The idea of sexual selection in this scenaro makes no sense to me.
It basically either proposes that humans consciously make all of their decisions based on it which is not true or it proposes that we have lizard brains with programming that causes us to subconsciously make our decisions based on it which is very hard to believe.
I'm pretty sure the only reason that most people have sex is because it feels good and not because of some complicated scientific mumbo jumbo.
And the whole women not playing chess thing is in my opinion a completly social construct because peer pressure is a #@$!...
We have got lizardbrains! Deep inside under the neocortex which does the more advanced stuff like reasoning, is the reptillianbrain where our deepest and oldest habits are 'seated', like fear. Not sure if it has alot to do with partnerselection, but there is no need for too. Also the whole evolutionary thing isn't that mumbo jumboish!
I admit straight away that social construct also has to do alot with it. Therefore more men play, and more men = bigger chance of champions being men.
But think of this example:
60 cave(wo)men: 30 male + 30 female
10 males are strong and fit
10 males are not so strong, but they are very kind
10 males are weak
15 beautiful women
15 not so good looking women
Natural selection: (for the example only males will get selected)
Flu strikes when these men are kids:
4 strong get infected, 2 die
5 not so strong get infected, 3 die
6 weak get infected, 4 die
When they are middle aged they have fights to establish their position in the group:
2 strong guys die
3 not so strong kind guys die, they are friendly and dont get fighted that much
4 weak guy dies
And not to forget the factor (bad) luck:
1 strong man is struck by lightning and dies.
So by the time they are ready to mate we are left with:
5 strong guys
4 nice guys
2 weak guys
Sexual selection
30 women can now choose from 11 left guys. Chance are that they will choose for either the strongest or for the kind guy. The kind guy will probably stick with them = higher chance that offspring grows up.
The strong males (who push the weak aside) will probably choose the beautiful women which probably results in strong offspring.
The strong males also have more casual sex, which results in extra offspring.
The kind and weak guys can reach a step higher by putting in their best effort. Who will do extra good? They are not very strong, but perhaps they have other qualities: good talking, being kind, being smart. So from those groups the people with other good qualities will also have a bigger chance to reproduce with a more beautiful woman (=stronger kids in theory) or with more women (=more offspring)
And then it starts all over, but from the first generation the weak guys have hardly reproduced. The strong or the "hard working" guys did reproduce.
And if you do that experiment a million times over time the males get stronger and smarter.
And all this also apply to women, but since they get much much much fewer children the effect is much less strong.
There is a pretty big flaw in your model. Women outnumber men significantly. It is the women who will have to compete for the men in this scenario.
Not sure, I do know that my dad taught me chess and my mom doesn't know how to play. Could be due to lack of interest. After all, it's a dumb game where you have to think and can't even dress up the pieces...
Depends if thats what the female thinks, if they like dressing up then sure. Many people I know who are females but don't play chess say they think it's boring, I think there could be lack of interest.