I don't recall saying you can't do it that way, and certainly didn't mean to.

What I was hoping to do was to explain why you CAN do it that way, since the same thing threw me off when I started thinking about it.

I also like excession's example of running it twice for the separate pots, as it clearly illustrates the problem I was trying to address.

I'm still not getting the claim, though, that the two are independent events. They're connected by an "if-then" statement: namely, if you win main pot, you must win side-pot. Clearly not the case if you run it twice. Then you can win main pot and lose side-pot, the one impossibility in point of fact.

Technically they aren't independent, since the short stack's cards are dead in the sidepot, which affects the equities. Not a big deal in this case, but if he had AK, other villian had AK, and you had TT, it would be noticeable.

Summing the equities would still be valid though.

Ais:

If you can compute the equity in the two pots as if they were independent events, and come to the correct conclusion, then for mathematical purposes they are independent events. You don't have to get into the complicated math of "If x then y." You can if you want to, but it's not necessary.