I think the point is that your strategy isn't independent of your opponent. Maybe a similar example is nontransitive dice: https://en.wikipedia.org/wiki/Nontran

I think the point is that your strategy isn't independent of your opponent. Maybe a similar example is nontransitive dice: https://en.wikipedia.org/wiki/Nontransitive_dice https://en.wikipedia.org/wiki/Nontransitive_dice In other words, it isn't sufficient to shoot for the highest score possible.