Imagine this Chinese roulette, but you forget the number N of how many games you already played. In that case, it is more reasonable to bet on a smaller number.
Not sure I follow—the idea is that the parameter b gets randomized at every game, so why would this change the optimal strategy? Each game is its own story.
If we add here the idea that firing the gun has only a probability p to broke the vase, we arrive to SSA-counterargument to anthropic shadow recently suggested by Jessika. That is, most of the observations will happen before the risk event.
I think this is roughly equivalent to what the blanks do? Now you just have a probability of b+(1−p)(1−b) to not break the vase in case of a loaded chamber.
2 Imagine another variant. You know that the number of played games N=6 and now you should guess n—the number of chambers typically loaded. In that case it is more reasonable to expect n=1 than n=5.
Only if you know that the games lasted more than one turn! Also this only makes sense if you assume that the distribution that n is picked from before each game is not uniform.
But yeah, things can get plenty tricky if you assume some kind of non-uniform distribution between worlds etc. But I’m not sure with so many possibilities what would be, specifically, an interesting one to explore more in depth.
Not sure I follow—the idea is that the parameter b gets randomized at every game, so why would this change the optimal strategy? Each game is its own story.
I think this is roughly equivalent to what the blanks do? Now you just have a probability of b+(1−p)(1−b) to not break the vase in case of a loaded chamber.
Only if you know that the games lasted more than one turn! Also this only makes sense if you assume that the distribution that n is picked from before each game is not uniform.
But yeah, things can get plenty tricky if you assume some kind of non-uniform distribution between worlds etc. But I’m not sure with so many possibilities what would be, specifically, an interesting one to explore more in depth.
My point was to add uncertainty about one’s location relative to the game situation—this is how it turns into more typical anthropic questions.