If this sort of help is still available, I have some math I’m working through for a post that I’d love to have checked—a page and a half of fairly basic statistics.
Here are some initial thoughts. I haven’t finished working through it, so more to come:
Perhaps you should specify if the probability of detecting another player is an overall probability or on a per undetected player basis (so when there is only one player they haven’t detected yet, when they detect a player it will always be that player they haven’t detected)
in the definition of L_K, why is P(K survives turn i) outside the summation? What does i refer to then? Is P(K survives turn i) a constant ? Wont it in general depend on the current state of play?
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.
If this sort of help is still available, I have some math I’m working through for a post that I’d love to have checked—a page and a half of fairly basic statistics.
It can be found here (pdf): http://dl.dropbox.com/u/430270/lwalienprisoners.pdf
Thanks!
Here are some initial thoughts. I haven’t finished working through it, so more to come:
Perhaps you should specify if the probability of detecting another player is an overall probability or on a per undetected player basis (so when there is only one player they haven’t detected yet, when they detect a player it will always be that player they haven’t detected)
in the definition of L_K, why is P(K survives turn i) outside the summation? What does i refer to then? Is P(K survives turn i) a constant ? Wont it in general depend on the current state of play?
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?
I’ll take a look at this in the near future.