[JoshCole]

On further reflection, you're right, I'm conflating it.

My correction is still valid though. You're not handling step ten properly. You didn't work over the information sets, didn't solve the actual graph that is the game, didn't handle the under-specified policy function.

To try and show you that your solution isn't the actual solution: well, both options have the same EV. So I choose switch every time, because why not. As you are no doubt aware I never get to have EV because I'm constantly swapping. The sixty is a mirage. For my policy choice, the answer was undefined or zero depending on how you write it down. But you told me they had the same EV. So if they did, why did my choice not produce that EV? Ergo, your solution only appears to be giving you the EV.

Think about that for a while and you'll start to realize why I honed in on specifying a recurrence relationship with the terminal keep node and why I'm so eager to escape the trap of their flawed problem model.