out EJ with Magnus? Could he checkmate me in 20 moves? I’m assuming that Magnus will be told some sense of my ability, so’ll know ahead of time that he doesn’t need to play safe.

Or am I being too pessimistic? If my only goal is to delay the inevitable, could I drag things out to 40 moves? For that matter, how long could EJ last against Magnus, if again his only goal were to maximize X? 60 moves? 70 moves?

I really have no idea. But some of you must know.

P.S. The commenters have convinced me that I need to at least consider the possibility of a draw or of me winning, as this can affect my opponent’s possible decision to try for a go-for-broke mating attack in the middle game.

So let’s go with this payoff structure:

– If EJ wins in less than X moves, where X < 50 moves, then he gets $1000 * (50 – X).

– If EJ wins but it takes him 50 moves or more, then no money changes hands.

– If the game is a draw, then no money changes hands.

– If I win, then no money changes hands.

This would give EJ every motivation to go for broke. But not to be sloppy: being sloppy could cost him a chance for that quick victory!

Alternatively, we could motivate more careful play on EJ’s part by requiring that he pays me $5,000 for a draw or $10,000 for a win.

P.S. OK, EJ and I just played. He threw lots of pieces at me, at one point I think I was ahead, but he eventually figured out how to move in on me too fast than I could defend. 32 moves. I guess I owe him $18,000 now.

41 Comments

  1. Ed Ally says:

    5 to 10 moves either one.

    2300 vs 1400? – with that gap don’t think
    you would get to 30 moves , maybe 20.

    • JFA says:

      ^ This comment is the only one necessary.

      Andrew, what happens when you play a chess bot rated at 2300?

      • Andrew says:

        OK, I just went to a website that said it would play me against bot that plays like a 2300-level player. I went on and played. I played pretty fast, maybe blitz speed. I made a blunder around move 4 in the opening—not a major blunder like moving a piece, but a wasted move, enough so that after move 4 I felt that I had no possible chance of winning. The bot used some passed pawns to defeat me. I did not try particularly hard to prolong the game: basically, I played the way I would play any game where I was behind: i tried to slow the opponent’s advance, parry or forestall obvious threats, and (hopelessly) try to come up with a plan of my own to use my pieces together. The bot checkmated me on move 40.

        On one hand, I think it I were to put more time into the early moves, I could usually avoid a blunder on move 4. On the other hand, I’m pretty sure I’d blunder before move 10, so I don’t know how much that would really matter. I think the bot could’ve beaten me faster by taking a more aggressive approach. It beat me by doing what was necessary.

        So I learned a bit from this experiment. Given the way I was playing, the bot could’ve beaten me in much less time. And I don’t think that I would’ve been able to prolong the game using a different strategy. I was already trying to stay afloat, and I often traded pieces just because that was really the only thing I could do.

        So my best guess now is: EJ in 30. Maybe 25 or 20.

        • Mathijs Janssen says:

          I feel like you’re still not appreciating how much the requirement of winning quickly or losing slowly changes the game. Consider a position with an extra rook for white, no other pieces but the kings and 7 pawns each, say the c-pawns missing. Clearly such a position is dead lost for black and would only arise after really uneven play. But it would probably take about 20 moves to mate from there. This gives tremendous power to the defender: he can basically say “I’m willing to lose a piece to trade queens, or lose a pawn to trade knights, and it will be a good trade for me”. This means in turn that attacking gets much harder for the aggressor. Normally in an attack it’s fine if you win by winning back your sacrificed material plus interest. Here getting an extra rook out of the attack means that you’re gonna hit 50 moves; it’s mate or go home.

          As long as the defender is aware of this, he doesn’t actually have to be a very strong player. Just avoid dropping pieces, unless you get some extra trades out of it. With such a strategy you will lose for sure, but it will likely take more than 50 moves.

          In a normal game I would not be surprised to see a game between a 1400 player and a 2300 player end before move 30, by resignation or even by mate. But that’s really because the aim of the game is different for both players.

  2. Adrian Bunk says:

    It would be a completely different game.
    A 1400 player specializing in it might be able to survive 50 moves against Magnus.

    You would prepare by searching for opening variations that quickly lead to an endgame.
    Find a way to exchange queens and many other pieces early.
    Playing an endgame until mate will rarely end under 50 moves.

    • Terry says:

      Good points. You want to get to a king-and-pawn endgame where things get dragged out. Exchange wherever possible.

      Even mating with a king and rook versus a king takes a lot of moves.

    • Phil says:

      I think this implicitly assumes that the better player will be trying to play the objectively best move, as in a normal game. The better player will keep pieces on the board — their own, anyway — and play for complications. The lesser player will eventually make a significant mistake and lose material, and it’ll be quick after that.

  3. Jackson Monroe says:

    Depends on the time you have. Even a 1400 can defend for 20 moves by playing very passively against someone very strong if they aren’t trying to win. You can lose really quickly when you try to maintain equality and the tension in the position increases. 20 moves seems easily doable against a 2300, with Magnus too I think.

  4. David J. Littleboy says:

    How much time do you have to prepare? If you can put together an opening repertoire that allows you to get to closed positions, (e.g. French defense as black), maybe you can hold on beyond 20 moves. Get a chess program and play it. A lot. It’ll point out your mistakes. Mercilessly.

    But as Ed says, that’s an enormous gap.

    That’s the advantage of Go over chess: the handicapping system works well, and players of quite different strengths can have interesting games.

    • Ben says:

      > Get a chess program and play it. A lot. It’ll point out your mistakes. Mercilessly.

      Oh that’s a good point. Chess program seems like it would be a good substitute here.

      • David J. Littleboy says:

        When the dedicated chess machines came out that played substantially better than my 1600 or so back in the late 1980s, I spent a lot of time playing one. The bottom line was that once the position opened up, the machine would find something I couldn’t see. At which point, the game would be quickly over.

        Current programs can be set to a rating level, and have different personalities (more or less aggressive). There may be a program that can be set to maximum Tal-like play.

        Still, actually wining requires that one’s opponent’s pieces be less effective overall (and that you have power/mobility/piece count superiority around the enemy king), even if there are more of them. Close the position, develop as many pieces as possible (second rank behind pawns is fine), castle, queen also to second rank (if your queenside knight, bishop, and rook are undeveloped, your opponent will find a piece sacrifice on the king side), and tread water. A 1600 player should be able to hold out against anyone for 25 if not 30 moves. But it will require some opening study; someone who is 1400 and not a dunce will quickly become 1600 with study.

        I recommend these books (sorry for the terrible image; it’s from 1970 or so):
        https://pbase.com/davidjl/image/170642436

  5. Ben says:

    > Say I have to pay him $1000 * (50 – X)

    Also this is an incredibly high stakes game.

  6. Zach Himmelsbach says:

    Time controls will likely be a big factor here. The less skilled player needs to balance a) spotting mate threats with b) not running out of time. My guess is that the expected payout for the stronger player is decreasing in the length of the games. A 1400 player can probably work out an early mate threat given enough time. To be concrete: In a 1 minute bullet game, I think the strong player is getting paid-out big relative to their payout in a 1 hour game.

    The tough part here is considering how a strong player could adjust their approach given the rating of their opponent. Let’s assume, to find a bound, that they can’t do any better than their optimal play against strong opponents: Playing against chess.com’s maximum strength computer (which it says is like 3000, but who knows what that really means), I can regularly last about 30 moves (I’m around 1400). So, I’d guess that the _maximum_ payout for the 1400 player against a Magnus-level opponent is about $10,000 here.

    The optimal adjustment for the stronger player is probably something like: play sharp, unusual openings with chances for hard-to-spot traps. Playing unsound sacrifices is probably good, too: the weaker player probably can’t muster the optimal defense. The weaker player also has to be weary of accepting sacrifices (knowing that they can’t judge as well as the stronger player whether the sacrifice is sound), so unsound sacrifices that are traps when not accepted are probably a good bet.

    One way of estimating the potential benefit of this kind of optimization would be to look at the performance of 1400 level players on defense-themed chess puzzles under time constraints.

    With the weaker player around 1400, my money is still on the time control being the critical factor. (One other thing is that the size of the bets may differentially affect the performance of the players.)

    • jim says:

      “The weaker player also has to be weary of accepting sacrifices (knowing that they can’t judge as well as the stronger player whether the sacrifice is sound), “

      Why should we assume the weaker player knows they can’t judge sacrifices as well? Perhaps that’s why they’re the weaker player.

    • Andrew says:

      Zach:

      I agree regarding time control. Who knows what would happen to me in a blitz game? In the above post, I was assuming a time control appropriate to a mellow but not boring game, maybe 20 or 30 minutes each.

  7. Steve says:

    Do you mean total moves or your moves? Also, does Magnus care about the risk of losing or is he only trying to maximize $1000*(50-X)? If you mean total moves, then I think for intermediate players, the average game is around 40 to moves. My kid is 1200 player, an intermediate player. His games and the games of his peers are typically under 50 moves and seldom over 60, but of course he wants to win. An intermediate player shouldn’t be getting checkmated in under 30 moves. If they are, then the are doing something boneheaded in the opening. It doesn’t matter how much better Magnus is. If an intermediate player protects his pieces during the opening, the game is going to take 40 to 50 moves. If Magnus cares about losing (the games are rated), he should opt for a strategy of playing you normally (without regard to the number of moves). He should be able to win most games in around 50 moves or less. If he doesn’t care about losing, I think he should still opt for the same strategy. Let’s say that he takes a different strategy and throws out very unconventional openings that give you a chance to win. He will get a few quick checkmates, but he will also open up the possibility that you can beat him. If that happens, since you don’t care about winning, rather than checkmating him, you will keep the game going on indefinitely and he’ll have to pay you. So, I think that offer of the money will not change his strategy. He will play conventionally and beat you in the average number of moves, which is under 50.

    • Andrew says:

      Steve:

      I’m counting moves, not half-moves. Regarding the strategy issue, I don’t think that Magnus (or even EJ) has to worry about losing to me. Magnus could be behind a rook, and I think he could catch up. Or at least get a draw. SO to win the $, I think he’d want to do some special things to bring the game to a faster conclusion.

      • John Reid says:

        Andrew: Magnus can beat IMs (Lawrence Trent) at rook-odds so I have to agree that he could catch up against you. https://twitter.com/lawrencetrentim/status/638967300826132480?lang=en

        I think the answer to the original question depends a lot on playing styles but surely it isn’t too hard to get to 20 moves despite the rating difference. If I had I had to offer a spread it would be around the 28 move mark.

        Magnus did play a famous Liverpool footballer (another chess player called Trent funnily enough) in an exhibition match a while ago. It was ugly although I bet you would play better. https://chess24.com/en/read/news/carlsen-beats-trent-alexander-arnold-co-13-0

        John Reid (Hackney Chess Club)

      • Steve says:

        Andrew:

        I still think his optimal strategy is to play you just the way he would play anyone at your level. He picks an opening that only grandmasters are proficient with and he will win most of the time in less than 50 moves. If he actually does something really unconventional (for him, not you), he will may get you in early checkmates but he does risk getting into much longer games because he created a vulnerability that you could exploit to get him into a longer game. In other words, I think the payoffs may be like this:
        Magnus plays it straight 99% of the time his wins in 45 moves and the rest are ties: his average payoff is $4550
        Magnus engages in reckless strategy. 10% of the time he wins in 30 moves, 80% of the time he checkmates at 50 and 10% of the time he checkmates you at 55 moves. His payoff is $2500. I am simplifying of course, but if I am correct that he has a very high chance of getting you in under 50 moves by engaging you with whatever his standard openings would be, then you see my point. He doesn’t need to take any risks. Of course, in actual practice, he would learn your weaknesses pretty quickly and that I think would make him take even fewer risks because he’ll find an opening that is standard for him but you are shaky on and he’ll just keep doing variations on that and get you in check even quicker. But I stand by the conclusion that a conversative (for Magnus) strategy has a higher payout. Maybe if you lower the number to 40 moves it would make Magnus take risks.

        • John Reid says:

          > Magnus engages in reckless strategy. 10% of the time he wins in 30 moves

          I’m guessing more like: Magnus engages in reckless strategy. 90% of the time he wins in 30 moves

          It does depend what you call reckless though. I’m very much on the other side that Magnus should mix it up if he wants to win quickly. He needs to achieve a position on the board that Andrew has no experience with. That is where a difference in class will tell the most.

          • jim says:

            Exactly. An unconventional opening that he’s studied, but that Andrew hasn’t. Neutralize Andrew’s modest knowledge by avoiding any situation where he might be able to use it. Attack aggressively too to shake the confidence of the lesser player.

  8. The Dude says:

    Just open up Stockfish, which is way stronger than Magnus, and try it. I believe you can get weakened versions that double play at arbitrary levels too if you want to generate data on the gradient.

    • TheDude says:

      Just got to 25 moves against stockfish 8 while moving really fast. I’m like a 1500 on lichess in classical.

      • Phil says:

        Stockfish is trying to play the objectively best moves most of the time. That’s a different game. If it were optimized to beat weaker players as quickly as possible it would avoid exchanges, sacrifice material for a strong attack, etc. Look at any game by Paul Morphy in a simultaneous exhibition. Of course, Murphy’s opponents weren’t trying to just drag things out. But in those games Morphy knew he was playing weak players and he was trying to win fast, so he played an attacking style that wasn’t objectively optimal but didn’t have to be.

    • Andrew says:

      The:

      Sure, Stockfish is better than Magnus. But Stockfish is just trying to win, it’s not taking advantage of the knowledge that I’m a patzer. Part of my framing of the problem is that my opponent is aware of my patzer status.

  9. Mark Samuel Tuttle says:

    I’m reminded of my early attempts to beat a computer at chess. I learned that if I gummed up the middle of the board, refusing to advance much, or exchange pieces, that the computer fared less well than with a “cleaner” board. This was a crude way of focusing on defense, vs. offense. Eventually, the computer would do something I could take advantage of. Of course, if I did something stupid the computer would still win, but in the mean time, I could last much longer.

    Might be worth a try vs. your gifted opponent.

  10. Mathijs Janssen says:

    I think this is a much tougher challenge for the 2300 player than you think. It will also depend on his playing style. The goal in a normal chess game is just to win, not to win fast. Basically the only way to give mate in under 50 moves is to do so in an attacking game. A “normal” one-sided game where, say, the 1400 player is a bit worse out of the opening, loses a piece in the early middlegame and then just drags the game on will probably last well over 50 moves. Even something simple like mating with a rook against a bare king will take maybe 15 moves. Games usually don’t last nearly that long because the losing player will resign a hopeless position. But for a 1000 bucks a move, I guess most people would keep playing.

    The 2300 player would have to take risk in order to get the move count down, going for a quick mating attack. But that is not the way every 2300 player likes to play. I would take Andrew’s side of the bet here. In fact, I think the argument that the 2300 player will surely win doesn’t really hold up here; you will need to specify the pay-off if he loses as well. After all, he might start playing risky sacrifices in the hopes of ending the game quickly.

    (I’m a 2000 level player, for the sake of reference.)

    • Andrew says:

      Mathijs,

      Here’s another way to put it I play Phil sometimes. He beats me about 4 times out of 5. OK, he’s been playing a lot recently, so maybe now this would be 9 times out of 10 . . . maybe he’s an 1800-level player . . .

      Anyway, here’s the point. On the occasions that I win against Phil, two things happen: (a) I play flawlessly (that is, “flawlessly” for me, i.e. no major blunders), (b) Phil blunders, or at least misses some opportunities. When I win, I’m happy, but it always feels like fluke, not so much that I outplayed him as that I got lucky.

      Let’s say that EJ plays me and wants to win the money, so he tries some traps. So maybe he’s playing effectively at a 2000 level instead of 2300? He’s playing unsoundly but he can go into damage control mode as necessary if he falls behind. Meanwhile I’m trying to simplify the position, exchange queens, etc.: I’m not playing at my best either! I still think it would be very hard for me to beat him. As long as there are some pieces on the board, he can come at me. And if it does get to an endgame . . . well, let’s just say that I’m a typical 1400-level player. I’m terrible at endgames. I guess I could imagine a scenario where EJ goes for the big $, sacrifices some pieces in a big attack, but I manage to stay alive . . . then I’m up a couple of pieces, but EJ still manages to get rid of all my pawns, it’s K+B+N vs K and I still have to call it a draw.

      In any case, your comment has convinced me that I need to change the payoff structure. I’ll do so in a P.S. above.

    • Ben says:

      > It will also depend on his playing style.

      Yeah it’s kinda cool how people who are better at things than you can tell you more about what you were doing that you knew you were doing.

      It’s like the model you’re working with in your mind of what you’re doing is simpler than the model that they’re fitting when they’re watching you. There’s the true you, and there’s the you you know about, and somehow the model they have can be closer to the truth (I guess this is the being in someone’s head thing)!

      Games with skill gaps are pretty cool. I like the first three mins of the documentary: https://www.youtube.com/watch?v=6tgWH-qXpv8 . It’s like some dude playing 1 vs. 3 in a fighting game and winning.

      I guess something like Poker is kindof different in that you’d expect the better player to lose with some regularity. Part of the skill is that the cost function is being worked out in the process as well.

  11. Phil says:

    No way do you make it to fifty moves. OK, every once in a while, sure, anything can happen, but I think you’ll be hopelessly lost by move 14 or so, and a skilled player will find a quick checkmate. If you make it to thirty moves you should be proud.

    You’d be better off with a long-play game because in a blitz game you’ll blunder or fall for a simple trap. But even in a slow game you won’t last many moves. A losing position in ten to fifteen moves, and then at worst another fifteen if the best your opponent can do is trade down, queen, and finally mate you. But I bet he’ll find a way to keep the queen on the board (his, anyway; maybe not yours) and go for a quicker mate.

    Don’t accept any gambits. Not even the Queen’s Gambit.

    Not that this proves anything, but if you want to see a strong player vs a weak one, where the weak one tries to keep everything closed, check out the first game in the YouTube video “Paul Morphy is Not Strong: The Refutation” with GM Ben Finegold. (I’d post the link but I think this comment would go to spam then).

    By the way you are overestimating my strength, but thanks!

  12. TAS says:

    I will now be very disappointed if this game doesn’t happen! (With EJ, I imagine Magnus would be a bit more difficult to get.) Instead of money, I propose that the payoff structure involves blog posts mentioning Bayes factors (a favorable outcome for EJ translates into Andrew blogging about how great Bayes factors are; a favorable outcome for Andrew translates into EJ blogging about how much Bayes factors suck.)

  13. Not Trampis says:

    wouldn’t it depend if you are a ROOKie or not.

  14. Yuling says:

    The payoff looks like a call option with strike price K. Based on some stochastic calculus theory we could not only solve the fair price K but also price this option after k<50 realized moves.

  15. Olav says:

    Here’s what happened to Bill Gates (granted he probably wasn’t trying to drag the game on for as long as possible): https://www.youtube.com/watch?v=84NwnSltHFo

  16. David Joerg says:

    So, I have some credentials in this subject:
    * I entered the “Finding Elo” competition on Kaggle and took 2nd place.
    * I built a virtual chess coaching app called “Learn Chess with Dr. Wolf”
    * I built some unreleased products that coach chess players of various levels.

    The big problem you have as the 1400 rated player is your tendency to blunder. 1400 rated players blunder all the time. And it’s not just blunders like putting a piece where your opponent can capture it. It’s next-level blunders like leaving yourself exposed to a fork, or next-next-level blunders like making a move where your opponent can force you in your next turn to be exposed to a fork. Or even more subtle stuff where you have no choice but to give up the right to castle.

    Anyway, what EJ will do is create situations that have high blunder potential for you. He will play threatening moves, where the threat is subtle and you may not notice it. Or where he’s threatening two different things, and you may not notice both threats, and there’s only one move that defends correctly against both.

    So, he’ll keep creating significant tactical threats, you won’t notice them all, and each one you don’t notice will cost you material. By move 20 you’ll be playing down significant material, and then he’ll force trades.

    This is all because of the 900 point difference. The problem you’ve posed is much more interesting when the point difference is smaller, like 300 or 200 points. Then the lower-rated player can adopt a defensive playing style.

    The interesting part of your question is: “what happens when there are asymmetric payoffs to the two players? how do their playing styles change?”. And the playing styles _definitely_ change as a result, and can be quantitatively characterized. The quantitative characterization of playing style in chess is pretty much an open question — a few researchers have been nibbling at it but nobody has taken it seriously. Everyone serious in chess has been obsessed with the question about how to make computers win more, and have pretty much ignored all the other questions! I want the field to myself so I’ll stop there :)

    • Andrew says:

      David:

      Thanks. Regarding the prolonging-the-game question: Yes, I think it’s only interesting with that huge ability gap. For example, I think Phil’s the equivalent of about 400 rating points better than me, and he can beat me most of the time, but I think if my only goal were to last a long time, I could probably drag Phil out to 50 moves. When he beats me, it’s by the accretion of advantages. Yes, I blunder, but also he will use his pieces together so that he’s attacking one spot with three of his pieces and I can’t defend it without giving up something else. One thing that stops Phil from easily destroying me, though, is that he has to worry that I might do this to him! It happens sometimes. On the other hand, if Phil was playing me and was willing to risk a loss but wanted to checkmate me in 50 moves . . . I guess he could probably do it. 50 moves is a long time. I expect that with some practice and training, I could develop an effective drag-it-out strategy, but I don’t know that I could just do it cold.

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