Doesn’t seem to want to let me edit the comment above, but I could have explained this clearer. The figure (8p-6p^2)/(p+1) is actually a weighted mean of Ex and Ey where these are the expected values at X and Y respectively. Specifically, this value is:
(1*Ex+p*Ey)/(1+p)
Now, the expected value calculated from the planning optimal decision which is just Ex. We shouldn’t be surprised that the weighted mean is quite a different value.
Doesn’t seem to want to let me edit the comment above, but I could have explained this clearer. The figure (8p-6p^2)/(p+1) is actually a weighted mean of Ex and Ey where these are the expected values at X and Y respectively. Specifically, this value is:
(1*Ex+p*Ey)/(1+p)
Now, the expected value calculated from the planning optimal decision which is just Ex. We shouldn’t be surprised that the weighted mean is quite a different value.