Post #3144005

2026-05-23 00:40 UTC

That's not how standard deviations work though. The point is that if you are n players, the probability of any given player starting is 1/n. After an arbitrary number of dice throws, the probability that a given player is ahead *remains* 1/n, when you account for the throw that decided who would go first. Let's put it this way: Would it be "more random" who goes first if you throw ten dice to decide instead of one? Of course not. But that's essentially what you're doing when you go "warm up" rounds. You're just throwing the dice more times, and letting whoever has the highest total go first. Clearly, the probability that any given player gets the highest total remains 1/n, regardless how many dice are thrown.

Replies (1)

@Amir@lemmy.ml 2026-05-23 09:21

I didn't mean dice rolls for who starts, but moving around the board. If you go around the board 0 times, there's a 100% chance the player who started will be ahead. If you go around the board 1 times, there's a less-than-100% chance the player who started will be ahead. Every added round around the board increases the.standard deviation of spaces moved. While the expected amount of spaces moved will still be higher for the first mover after their turn, the significance of this difference goes down as the standard deviation goes up. Therefore, running 100 rounds around the board before starting the game will change the first-mover advantage from being ahead 100% of the time to, likely slightly more than 25% of the time but very close to 25%.

Open ##3144006