Flush Draw v. Made Set on Flop/Hold Em

[TaintedRogue]

10/20 HE

I sometimes find myself knowing that my opponent has flopped a set. The tell is just too obvious. Corona's will do that.......

So, what kind of odds am I going to need to continue when I hit a four flush on the flop? The following is what I came up with. Let me know if you agree.

We'll say I have A [img]/images/graemlins/spade.gif[/img],K [img]/images/graemlins/spade.gif[/img] in the big blind, one person in MP opens and the button raises & I just call, looking for a return on my deceptive play later. MP also calls.

We have 3 players and 3.25BB in the pot.

Flop: Q [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/spade.gif[/img]

I notice that the Button has sat up and put his Corona in the cup holder. I check, MP bets, and the Button confirms my read, lighting up, hesitating, then deciding to raise now. I look over at MP, and, he has realized his doom and I can tell he's not happy. He finally looked at the Neon Light above the Button's head, and having completed grade school, he can read it: SET........

Right now there is 4.25 BB in the pot & I have to call one to see the Turn. MP folds.

Now, I know, due to the alcohol level in the Button's bloodstream, that he will call the River if I make my flush, so I can count on winning 6.25 BB's, however, I may be outdrawn, so I am actually risking 2 BB's to win 6.25 (the call of 2 SB's on the Flop and the call on the Turn) which is 3.125:1. Is this a +EV proposition to call on the Flop? Here's my math:

I'm not guaranteed that MP flopped a pair, so I can't count his cards, however, I can count one of the Button's, as I know it cannot be a spade. Since he has a Set, his spade is either on the board, in the deck, or in his hand, however, one of the cards in his hand is guaranteed to not be a spade. I have 8 spades on the Turn & 7 on the River that can make my flush without pairing the board.

The Button will make his house on the Turn (we subtract my two known cards from the deck) 7/45 = 16% of the time & I'll lose the 1 BB I put in on the Flop.

This is a -EV of -.16

I will make my flush on the Turn (We substract his one card that isn't a spade from the deck) 46/8 = 17% of the time and then he outdraws me on the River 10/44 = 23% of the time.

(.17*.23)*-2BB = -.08 BB's.

I will make my flush on the Turn 17% of the time and he doesn't outdraw me on the River 34/44 = 77% of the time.

(.17*.77)* 6.25 BB's = +.82 BB's

We will both miss on the Turn (30/45=.67)& I will make my flush on the River 7/45 = 16%

(.67*.16) * 6.25 = +.67 BB's

Neither of us will make our hand on the Turn 67% of the time and I will not make my flush on the River 84% of the time.

(.67*.84)*2 BB's = -1.13 BB's

Add it all up: (-.16)+(-.08)+(+.82)+(+.67)+(-1.13)= -.05

So, it appears we need to win slightly more than 6.25 BB's in this scenario in order for it to be a +EV proposition.

Anyone care to confirm my math? Remember, there are times I substract 1 more known card when I know that the Button has a card that isn't a spade and two cards when I am computing the odds for both of us.

Thanks,
Ken