If you don’t get told I don’t think it does then, no. It just changes the probabilities in a more confusing way, but you still have no particular way of getting information out of it.
As a player, who by definition must be still in play, you can’t deduce anything from it. You only know what whatever your odds of surviving an extra round were at the beginning, they will go down with time. This probably leads to an optimal strategy that requires you absolutely quit after a certain number of rounds (depending on the probability of the bullet being added). But that’s not affected by any actual in-game information because you don’t really get any information.
But that’s not affected by any actual in-game information because you don’t really get any information.
You keep on asserting this, but that’s not actually true—do the maths. A player who doesn’t update on them still being alive, will play fewer rounds on average, and will earn less in repeated play. (Where each play is independent).
The reason is simple—they’re not going to be able to play for very long when there are lots of bullets added, so the times when they find themselves still playing are disproportionately those where bullets weren’t added, so they should play for longer.
But the thing is, updating on being still alive doesn’t change anything—it can never drive your estimate of n up and thus save you from losing out. It could convince you to play if you aren’t playing—but that’s an absurdity, if you’re not playing you won’t get any updates! All updating gives you is a belief that since you’re still alive, you must be in a low-bullets, high-probability world. This belief may be correct (and then it’s fine, but you would have played even without it) or wrong (in which case you can never realise until it’s too late). Either way, it doesn’t swing your payoff.
In your added bullets scenario thinking about it there’s a bit of a difference because now a strategy of playing for a certain amount of turns can make sense. So the game isn’t time-symmetric, and this has an effect. I’m still not sure how you would use your updating though. Basically I think the only situation in which that sort of updating might give a genuine benefit is one in which the survival curve is U-shaped: there’s a bump of mortality at the beginning, but if you get through it, you’re good to go for a while. In that case, observing that you survived long enough to overcome the bump suggests that you’re probably better off going on playing all the way to the end.
If you don’t get told I don’t think it does then, no. It just changes the probabilities in a more confusing way, but you still have no particular way of getting information out of it.
As a player, who by definition must be still in play, you can’t deduce anything from it. You only know what whatever your odds of surviving an extra round were at the beginning, they will go down with time. This probably leads to an optimal strategy that requires you absolutely quit after a certain number of rounds (depending on the probability of the bullet being added). But that’s not affected by any actual in-game information because you don’t really get any information.
You keep on asserting this, but that’s not actually true—do the maths. A player who doesn’t update on them still being alive, will play fewer rounds on average, and will earn less in repeated play. (Where each play is independent).
The reason is simple—they’re not going to be able to play for very long when there are lots of bullets added, so the times when they find themselves still playing are disproportionately those where bullets weren’t added, so they should play for longer.
But the thing is, updating on being still alive doesn’t change anything—it can never drive your estimate of n up and thus save you from losing out. It could convince you to play if you aren’t playing—but that’s an absurdity, if you’re not playing you won’t get any updates! All updating gives you is a belief that since you’re still alive, you must be in a low-bullets, high-probability world. This belief may be correct (and then it’s fine, but you would have played even without it) or wrong (in which case you can never realise until it’s too late). Either way, it doesn’t swing your payoff.
In your added bullets scenario thinking about it there’s a bit of a difference because now a strategy of playing for a certain amount of turns can make sense. So the game isn’t time-symmetric, and this has an effect. I’m still not sure how you would use your updating though. Basically I think the only situation in which that sort of updating might give a genuine benefit is one in which the survival curve is U-shaped: there’s a bump of mortality at the beginning, but if you get through it, you’re good to go for a while. In that case, observing that you survived long enough to overcome the bump suggests that you’re probably better off going on playing all the way to the end.