Am I a Sucker?

On game theory and why I keep accepting draws when I'm winning.

*Hikaru voice* Welcome back, everyone. For today’s newsletter, I’m going to write about why I keep accepting draws in winning positions. Am I just one of those suckers who’s born every minute? Or is there something more complex going on here? Let’s hope it’s the latter!

But first, two pieces of housekeeping:

1. I appeared on the most recent episode of the Chess Journeys podcast! If you’ve never listened, it’s great in general, and I’m really happy with how our conversation went. We talked about my chess history and approach to playing, the newsletter, losing to kids, and many other things related to chess. In the process, I came up with a great¹ Chessable course idea that someone else should jump on. Check it out!

2. Last week, I made a pact, per Anne-Laure Le Cunff’s book Tiny Experiments: I would analyze every one of my online games for 90 days. Ben Johnson mentioned it in this week’s Perpetual Chess Linkfest in a way that made me feel like I need to provide some regular updates on my progress. (Also, Ben: I promise I’m not lying.) So: so far, so good! Since the day I published that piece, I’ve analyzed every online game I’ve played, producing 17 different takeaways. You can check them out here.² Honestly, I’m feeling like this is super-useful: it’s doing exactly what I hoped it would, which is making me think more deeply about my games, providing insights into where I’m weakest, and helping me steer my training. For what it’s worth, I’ve also achieved my highest-ever rapid rating while doing this, which is 1733 — I’ve got my eyes on 1800 now.

Okay: let’s get to this week’s theme. You might remember that, a few weeks ago, I wrote about the general question of accepting a draw offer or risking the safe result in order to go after the bigger win.

In that particular case, I decided that I was pleased with the draw, even though I’d taken it in a position where I had a clear edge — I’d spent the whole game expecting that I was going to lose, and my opponent was higher-rated than me, meaning that the draw felt like a relative victory. (And all of this stuff ends up being psychologically relative.)

But I also mentioned at the end of the piece that “in the future, in similar circumstances, with this experience under my belt, I might be emboldened to fight for the win.” I’ve spent the few weeks since writing about wanting to become more risk-seeking, to adopt more of a promotion-focused mindset (prioritizing improvement and stretching my abilities) than a prevention-focused mindset (settling for the safe result).

So when, at the end of my last game, I reached yet another uncertain position in which I was offered a draw — you have to imagine that I fought on, right? That I took the risk? That I reached for the brass ring?

A Position.

It’s move 31. Unlike my last two opponents, who were children, the guy I’m playing is 68 years old³, and while he was rated in the mid-1800s ten years ago, he’s currently at his rating floor, which is 1600.⁴ But I misplayed the opening, and I’ve spent the whole game trying to keep my head above water. (Much like the last game I wrote about in which I accepted a draw.)

One more piece of information: I have about 25 minutes on the clock. My opponent has an hour. That’s a big difference.

So we’ve arrived here. Two moves ago, my opponent offered me a draw, but I said, “play on,” like a champ. Now I’m looking at the board, and I’m looking at my clock, and, with his draw offer ringing in my head… I’m struggling to make sense of it. There are… opposite-colored bishops. That’s drawing, right? But the queens are still on the board… which makes a big difference. The connected pawns on d4 and c4 could be dangerous if they can pass… but they’re also targets. His queen is undefended, and mine’s on a nice battery pointed straight at his king. But he’s defending both the 1st and 2nd ranks.

Am I ahead? Is it even? What do I do? How much more time does he have than me? Who is “me,” really? All of these questions are flying through my head — and, my confidence shaken by this bruiser of a game, I now ask if the draw offer is still on the table. He says yes. I accept. 1/2-1/2.

At home, I plug the position into the engine. This time, there’s no ambiguity. I have a distinct advantage. If I can find the right move, which is b5, then the engine is giving me what essentially equates to a winning edge — in the 2.5-3 range. Even if I don’t find that move, I’m still significantly better. Here’s a video to walk you through what’s going on — as always, skip if you’re not interested in the deeper chess analysis.

After seeing the engine’s conclusions, I immediately thought about two of the comments that were left on my last newsletter about the draw I previously accepted. Ben Johnson pointed out that the one thing missing from my write-up was an analysis of the possible variations. This makes the essential point that chess is never a game of pure hypotheticals: there are always moves that could be played. But it also highlights what was interesting about the situation I’d found myself in — while I was standing over the board, I couldn’t think of any variations. I felt like I’d hit a dead-end. That was part of why I accepted the draw — mentally, I’d run out of gas. All I could see was the draw.

In this game, I found myself facing a similar problem. With the draw offer on the table, I experienced a kind of cerebral scrambling. Forget about what moves I could play — could I win? Where’s checkmate? What’s the undeniable continuation? This isn’t how you should think about chess, because it shifts the focus from “where are the imbalances and how can I take advantage of them” — Silman’s constant point — to “can I see the future?” And if you can’t see the future — which, I don’t know about you, but I can’t — then you panic and throw up your hands and say, “Well, I guess it’s a draw!”

But then I thought about the other comment I received, from Jeremy Kane: “Next question, was getting you to think about evaluations and emotions instead of calculating why your opponent offered the draw?”

Jeremy… I think you’re on to something.

I have been offered draws when I was losing and my opponent was winning. So it isn’t like a draw offer is a guarantee that you’re winning. But it undeniably gets you thinking about evaluations and emotions instead of calculation.

So how should you think about a draw offer when you receive one? Should you immediately be suspicious? Should it be a sign that you’re probably ahead, and that your opponent is resorting to gamesmanship in order to distract you — to get you thinking about the result instead of variations on the board?

That was my initial instinct, which is why I tried to play on — but once the draw had been offered, I found myself once again stuck in that place where I had to be willing to pass up a sure thing in favor of a greater, but hypothetical, reward. And that screwed with my head.

This being a newsletter about how I can use non-chess ideas to improve my chess, I went off in search of a deeper understanding of what’s happening here from a game-theory, bargaining perspective — leading me to Thomas Schelling.

At the top of his “An Essay on Bargaining,” which is collected in the seminal book The Strategy of Conflict, Schelling — winner of the 2005 Nobel Prize — writes:

The purpose of this chapter is to call attention to an important class of tactics⁵, of a kind that is peculiarly appropriate to the logic of indeterminate situations. The essence of these tactics is some voluntary but irreversible sacrifice of freedom of choice. They rest on the paradox that the power to constrain an adversary may depend on the power to bind oneself; that, in bargaining, weakness is often strength, freedom may be freedom to capitulate, and to burn bridges behind one may suffice to undo an opponent.

Schelling goes on to describe this class of tactics, and, it turns out, they perfectly encapsulate the potency of the draw offer in chess. To understand why, let’s first ask: what is the goal of a draw offer? A draw, of course. But more fundamentally, the goal of a draw offer is to persuade someone that they should consent to a worse result than the one they want. They want to win; by accepting a draw, they acknowledge that they will not. And you’re willing to bind yourself to the draw in order to do that, forgoing your own desire to win.

By offering a draw, a player is, in Schelling’s parlance, “accept[ing] an irrevocable commitment, in a way that is unambiguously visible… [squeezing] the range of indeterminacy down to the point most favorable to him.” In other words, they aren’t just suggesting that the game is even — they’re trying to “make it true” that the game is even by committing themselves to an even result.

Obviously, anyone who offers a draw wants a draw, rather than to play for a win. Otherwise, they shouldn’t offer it.⁶ The person being offered the draw — me, or you, or anyone else —should know this. But let me introduce another scenario out of Schelling to dig deeper here.

Say you’re selling a house, and a prospective buyer offers you $500,000. Often, this would be the jumping-off point for more negotiations. But let’s say that seller insists they’ll pay $500,000 and not a penny more. Their success in convincing you to accept this is going to depend on two things: 1) whether you have other, better offers or think you could get better offers; and 2) whether you believe them. Is this just a negotiating tactic, and they would be willing to pay more if called on their bluff? Or have they convinced you that this is the truth? Schelling stresses the importance of this — it’s all about the appearance of truth. It doesn’t need to be the truth.

If you think of the entirety of a chess game as a kind of negotiation — I offer a move; you counter-offer a move; and we do this until one of us gets what we want — then the draw offer is the final offer, the “not a penny more” moment. Take it or leave it.

Now, your opponent might be losing; they might be winning. But one thing is for certain: they’re making you an offer. And this puts the onus on you to either accept or reject it. To do that, you have to start considering whether a draw is a “true” description of the game being played or not, as Schelling puts it. And to do that, you’re very likely going to be dragged out of the immediate mode of calculating your next move and into the murkier, more confusing realm of, as Jeremy puts it, emotions and evaluations. Do I have enough of an advantage to convert? Oh God, what if I don’t accept the draw and screw up? What if I play for another 90 minutes and lose and then I don’t sleep well and then tomorrow’s wrecked and so on and so forth.

What is the draw offer, then? It’s a device that serves to introduce the possible truth of a draw into the context of a game. By tendering this offer, a player makes the only move in chess that can be made off the board, that escapes the realm of the pure logic and undeniable reality of the pieces’ placement and enters the world of game theory, negotiation, and psychological uncertainty.

Ahead of Kahneman and Tversky, Schelling is applying the future insights of prospect theory, but within a different framework. Rather than focusing on the dynamic that people are risk-averse and prefer lesser known outcomes to greater unknown ones, he is highlighting the reality of negotiations, in which Party A is trying to make Party B agree to Party A’s desired result in lieu of Party B’s own. But the insight is similar: if you can make your negotiating partner believe in the truth of your proposal — you will not pay more than $500,000; the game is drawn — then it’s very likely that they will accept this known outcome rather than continue to chase their unknown but preferred version.

And this can be just as powerful coming from a lower-rated player as a higher-rated player. Sure, I’m happy to get a draw against a higher-rated player — that’s a success. But I really don’t want to lose to a lower-rated player — and a draw prevents that.

I know all of this is a bit abstract. But the point I’m trying to make is that, per Jeremy’s comment and Thomas Schelling’s work, the draw offer is a tactic in and of itself — and I need to start seeing it as one. It isn’t that every draw offer comes from a player who’s losing, and that it’s some sort of trick: I’ve experienced firsthand that that isn’t the case. It’s that the offer diverts your attention away from the board; it lets your opponent, to borrow Silman’s terms once again, force their agenda.

It’s fine if you’re okay with the draw. By all means, take it. But if you want to fight for the win, then you need to be able to put the offer aside, ignore the alleged truth your opponent is trying to sell you on, and look at the board with a clear and unweighted eye.

And per Ben’s comment, that means: calculate some moves. Play chess, baby.

1. Terrible?

2. As I mentioned last week: as much as I’d love to provide the full analysis for you all to check out, I feel like I’m already revealing quite a lot about my style for any opponent who bothers to Google me. Sharing full analyses of every game I play would probably be a bit much. That being said, if you ARE ever curious to see how I’m doing these analyses, feel free to email or message me and I can send you one to take a look at.

3. He told me his age after the game.

4. I looked this up on the USCF website, but he also told me about it after the game.

5. TACTICS????? THAT’S A CHESS WORD.

6. I’d be hard-pressed to believe there’s any good reason to offer a draw if you believe you’re winning.