[Math] - Check-Calling Out of Position

[gianttwinky]

Say villain is a LAG, and opens 25% from middle position, we flat KQ from the big blind.

Flop 742.

Suppose villain cbets 2/3 pot with 100% of his preflop range, is our hand good enough to check-call?

In a vacuum, check-raising this hand is probably more +ev than check-calling, but as part of our overall strategy, we should generally be raising hands that are good enough to raise for value, and only be bluffing with hands that aren't quite good enough to call, which is why I pose the question above.

My thinking is as follows: In order to profitably check-call a 2/3 pot bet on the flop, we must be able to continue profitably on ~30% of turns. Since we can hit a K, Q or backdoor flush draw, there are ~33% of turns we can profitably check-call on.

If we turn our backdoor flush draw, and villain cbets 2/3 pot again, there are ~33% of rivers we can profitably check-call on again.

On top of this, if villain checks back on the turn, we can profitably bluff many rivers.

Is my line of thinking that since we can continue on 33% of turns, and 33% of rivers profitably after facing a 2/3 pot flop cbet, check-calling the flop is +ev correct, or am I missing something?

[jupiter]

Just some thoughts I had:

100bb starting stacks, 6.5bb pot on the flop. Say villain bets 90bb on flop. You could call now and continue profitably on all turns. However flop call was horrible.

Not sure what equity of KQ w/ backdoor flush is on flop vs villain's range; let's say it's 18%. 6 cards ~12% give you top pair, 9 cards ~18% give you a flush draw. So 6/47 times you will have let's say 60% equity. 9/47 times you will have 30% equity. 32/47 times you will have let's say 10% equity. This is roughly 20% equity and is definitely optimistic (damn, 18% wasn't a bad guess).

You can't make a bad call on the flop in order to make break-even calls on the turn/river. Side note though: if villain bets 2/3 pot, you are getting 5-2 to call (slightly better than 2-1) which needs about 28% equity to break even.

BTW, I think c/r and c/f are better than c/c.

[MC TRON]

Originally Posted by jupiter

You can't make a bad call on the flop in order to make break-even calls on the turn/river..

This ^

and...
I think the real problem comes when estimating how often V is going to barrel turn and river seeing as it's nearly impossible without a massive sample, and even then we don't know what the turn and river cards are going to be.

I can't remember who it was (could have been aejones) but they basically said that the less controllable/reliable info you have, then the less inclined you should be to let V make the decision.

i.e on the flop, V has a very high chance of c-betting, so we should should check to him and let him do it, and on the turn, say if a K rolls off, and V is likely to barrel as a bluff, then we should check again, because again we have a relatively large amount of controllable information.
(not saying that I advocate a c/c on the flop though, I just mean that if V is likely to bet, let him bet, but if future streets are going to be a guessing game, then either fold, or take the initiative with a c/r and put V to a decision rather than letting him put you to a decision).

It's hard to think about these spots mathematically when my maths is so rubbish.. :s

[OttoPilot]

Originally Posted by jupiter

Not sure what equity of KQ w/ backdoor flush is on flop vs villain's range; let's say it's 18%. 6 cards ~12% give you top pair, 9 cards ~18% give you a flush draw. So 6/47 times you will have let's say 60% equity. 9/47 times you will have 30% equity. 32/47 times you will have let's say 10% equity. This is roughly 20% equity and is definitely optimistic (damn, 18% wasn't a bad guess).

If you stove it you'll see your equity is much higher here, more like 46%.

The rest of the question obv depends completely on how villain plays the turn and river and I guess an argument can be made for calling versus villains that both barrel a ton and villains that don't barrel at all, as long as we have a plan for how to proceed on different cards.

[guitarizt]

I think check call or c/r flop are fine depending on the person you're playing and how you think they'll react, but I've started leading here a lot because people don't play back enough at micros.

[OttoPilot]

What else is in your leading range here?

[JamesMa]

I think there are many more things to consider than simply his cbetting range and bet size in order to more accurately analyze the odds and it just really gets too complex I think without putting in serious time. You'd have to analyze all the different turns and rivers and how they may influence villain's double/triple barreling frequencies while also trying to figure out what his turn/river betting ranges look like on bricks.

I would call in that spot vs some players and fold against others, sometimes lead and sometimes throw in a cr, really does depend on things including gameflow