Religion is a payday loan against reality. As someone that grew up in a religious household, I am certain that no matter how well-intentioned people are, someone is going to have to foot the bill.
This game seems to do weird things if you have a player able to disclose their choice in advance too. Stating that you will choose 42 is stronger than stating you will choose 1, assuming other players only maximize their own odds of winning. It's kind of like a convoluted game of chicken.
Leftists believe in egalitarianism, but this is very different from giving up personal freedom for collective values across the board. For one thing, leftists generally don't believe the collective values you've listed have value to begin with. It's also noteworthy that your examples target taking from those who already have less.
Perhaps an interesting piece of this is that high-level play is becoming so close to computer play that cheating is increasingly difficult to uncover. I feel that something in the sport has become lost from all this.
I think you're spot-on here. Authoritarian-made realities seem to be the historical norm. Just look at the Roman Catholic Church at the height of its power. If anything, we were under a Dunning-Kruger effect before. We have more opportunity to realize now that truth is actually very difficult to pin down.
I'm actually working on a rogue-like chess game as an independent project right now! It got me thinking and researching more deeply about variant chess. My favorite so far is Fog of War.
I believe there are a significant amount of these people that won't actually argue that just because the Spanish flu was worse in this way that the Covid pandemic isn't a problem.