And then you can correct for the double-counting. When would you like to count your chickens? It’s safe to count them at X or Y.
If you count them at X, then how much payoff do you expect at the end? Relative to when you’ll be counting your payoff, the relative likelihood that you are at X is 1. And the expected payoff if you are at X is p^2 + 4p(1-p). This gives a total expected payoff of P(X) E(X) = 1 (p^2 + 4p(1-p)) = p^2 + 4p(1-p).
If you count them at Y, then you much payoff do you expect at the end? Relative to when you’ll be counting your payoff, the relative likelihood that you are at Y is p. And the expected payoff if you are at Y is p + 4(1-p). This gives a total expected payoff of P(Y) E(Y) = p (p + 4(1-p)) = p^2 + 4(1-p).
I’m annoyed that English requires a tense on all verbs. “You are” above should be tenseness.
And then you can correct for the double-counting. When would you like to count your chickens? It’s safe to count them at X or Y.
If you count them at X, then how much payoff do you expect at the end? Relative to when you’ll be counting your payoff, the relative likelihood that you are at X is 1. And the expected payoff if you are at X is p^2 + 4p(1-p). This gives a total expected payoff of P(X) E(X) = 1 (p^2 + 4p(1-p)) = p^2 + 4p(1-p).
If you count them at Y, then you much payoff do you expect at the end? Relative to when you’ll be counting your payoff, the relative likelihood that you are at Y is p. And the expected payoff if you are at Y is p + 4(1-p). This gives a total expected payoff of P(Y) E(Y) = p (p + 4(1-p)) = p^2 + 4(1-p).
I’m annoyed that English requires a tense on all verbs. “You are” above should be tenseness.
EDIT: formatting