Counterintuitive economics of a chess tournament | Hacker News Reader

Counterintuitive economics of a chess tournament

davidsmerdon.com

34 pointsrkrzr46 comments

I'm not sure that it makes a difference in this case, but it is insufficient in situations such as these to look at just the expected return. A rational agent's actions are determined by expected utility, which could be highly non-linear depending on myriad factors such as the player's net worth. i.e. it could be rational to trade a lower chance of the largest payoff for a more consistent payoff of a lesser but still substantial amount, even at the cost of a significantly smaller expected return.

See the St Petersburg paradox for a good example of this. https://en.wikipedia.org/wiki/St._Petersburg_paradox

Another example that we all participate in is insurance. We all make an expected loss on insurance, but we lower the variance of our outgoings by doing it, so most of us are happy to take the hit.

Given the difference in rating, McShane was likely at a disadvantage.

So, if I'm McShane, do I push when my most likely outcome is draw or loss? That's actually a pretty tough calculation. Nakamura clearly was not going to let him go into the opening line that he wanted to which was going to make the game much more difficult. McShane probably should have pushed for a win since he was going to be at a disadvantage relative to the tiebreakers anyway. However, that's a tough call. Add in some fatigue and taking an easy draw to get past the person ranked second in the world doesn't look that unappealing.

Nakamura, on the other hand, is one of the absolute best players at speed-type chess which is what was going to be the tie-breaker. So, he has a huge incentive to take an easy draw and rest up for where he has a big advantage, and zero incentive to put anything at risk. Nakamura is absolutely not going to let McShane go into his preferred opening when the draw is just fine.

Finally, please do remember that 50%+ of grandmaster games wind up in a draw anyway. So, both of them can decide to press on, waste a lot of energy, and be in the same situation as the nine-move draw anyway.

Given that Nakamura won the whole shebang, it sure looks like he made the right choice.

This stuck out to me:

> Even under some very tolerant assumptions, the expected payoff from playing on, for either player, was greater than the expected payoff from accepting the repetition.

Payoff, sure. But it's well-known that the marginal utility of money is not linear, which means people tend to value money differently based on how much of it they have (poor people value a dollar more than rich people). This indirectly means some level of risk aversion is actually an optimal choice. Turning down a gamble, even if the expected payout is positive, can be rational.

This is well studied in economic theory: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenster...

Without invoking the maximization of utility we could use game theory and ask if the players were simply minimizing their maximum regret. It was during the qualification rounds, not the finals. It looks like they each preferred taking an advantage or a draw (chosen by their opponent) over playing against a world-class player at a slight disadvantage.

Nakamura's shown that he'll play interesting and sometimes dubious moves because he wants chess to be more entertaining for spectators. He spends a lot of time playing online against weaker players so they can have the memory of that one time they played against one of the best. He's done so much for chess and its popularity that if he takes an early draw once in a while he gets the benefit of the doubt.

A few thoughts:

- They say this is terrible for television, but I bet they love it! I wasn't aware of this tournament until this story. TV tries its best to manufacture strife and drama.

- In Go you simply aren't allowed to repeat a position (ko). I wonder how profoundly it would change chess if you simply weren't allowed threefold repetition. Or if you weren't allowed it within the first x moves?

- What if a draw earned you 0.4 points instead of 0.5? Maybe that doesn't matter with so few games, or does it?

I've always found it interesting that that's basically how most soccer games work, except that a draw is worth 1/3 instead of your proposed 2/5.

Could someone provide some context? Had Nakamura and McShane already played each other, and the second game looked like it was going to become an exact copy?

This was their first meeting. The line that Nakamura would have had to play to avoid the repetition was one that McShane had won a smooth victory in earlier in the tournament, so he was leery of going into it.

This is why Linares tournament was so successful; the organizer wouldn't put up with these quick draws.

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