Calling from the BB with a small pair, playing for set only.

[brimstone1]

This is a theoretical question; I want to work on my poker math, for I believe it will further my understanding of every situation.

By the way, the questions I ask are not rhetorical. Every question mark is a point at which I'm not sure of what I've done, so please feel free to answer/rebuttle/flame.

So, in this crazy world:

3 folds, BTN raises, SB calls, Hero...

Hero holds 22-66 and will play fit-or-fold on the flop.

Hero gets 5:1 on his call, hoping to hit the set 8:1 (%11?) and take down the pot with a c/r to BTN's contiuation bet.

Flop: (6 SB)

Hero hits set (11%)
SB checks, Hero checks, BTN bets, SB folds, Hero raises, BTN folds.
-------------------------
+7 SB

Hero misses (89%)
SB checks, Hero checks, BTN bets, SB folds, Hero folds.
-------------------------
-1 SB

EV: (7sb * 0.11) - (1sb * 0.89) = 0.77 - 0.89 = -0.12 sb


But of course, this isn't necessarily true.
How would I go about putting percentages to the times where BTN calls our c/r, or SB calls BTN's bet?

So I thought about this for a while, and am going to try to rationalize the numbers I present.

SB hits a pair with XY on the flop ~33%, but some are bottom pairs that he may not want to continue with (although not necessarily true for lower 6-max games, heh), and sometimes he will flop a nice draw that he may want to continue with. Let's say the flop comes 3 6 9 rainbow, SB will hit each of them 11% of the time, won't he? He doesn't like bottom pair, he enjoys the middle pair 50% of the time, and he will certainly call 1sb with the top pair.

So only looking at the times he flops a pair, he won't continue with bottom pair (33%), he wont continue with half of his middle pairs (16.5%), and will call 1 sb with the rest (49.5%). We round up, and call SB's call as 0.5SB.

But, they both fold to our c/r in this vacuum, not because that is what will happen, but because I have no idea how to go on with calculating the times he will continue with a draw, and what BTN's response will actually be (him holding overcards and getting 10:1 including SB's call).

So now, with SB's 0.5sb call, the situation is:
(7.5sb * 0.11) - (1sb * 0.89) = 0.825sb - 0.89sb = -0.065sb

Yay, we're almost breaking even at this point.

Can I comfortably rely on the assumption that the number of times the BTN and SB, or BTN alone will call my check-raise and perhaps pay me off more on the turn and river will offset the number of times I will be outdrawn or already beaten by a higher set to say this line is +EV?

If so, calling with any pair getting 5:1 from the BB against a steal and playing fit-or-fold on the flop can be +EV.
Praise implied odds.

[colgin]

I am by no means against trying to do some concrete math to solve discreet problems. But here you are getting way too abstract to come up with anything of real use IMO.

The simple answer to your original question is that in a typical small stakes SH game it should be very easy to make up with implied odds the 3 Sbs that you need to when you flop a set here against 2 opponents. The exact line you take will vary depending upon your oppoents and the specific flop. If you post some specific hands in which you have flopped a set out of the BB against a Button steal and SB semi-cold call I think you will get many responses on how to extract the most value.

[kross]

If button bets, SB folds, what's wrong with C/R'ing a ragged flop regardless of whether we hit a set or not? The flop probably missed him, you likely have the best hand...

[brimstone1]

What I can post, due to my sample size, are hands where I call the BTN raise with 22-66, check the whiffed pot, and fold to his contiuation bet.

So I wanted to go "behind the scenes" and see for myself if the line I was taking was appropriate or not. I think there is merit to what you are saying though; surely the line I take will heavily depend on the flop texture, my opponents ATSB and several other important factors. I may choose to lead a monotone flop but check-call with a very aggressive opponent on a non-connected rags flop.

This was just a brain workout for me. I've stayed on the surface of things and taken them as they are for too long in poker.

[colgin]

My bottom line is that with SB in you should be able to call profitably with any pocket pair in the BB even if you are just playing for set value (which I am not recomending should be your attitude, BTW). However, in a HU situation I seem to recall Peter Rus having an excellent explanation of why you cannot play small pocket pairs for just set value but need to extract some value when you don't hit to make them worth playing. I believe he was also talking about tougher games. In small stakes games with two opponents, I think you can just play for set value though. Obtaining maximum value will depend on a host of factors though.

[brimstone1]

I'm really not too comfortable with c/ring a bare small pair on a flop against a steal. I start to feel like I'm spewing when he calls my flop raise, and I'm stuck with the impetus on the turn and facing (more than often, considering we have 22-66) an overcard.

Don't get me wrong, I will c/r and lead any turn against high ATSB/aggressive opponents. As I said, this was just a workout.

I've been steadily losing money at 1/2 6-max, and I really want to find my leaks. So I've actually made a list of things to do, and this was one of the many "calculate EV of this specific line" to-do's.

I've spent enough time on just laying around and waiting for information to come at me, so this is my new approach [img]/images/graemlins/tongue.gif[/img]

Considering I've been studying for a year, and have played over 50k hands at limit, and another ~120k hands at NL tournies, I think its time I should be able to beat 1-goddamn-2 6-max [img]/images/graemlins/grin.gif[/img]