Let's see how it works mathematically:
KQ, QJ? There are 16 hand combos of these total.
What else? Busted draws: KJ, K10, J10, 910, 9J, 89, 810, 56 - I think this is fair:
8 hands
Straights: I think really only 56 (6 hands total minus 56
) 67 (9 hands)
That's 15 hands! I'll be generous and include only 10, with the assumption that he raises the turn with the other 5. So
10 hands
Sets: really only 4's, 7's, 8's - 9 hands; I'll only count
4 hands
Anything else? We'll do
2 hands for 99 and some random hand. (Include with FD hands)
So what do we have if we value bet?
16 hands that call a value bet of $3
win $9.70 (40%)
10 hands that fold to a value bet
win $6.70 (25%)
14 hands that shove over us and we call!
lose$6 (35%)
EV= .4(9.70) +.25(6.70)+.35(6)
= 3.6+1.6 -1.8
= apx + 3.5
If we check, what do they do?
16 hands (40%)
12 check behind and
win $6.70 (75%)
4 bet $3 and
win $9.70 (25%)
10 hands (25%)
3 check behind and
win $6.70 (30%)
7 bet $3 and
win $9.70 (70%)
14 hands that bet $3, and
lose $3
EV= .4(.75(6.7)+.25(9.7))+.25(.3(6.7)+.7(9.7))+.35(-3)
= .4(7.3) + .25(7.3) -1
= 2.8+1.9-1
= apx $3.8
Play with the numbers. According to my crunching you'll make 3BB more on avg if you c/c and he behaves the way I said he did.