Phoebe,

Let's consider a particular case, so I can illustrate my point with numbers.

I ran MGP's BJCA for a SD game with ES (good luck finding THIS game!). When I checked the Composition-Dependent EV's for the hand of 8,9 vs. A, I got an Early Surrender EV of -0.257575757... or -17/66, if you prefer rational fractions.

So why didn't we get -0.5?

The answer is that the EV's shown for American-style rules are traditionally the "No Blackjack EV's": in other words, they're the EV's if the dealer does NOT have BJ. The reason for showing the NoBJEV's is that, with American-style rules, these are (typically) the EV's once the player gets to act on his hand. However, with ES the player gets to act BEFORE the dealer checks for BJ (just like in a ENHC game).

So, how are the EV's before and after checking for BJ related? Here's the equation:

EV = -1*Pdbj + NoBJEV*(1-Pdbj)

where "Pdbj" is the probability that the dealer has a BJ, "NoBJEV" is the EV once we know the dealer does NOT have a BJ, and "EV" is the EV BEFORE the dealer checks for BJ.

If we rearrange to solve for NoBJEV, we get:

NoBJEV = (EV + Pdbj)/(1-Pdbj)

For our case, EV = -1/2 (obviously), and Pdbj = 16/49 (since three non-X's have been removed from a single deck). Plugging these into the equation gives:

NoBJEV = (-1/2 + 16/49)/(1 - 16/49) = -17/66 =
-0.257575757...

which is the value reported by the software.

Hope this helps!

Dog Hand