Looking back, I think I got my numbers mixed up (thanks, beer!). $12 or $13 is probably the number I'm looking for, not $26.

Anyway, my logic is if I am at or higher than the median after I have drawn half the deck, then that means there are more black cards than reds in the remaining deck and I have a greater chance each draw of losing a buck than gaining.

So it is in my best interest to pull out at that point, than to try my luck against ever worsening odds.