A River Spot Where Conventional Wisdom Fails

I haven't had much free time lately as you may have guessed from the recent shortage of blog posts. But I wanted to share a fairly common limit hold-em situation that most people misplay. In fact, I misplayed it this morning while 9-tabling. It was a split decision that had to be made and I reverted to conventional wisdom and took the wrong action.

Here is the hand. This was a blind on blind battle (I'm in the small blind). My opponent is a decent regular from what I've been able to gather.

Dealt to TPirahna [5h Ah]
TPirahna: raises $10 to $20
rSMig: raises $10 to $30
TPirahna: calls $10
*** FLOP *** [7s Qs Jc]
TPirahna: checks
rSMig: bets $10
TPirahna: calls $10
*** TURN *** [7s Qs Jc] [4h]
TPirahna: checks
rSMig: checks
*** RIVER *** [7s Qs Jc 4h] [4d]
TPirahna: checks
rSMig: checks
*** SHOW DOWN ***
TPirahna: shows [5h Ah] (a pair of Fours)
rSMig: shows [8s Ad] (a pair of Fours)

Conventional wisdom says I have a weak showdownable hand on the river, therefore I should check with the intention of calling if my opponent bets.

If we try to figure out our opponent's range of hands on the river, the choice becomes clear.

Our opponent 3-bet preflop so his range becomes a lot of Ax hands, pocket pairs, and KQ, QJ, etc type hands. He bets the flop which does nothing to change his range since players bet here 99%+ of the time. When he checks the turn after we call the flop, his range becomes much narrower:

When he checks, it's unlikely he ever holds a Queen, Jack, or big pocket pair. It's also unlikely that he holds a hand that has missed the board completely and holds no showdown value like 9T, or 89 since most players will bet the turn with these hands understanding that they are giving up if they check. So, his hand becomes small pocket pairs, possibly a hand like A7, and then a variety of Ax hands, most of which we chop with when the river pairs the four.

So on the river if we check:

He likely checks back all hands worse or the same as ours.
He likely bets some hands better than ours like A7 or maybe TT under the assumption we would bet anything better than that once he checks the turn.

If we bet:

He calls the few hands he would have likely bet anyway had we checked like the A7 or TT mentioned above so we lose nothing in this case. If he's very passive it's possible he'd check these hands but because they make up such a small portion of his range and most of the time he'd bet them anyways, it's a very small loss in value.

He may fold his Ace high hands. When we call a QJ7 flop after being 3-bet, it's hard to believe we have anything worse than Ace high. Hands like KT, T9, and flush draws would check-raise the flop. So our range becomes a lot ace high, pocket pairs, and one pair hands with a Jack or Seven in them. If he understands this and also mistakenly believes that I would always check ace high in this situation (as most people believe), then he has a fairly easy fold. Even if he only folds a very small % of the time, it's a big gain to us because he has forfeited half of a 4 big bet pot.