4 ms·

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

by 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.

by dkbrk 11y ago

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.