what are are saying, in terms of my post, is this:

A2-A6, AT- opponent calls your raise. EV of raise is (your raise)

AJ - EV is 0

A3, A5, A8, A9,AQ,AK - opp rarely has these.

AT - EV of raise is (whatever you raised).

These are fine assumptions, if your opponent is this bad. This should in no way be your standard assumptions.

i understand we may be wrong here.
you say this, but you are ignoring the money you lose when you are wrong that you would have saved by checking behind.

I'll make it easy. You raise the 50 on the river Assume opp either has A2 or A9

A9 - you lose 50.
A2 - you win 50 (assume opp calls always)

EV = 0

You can see that if opp folds even once, in the long term your 50 dollar bet will not show a profit.

Now. If you add in more hands you beat that opp may call with, your EV goes up.

25 % A2
25 % A6
25% AJ
25% A9

Over 4 hands, you'll win 50 twice, lose 50 once, and gain 0 once. Your bet shows a 50 dollar profit. If you add in A8, A5... I hope you can see where this is going.

you are fixated on this

if we feel we are ahead
it doesn't matter if we're ahead right now when evaluating the raise. It only matters if we are ahead when the raise is called. [/quote]