Quote from speculatus:
Game theory does little with reality. You are long and want to get out. You place your offer on the book. The price tanks more. You trying to chase the price and finally give up hitting the bid. If you feel that the price will move higher (or see the offer being hit, but you are somewhere at the end of the queue), you probably want to keep the position, but you won't be able to cancel your offer quickly and get a fill. So where is 50/50?
PS: chasing the price (i.e. shooting cancel/replace) doesn't always come for free. Some brokers (IB for example) charge a fee for every order cancel/replace.
You talk about you seeing the offer being HIT, thinking that it will go up. I'm sure that you are right, however if you didn't know that the stock price is 50/50 to go up vs down.
Spec,
you're a smart guy on hear. I hear many of your 100 or so post, however, I still stay with my statement "your expected value is the same when you hit the bid or chase the bid being in last position"