[highlight] No-brainer bet on the river?

PokerJuice Hand History #5572

Blinds: $0.50/$1.00
SB ($100.00) 100bb
BB ($100.00) 100bb (Hero) J♥ 6♥ J♦ 4♦
CO ($100.00) 100bb
BTN ($100.00) 100bb (Villain)

($1.50, 4 players)
CO folds, BTN bets $2.50, SB folds, BB calls $1.50

($5.50, 2 players) J♠ Q♣ 5♣
BB checks, BTN checks

($5.50, 2 players) J♠ Q♣ 5♣ 5♠
BB bets $3.75, BTN calls $3.75

($13.00, 2 players) J♠ Q♣ 5♣ 5♠ 9♠

BB ???

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In spots like these, do you feel like Steve Martin?

If not, maybe you should. Sometimes the most common line isn't necessarily the most +EV line.

But is potting the best play?

So how to tackle this situation?

As always, we need to assign a range for our opponent. Pretty much always our decisions are based to our opponent's range. Let's start from the preflop.

Preflop
Villain opens from the Button, so his range can be pretty much anything.

Flop
When he checks, we can assume that he doesn't have a strong value hand. So we can exclude QQ, 55, QJ, AA/KK with clubs and AKTx from his range.

Turn
When he calls the turn, he has something. Gutshot without a flush draw would fold, so his range is most likely flush draws with a piece of the board (gutshot, OESD and/or pair). Of course when flop goes checked Hero's bet looks like a bluff so he has some bluff catchers in his range too. Mostly AQ or dry overpairs and J5 too.

River
River completes backdoor flush and some of the straight draws. First question is how often does that river hit our opponent's range?

Using PokerJuice we can see that he has flush around 37% of the times. He has straight 14% of the times and 99/J5 for 4% of the times.
If we bet, he probably calls with medium+ flushes and full houses. With straights it's a bit closer. And he folds all his air/weak hands. If his calling range is T high flushes and better, he calls 30% of the times. If we check, he will check back overpairs, straights and flushes up to Q high. He will bet hands that are better than his check range and hands that are worse than his check range. His check range is 60% of his range.

So to put this all together, this is what we get:

WE               OPPONENT
check      check 60%, bet 40%
bet        call 30%, fold 70%

With checking, we get at least one bet for value 40% of the times. With betting, we get that value 30% of the times. If we assume that we both have same betsizing, it is better to check-raise as we get value more often that way. And there is also a bonus value if opponent has a strong hand (nut flush or full house) and calls Hero's check-raise (as it doesn't make sense).