Probability is on a per player basis (ie: each turn, a player has a chance p for detecting each undetected player). I’ll edit this so it’s more clear.
For L_K (as well as L_R and L_P), the term outside the summation is essentially (probability the player survives the whole game) (game length). It’s necessary since the game is of fixed length, and the summation is adding (probability of dying on turn x) (turn x). Consider if the probability of detection is zero, and players will never die—without the term outside the summation, the expected lifetime calculation will return zero.
Thanks for looking at it.
Probability is on a per player basis (ie: each turn, a player has a chance p for detecting each undetected player). I’ll edit this so it’s more clear.
For L_K (as well as L_R and L_P), the term outside the summation is essentially (probability the player survives the whole game) (game length). It’s necessary since the game is of fixed length, and the summation is adding (probability of dying on turn x) (turn x). Consider if the probability of detection is zero, and players will never die—without the term outside the summation, the expected lifetime calculation will return zero.
One more comment:
Is P(K survives turn i) correct? The formula assumes that the chances of surviving are all independent, but I’m not sure that would be true.
I didn’t see anything else that stood out to me.
What are you trying to learn or show with the model?