[roggles]

[ QUOTE ]

I have no idea how all people who think this way think. (Which is part of my math-blindness.) We don't know what the future bets in the hand will be. This is always a call with the understanding you have to catch to bet or call.

[/ QUOTE ]
The hands being 2:1 is under the assumptions that the hands are shown down. Since you have a way inferior hand with A2J you need to catch really good (i.e. the person with 678 must also catch bad) to be able to continue to play the hand after 4th, with your own (bolded) strategy. You will have to fold 4th so often that you are not getting odds to call here as the bring-in with A2J.

Rusty put the same thing in a different way. You are 1:2 to win the hand with A2J. So you have pot odds to call and see the hand down if the completion of the bring-in is the final money you have to put into the hand. However, to see the hand down you usually have to call a bet on every street, and the bring-in + antes already in the pot makes a very small amount compared to calling down a bet on every street. So you actually don't have pot odds to make the call.

[ QUOTE ]

Not according to what I've read. You have four possibilities on 4th (or any other street) you catch/he bricks, he catches/you brick, you both catch, you both brick.

So, you have a 25% chance of getting even (you catch, he bricks) a 75% chance of at least improving your own hand (you catch/he catches, you catch/he bricks, you both catch.) Even when you both brick, you might "catch" if that brick is a duplicate of a hole card and he bricks paint.


[/ QUOTE ]
Your analysis assumes that you will want to keep calling with A2J vs 678 if you both catch good or bad, which you don't unless you want to put your money in bad. However, if you don't want to put your money in bad you won't put it in with A2J in the first place.

I don't know what to tell you, it is extremely intuitive that 678 is in a good spot against A2J, and I don't understand why you don't feel this way.