Profit by position: What would you pay to be psychic in poker?

So for several weeks I've been doing an experiment that Andrew and I came up with. I ran the math on all limit hold'em hands, and then constructed a set that I thought were playable for one bet, and another set playable for two bets. With a roughly repeatable preflop and postflop strategy, I set out to play 5 or 10,000 hands in exactly the same way. I basically set out to be my own poker bot, to test the actual profitability of my strategy against real humans.

I'm 4,400 hands in, and these are my results so far.  I was talking with Andrew about it and he pointed at my results from the button and the cutoff (position 1 off the button).  He pointed out that I was getting roughly the same playable hands at every position.  The distribution over time will give me Aces the same number of times from the button as it does from the under-the-gun spot.  But clearly, with all my hands evening out, I'm getting better profitability from the late position hands.  He said, "There you go, that's the value of position."

I remember another conversation we had about position where Andrew said, "Playing late position is like playing while being psychic.  You get to act after everyone else acts.  What kind of value would you put on being psychic?"

Apparently quite a lot.