Good or bad call? (5CD)

[Biggle10]

Button is bad. SB is relatively solid.

Hand 1242155685, Started at 9/6/2005 8:56 PM
Table 'Lowell': $2-$4 Limit Five Card Draw (Real Money)
Seat 2: SB ($32.55 in chips)
Seat 3: Biggle10 ($102.60 in chips)
Seat 7: UTG ($184.60 in chips)
Seat 9: Button ($503.55 in chips) (on the button)
*** Blind Bet Round *** :
Dealt to Biggle10: A[img]/images/graemlins/club.gif[/img]
Dealt to Biggle10: K[img]/images/graemlins/club.gif[/img]
Dealt to Biggle10: 9[img]/images/graemlins/diamond.gif[/img]
Dealt to Biggle10: K[img]/images/graemlins/diamond.gif[/img]
Dealt to Biggle10: 3[img]/images/graemlins/heart.gif[/img]
SB : Post Blind ($1)
Biggle10 : Post Blind ($2)
*** First betting round *** :
UTG : Fold
Button : Call ($2)
SB : Raise ($3)
Biggle10 : Call ($2)
Button : Call ($2)
SB draws 3
Biggle10 draws 3
Dealt to Biggle10: 10[img]/images/graemlins/diamond.gif[/img]
Dealt to Biggle10: J[img]/images/graemlins/club.gif[/img]
Dealt to Biggle10: A[img]/images/graemlins/heart.gif[/img]
Button draws 1
*** Second betting round *** :
SB : Check
Biggle10 : Check
Button : Bet ($4)
SB : Call ($4)
Biggle10 : Call ($4)

[Moneyline]

Unless the SB is a tight raiser I think the call (EDIT: I'm referring to the call before the draw) is fine. I think drawing 3 is the right move too. The thing I don't agree with is the call after the draw. For your hand to be best the button must be bluffing (probably on a busted draw), and the SB must be either a total calling station or trying to pick of a bluff with only 1 pair. Without reads I think there's no way overcalling with a pair of kings has a positive expectation. It's too likely IMO that either the button made his hand or the SB made something like 2 pair and didn't want to value bet into a draw.

Just my opinion...

[Biggle10]

I'm pretty sure the SB had QQ or less before the draw as I took down 2 aces. Button was on a draw. What are the odds that at least one of them improved? I'm not sure how to do the math. I *happen* [img]/images/graemlins/frown.gif[/img] to be right on this hand, but I'm still not sure if it was +EV longterm.

[Moneyline]

[ QUOTE ]
I'm pretty sure the SB had QQ or less before the draw as I took down 2 aces. Button was on a draw. What are the odds that at least one of them improved? I'm not sure how to do the math. I *happen* to be right on this hand, but I'm still not sure if it was +EV longterm.

[/ QUOTE ]

Doing the math is easy. Just look at the appendix of Super System. [img]/images/graemlins/tongue.gif[/img] If you don't own the book, you can check out the odds at Mike Caro's website: www.poker1.com/mcu/mculib_odds.asp

Far more important than the actual odds of them making their hands, IMO, is the chance that the button would bluff and the SB would call with a hand you beat. In my experience, this combo is very rare, certainly rare enough to make folding the right play. Of course, if you have reads on both players that lead you to believe you have a decent shot at winning the pot then you should call.

[Biggle10]

I'm going to make the assumption that button always bets regardless if he hits is draw or not. Big assumption I know. I realize that SB is less likely to call with just QQ or less and the button doesn't always bet busted draw. I guess this is just some 'poker theory' analysis. My math might be off.

P(Flush or QQ improves) = (1/4.25 + 1/2.5) - (1/4.25 * 1/2.5) = 54% that one or other improves. So basically I'm getting slightly less than 1:1 odds that my hand is best while the pot is offering me 5:1

Is my analysis flawed here? I'm not sure how to do the math, if villian only bets busted draw 1/3 of the time and the SB only calls with QQ unimproved 1/2 the time.

[MarkGritter]

[ QUOTE ]

Is my analysis flawed here? I'm not sure how to do the math, if villian only bets busted draw 1/3 of the time and the SB only calls with QQ unimproved 1/2 the time.

[/ QUOTE ]

Probability problems can usually be solved via brute force. Just list all the cases.

Button:
A) Flush draw comes in (1/4.25) and villian bets = 0.235
B) Flush draw misses (3.25/4.25) and villian checks (2/3) = 0.510
C) Flush draw misses (3.25/4.25) and villian bets (1/3) = 0.255

We only care about cases A and C, because in B there is no bet to call.

SB:
1) QQ improves (1/2.5) and calls = 0.4
2) QQ doesn't improve (1.5/2.5) and calls (1/2) = 0.3
3) QQ doesn't improve and folds = 0.3

So, we have 7 cases (A1, A2, A3, B, B1, B2, B3) covering all the possibilities. But, we know that Button bet and SB called, so we need to find the probability that they both missed given that action.

Cases where there is a bet/call are
A1 = 0.235 * 0.4 = 0.094
A2 = 0.235 * 0.3 = 0.0705
C1 = 0.255 * 0.4 = 0.102
C2 = 0.255 * 0.3 = 0.0765
Total = 0.343

(Adding in the remaining cases should total to 1.0 if I got the math right. B = 0.510, A3 = 0.235 * 0.3 = 0.0705, C3 = 0.255 * 0.3 = 0.0765, total = 1.0. So far, so good.)

34% of the time that the action goes bet/call. But you have the best hand only in case C2. C2 is 0.0765/0.343 = 22% of the these cases.

So, given the assumptions you state, you are getting about 3.5:1 odds on having the best hand.