NL 20, River, Lost Value?

JohnConnor

Ok, I'm new to this table so no reads. Decide to call in the BB getting 3/1 with what should be live suited connectors. Flop bottom 2 pair and I decide to lead out figuring that someone (the button raiser really) either has a K (or other pair they're willing to stick around with) or they don't. When he calls I am narrowing his range down to a K or perhaps another pair, or else he's floating. I check the turn to induce a bluff if he is floating and make a small raise for value if he has a hand. He tanks the turn and flats at the last second. Now I'm probably >90% sure he has a decent K which hasn't 2 paired.

Given this, am I missing out on tons of value by not betting the river? I'm going to call any bet but am expecting him to check. Running the maths really quick I guess:

If I check the river:

He checks back his big K 90% of the time - I gain nil. (£0 net win)
He bets his big K 5%, I call - I gain £10 (£0.50 net win)
He's on some mental bluff 5% - I gain £10 (£0.50 net win)

Whereas if I bet my tenner:

He calls 90% - I gain £10 (£9 net win)
He folds - I gain nil. (£0 net win)

So I win £1 when I check and £9 when I bet. Obviously these figures are pretty rough and ready but there's no really obvious flaw, is there? So I'm missing tons of value by not betting the river, it's that simple yeah?

I realise I haven't mentioned a set or 66 but they're extremely unlikely right and I don't want to go back now lol, I'll just bear in mind that they may affect the calculation a bit.

Thanks in advance for any help guys...

PlayerActionCardsAmountPotBalanceSeanDenSmall blind £0.10£0.10£27.01JohnConnorBig blind £0.20£0.30£19.80 Your hole cards54   gunn01651Fold    IVISONFold    belfastc24Raise £0.80£1.10£25.18SeanDenCall £0.70£1.80£26.31JohnConnorCall £0.60£2.40£19.20Flop  4K5   SeanDenCheck    JohnConnorBet £1.80£4.20£17.40belfastc24Call £1.80£6.00£23.38SeanDenFold    Turn  8   JohnConnorCheck    belfastc24Bet £3.00£9.00£20.38JohnConnorRaise £7.50£16.50£9.90belfastc24Call £4.50£21.00£15.88River  7   JohnConnor

CLIOKID

I think I prefer a check raise or check call on the flop tbh.

River play, I'm unsure of. He'd have to be pretty bad to call us with Kx if we shove.

LOL_RAISE

fold/3b pre

raise bigger on turn imo

if i was betting river, ~1/3rd pot imo