6 ms·

Counterintuitive economics of a chess tournament

34 points by rkrzr 11y ago

dkbrk 11y ago
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.
- sweezyjeezy 11y ago
  See the St Petersburg paradox for a good example of this. https://en.wikipedia.org/wiki/St._Petersburg_paradox 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.
- bsder 11y ago
  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.
throwaeayBan 11y ago
"Top female Prize " and... no top male prize...We can never be equal while there is any discrimination even when it is possitive. And please don't start with "we need more women in chess thus...". No, we need good players in ches and not insert anything here. And tell, what forces us to improve more than competition? Why play better when you will get prize anyway?
- CJefferson 11y ago
  What are you referring to? The phrase 'Top female prize' appears nowhere on the linked page.
  - slyall 11y ago
    They are referring to this page: https://millionairechess.com/prizes https://millionairechess.com/prizes Also prizes in each division for "Top senior prize (65+)" and "Best child under 13 yrs old"
    - throwaeayBan 11y ago
      Thank you. Exactly what I was refering to (was linked in article).
      - CJefferson 11y ago
        Then why specifically single out the female award, instead of the Under 13 and 65+. Why are you not demanding a '13-65' award?
        throwawayChess 11y ago
        Award for kids I can "justify" by "well, you went against all odfs and you... got somewhere" (still, would argue for separate group with separate prizes). Women are not going against all odds - remember they are equals, as capable and stuff. As senior prize - stupid. Should not be there. Why I singled out women? Because these "women only" prizes and headstarts are everywhere today. And I am pro equality - means no headstart for anyone.
TorKlingberg 11y ago
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?
- komaromy 11y ago
  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.
rm999 11y ago
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%93Morgenstern_utility_theorem#Automatic_consideration_of_risk_aversion https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenster...
nerd_stuff 11y ago
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.
pjungwir 11y ago
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?
- sanderjd 11y ago
  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.
lazyant 11y ago
This is why Linares tournament was so successful; the organizer wouldn't put up with these quick draws.

34 points by rkrzr 11y ago

dkbrk 11y ago

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.

sweezyjeezy 11y ago
See the St Petersburg paradox for a good example of this. https://en.wikipedia.org/wiki/St._Petersburg_paradox 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.
bsder 11y ago
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.

throwaeayBan 11y ago

"Top female Prize " and... no top male prize...We can never be equal while there is any discrimination even when it is possitive. And please don't start with "we need more women in chess thus...". No, we need good players in ches and not insert anything here. And tell, what forces us to improve more than competition? Why play better when you will get prize anyway?

CJefferson 11y ago
What are you referring to? The phrase 'Top female prize' appears nowhere on the linked page.
- slyall 11y ago
  They are referring to this page: https://millionairechess.com/prizes https://millionairechess.com/prizes Also prizes in each division for "Top senior prize (65+)" and "Best child under 13 yrs old"
  - throwaeayBan 11y ago
    Thank you. Exactly what I was refering to (was linked in article).
    - CJefferson 11y ago
      Then why specifically single out the female award, instead of the Under 13 and 65+. Why are you not demanding a '13-65' award?
      - throwawayChess 11y ago
        Award for kids I can "justify" by "well, you went against all odfs and you... got somewhere" (still, would argue for separate group with separate prizes). Women are not going against all odds - remember they are equals, as capable and stuff. As senior prize - stupid. Should not be there. Why I singled out women? Because these "women only" prizes and headstarts are everywhere today. And I am pro equality - means no headstart for anyone.

TorKlingberg 11y ago

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?

komaromy 11y ago
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.

rm999 11y ago

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%93Morgenstern_utility_theorem#Automatic_consideration_of_risk_aversion https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenster...

nerd_stuff 11y ago

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.

pjungwir 11y ago

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?

sanderjd 11y ago
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.

lazyant 11y ago

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