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

http://www.twodimes.net/

Notably, a jack or ten gives you a straight draw as well, making your hand a favorite on the turn. That means you're really looking at 15 outs on turn since there are an additional six jacks or tens that improve your holding, and don't make his boat.

You've got a 40% or so chance to win, and 2 of 6.25 is less than 30%, so you should definitely call. You can even raise the turn if you hit a Jack or Ten (non-spade).

[TaintedRogue]

[ QUOTE ]
http://www.twodimes.net/

Notably, a jack or ten gives you a straight draw as well, making your hand a favorite on the turn. That means you're really looking at 15 outs on turn since there are an additional six jacks or tens that improve your holding, and don't make his boat.

You've got a 40% or so chance to win, and 2 of 6.25 is less than 30%, so you should definitely call. You can even raise the turn if you hit a Jack or Ten (non-spade).

[/ QUOTE ]

Thanks, I missed that when coming up with this hypothetical hand. What if there is no str8 draw....is the math ok?

I don't quite follow the pot total:
Pre-flop, you've got 3.25 BB.
In the flop round, there are 3 small bets to you, which puts the pot at 4.75 BB since the MP bet, and, if you're getting one more BB on the turn and the river, that's 6.75 rather than 6.25 which you stand to win, and that puts you in the black.

You might also raise on the turn if you hit the flush and so on, but that's not part of the way that you set up the problem.

[ QUOTE ]

Notably, a jack or ten gives you a straight draw as well, making your hand a favorite on the turn. That means you're really looking at 15 outs on turn since there are an additional six jacks or tens that improve your holding, and don't make his boat.

You've got a 40% or so chance to win, and 2 of 6.25 is less than 30%, so you should definitely call. You can even raise the turn if you hit a Jack or Ten (non-spade).

[/ QUOTE ]

Hitting a jack or ten on the turn gives you four outs vs. a set, not six, in addition to your flush outs that don't pair the board. Raising for value with a flush draw + inside straight draw when heads-up against a set makes no sense, especially since the opponent will reraise. Also, if the turn is a non-spade jack or ten, you are still only 22.7% to win.

[ QUOTE ]

Hitting a jack or ten on the turn gives you four outs vs. a set, not six, in addition to your flush outs that don't pair the board. Raising for value with a flush draw + inside straight draw when heads-up against a set makes no sense, especially since the opponent will reraise. Also, if the turn is a non-spade jack or ten, you are still only 22.7% to win.

[/ QUOTE ]

(Wiping egg of of face.) Yeah, I read the wrong column on two-dimes.

[Cobra]

Hopefully someone else will check out my calculations but I think you can determine the break even pott odds as follows:

We first need to determine the five following probabilities:

A. Flush on Turn and blank on the river-8/45*34/44 = .1374
B. Blank on turn and flush on the river-30/45*7/44 = .1061
c. Lose on the turn - 7/44 = .1556
D. Blank on turn and lose on the river-30/44*37/44 = .5606
E. Flush on turn and lose on the river-8/45*10/44 = .0404

Lets assume the Y = current pot and x = amount you need to bet to call so y/x = is your pot odds.

When you win under A you win (Y+2x)
When you win under B you win (Y+2x)
When you lose under C you lose X
When you lose under D you lose 2X
When you lose under D you lose 2X.

So in order to find the break even y/x you would solve the following equation.

A*(Y+2X)+B*(Y+2X)=CX+2DX+2EX

Simplyfing we get Y/X = (C+2D+2E-2A-2B)/(A+B)

If we substitute our known variables in we get the break even pott odds as:

3.575:1

This is the first time I have done something like this so hopefully someone else will check my work.

Cobra