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Calculating Bluff Equity And Breakeven Points


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#1 Shimmering Wang

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Posted 12 August 2007 - 08:18 PM

On the turn, there are 5.5BB in the pot, after rake. You're thinking about whether to semibluff again, or take a free card. You have a huge draw, with 18 live outs. (For the sake of clarity, there are 46 unseen cards.) How often does your semibluff have to be successful (ie, lead to a fold from an opponent) to be a totally breakeven play? The betting ends after the turn, so don't concern yourself with implied odds. You will never be raised. Your opponent will either call or fold. You are always drawing to exactly 18 outs, and you are never ahead.Please show all work, and goodluck. This should be good for some of the people less experienced with the math involved in LHE.WangPS- I haven't really seen an in depth discussion of this concept here, or in Theory of Poker or anything, but I may have missed it. I haven't read much (books or here) in a long time. I sit down at my computer or in front of the TV with a pen and piece of paper and do stuff like this all the time.

#2 Shimmering Wang

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Posted 12 August 2007 - 09:40 PM

Come on, faggots. Even if you don't know the answer, give it a shot. I see some people loitering in this forum, not posting. I think the answer to this question is very important for all players of all calibers.Faggots.Wang

#3 Zach6668

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Posted 12 August 2007 - 09:51 PM

Your equity + fold equity = odds the pot is laying.If this is true, your bet is breakeven.This is basic. I'm too lazy/retarded to go into detail.
QUOTE (serge @ Tuesday, May 12th, 2009, 7:20 PM) <{POST_SNAPBACK}>
LETS GO PITTSBURGH
QUOTE (Acid_Knight @ Monday, March 10th, 2008, 4:15 PM) <{POST_SNAPBACK}>
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#4 Shimmering Wang

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Posted 12 August 2007 - 10:12 PM

View PostZach6668, on Monday, August 13th, 2007, 1:51 AM, said:

Your equity + fold equity = odds the pot is laying.If this is true, your bet is breakeven.This is basic. I'm too lazy/retarded to go into detail.
There are a lot of people who probably have absolutely no idea how to come up with a number here, and that's the point. It's all well and good to understand the underlying idea, but to be able to get a feel for exactly how good or bad a turn bet is in a situation like this, we need to know EXACTLY how rarely or often our opponent must lay down. The concept is basic, but the application is slightly more complicated. I'm sure most good players can do these things, but I bet most beginning and mediumish-experience level players couldn't write the formula out.And, for the record, you didn't even give an answer, so you are definitely not winning this thread.Wang

#5 Ouch-8s

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Posted 12 August 2007 - 10:18 PM

View PostShimmering Wang, on Sunday, August 12th, 2007, 11:12 PM, said:

And, for the record, you didn't even give an answer, so you are definitely not winning this thread.
I don't play games I can't win, like this thread or LHE. But I read.
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#6 SilverSeven

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Posted 12 August 2007 - 10:41 PM

Here's how I'd figure it out starting with zach's formula :

View PostZach6668, on Monday, August 13th, 2007, 1:51 AM, said:

Your equity + fold equity = odds the pot is laying.
So, we'd be looking to find the fold equity to balance the equation out :fold equity = odds the pot is laying - our equityfold equity = 5.5-to-1 - 18/46fold equity = 84.6% - 39.1%fold equity = 45.5%So, roughly, he has to fold half the time for the bet to be +ev.
QUOTE(serge @ Monday, February 11th, 2008, 3:49 PM) View Post
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#7 Zach6668

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Posted 12 August 2007 - 10:56 PM

Yeah, I don't even know if that's right.45% is definitely not right.On a straight up steal, our bluff only has to work 1/5.5 times, assuming we're drawing dead.I think I worded the equation wrong. Ever since I left high school, my brain has become completely retarded for math stuff. I don't understand why.I love math problems like this, so I'm interested in seeing how this turns out.
QUOTE (serge @ Tuesday, May 12th, 2009, 7:20 PM) <{POST_SNAPBACK}>
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QUOTE (Acid_Knight @ Monday, March 10th, 2008, 4:15 PM) <{POST_SNAPBACK}>
Zach is right about pretty much everything.

#8 SilverSeven

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Posted 12 August 2007 - 10:59 PM

View PostZach6668, on Monday, August 13th, 2007, 2:56 AM, said:

Yeah, I don't even know if that's right.45% is definitely not right.On a straight up steal, our bluff only has to work 1/5.5 times, assuming we're drawing dead.I think I worded the equation wrong. Ever since I left high school, my brain has become completely retarded for math stuff. I don't understand why.I love math problems like this, so I'm interested in seeing how this turns out.
Hmmm...this is quite true...guidance someone else ???
QUOTE(serge @ Monday, February 11th, 2008, 3:49 PM) View Post
If the Ottawa Senators win the Cup:

- I will donate $200 to the Daniel Alfredsson clown academy
- I will not watch hockey for a a period of 12 months
- I will wear a Senators jersey and say I am a Senators fan while walking up and down Yonge Street
- I will praise the city of Ottawa and their fine hockey team for a period of 1 year
- I will acknowledge that hell has finally frozen over
- I will cancel LeafsTV and NHL Centre Ice Package
- I will also give my fantasy team for a total of one year to an associate

#9 Zach6668

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Posted 12 August 2007 - 11:03 PM

I think this is the problem with yours:Our Equity = 18/44 = 40.9%Fold Equity = xPot Odds = 5.5-1 = 1/6.5 = 15.4%40.9 + x = 15.4x = -25.5%So, clearly I'm a tard.Wang, point me in the correct direction plz.(note, even if this worked, it still doesn't take into account the fraction of his call that we get.)
QUOTE (serge @ Tuesday, May 12th, 2009, 7:20 PM) <{POST_SNAPBACK}>
LETS GO PITTSBURGH
QUOTE (Acid_Knight @ Monday, March 10th, 2008, 4:15 PM) <{POST_SNAPBACK}>
Zach is right about pretty much everything.

#10 SilverSeven

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Posted 12 August 2007 - 11:22 PM

OK here's my second try :The pot is laying us 5.5-to-1 so we need to win 15.4% if the time for the bet to be +ev.We win anytime villain folds, plus anytime he calls and we hit, so, x being the odds (percentage) of a fold, we need:15.4% = x + [(1-x)*(18/46)]Solve for x, I get x=-38,9% WTF :club: SO...this bet is ALWAYS +ev...come to think of it now, the pot is laying us better odds than our draw...forget about fold equity...Does this make sense ???
QUOTE(serge @ Monday, February 11th, 2008, 3:49 PM) View Post
If the Ottawa Senators win the Cup:

- I will donate $200 to the Daniel Alfredsson clown academy
- I will not watch hockey for a a period of 12 months
- I will wear a Senators jersey and say I am a Senators fan while walking up and down Yonge Street
- I will praise the city of Ottawa and their fine hockey team for a period of 1 year
- I will acknowledge that hell has finally frozen over
- I will cancel LeafsTV and NHL Centre Ice Package
- I will also give my fantasy team for a total of one year to an associate

#11 Zach6668

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Posted 12 August 2007 - 11:53 PM

No, this makes no sense.I'm losing my mind.We don't have the equity we need for the bet itself to be +EV, from that theory. But that assumes we're getting called.God I'm tired.
QUOTE (serge @ Tuesday, May 12th, 2009, 7:20 PM) <{POST_SNAPBACK}>
LETS GO PITTSBURGH
QUOTE (Acid_Knight @ Monday, March 10th, 2008, 4:15 PM) <{POST_SNAPBACK}>
Zach is right about pretty much everything.

#12 CardWarfare

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Posted 13 August 2007 - 12:03 AM

My guess is 13. I'm not going to tell you how I got to that number, nor will I show any work. I just like the number 13.Seriously, though. Aside from my personal numerical preference, that's my answer. Final.

#13 BigDMcGee

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Posted 13 August 2007 - 05:20 AM

isn't it 1/10? If your equity in the pot is 40 percent, don't you just need him to fold ten percent of the time? Am I being to simple here?
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#14 Shimmering Wang

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Posted 13 August 2007 - 09:03 AM

Nobody is really all that close yet, but Zach has said a few things that seem to hint that he might have an idea how to do it.I'm going to give it some more time, let some other people have a crack.Wang

#15 Shimmering Wang

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Posted 13 August 2007 - 09:07 AM

View PostSilverSeven, on Monday, August 13th, 2007, 3:22 AM, said:

OK here's my second try :The pot is laying us 5.5-to-1 so we need to win 15.4% if the time for the bet to be +ev.We win anytime villain folds, plus anytime he calls and we hit, so, x being the odds (percentage) of a fold, we need:15.4% = x + [(1-x)*(18/46)]Solve for x, I get x=-38,9% WTF :club: SO...this bet is ALWAYS +ev...come to think of it now, the pot is laying us better odds than our draw...forget about fold equity...Does this make sense ???
A bet that is called is only +EV if you will win the pot more than half the time. Obviously, since we're winning only 18/46 times, we are definitely not winning more than half the time. If he calls 100% of the time, the bet is obviously -EV. But he will fold some percentage of the time to make up for what we lose by betting.Wang

#16 kkot

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Posted 13 August 2007 - 01:45 PM

edit: ****
wutwut00 on Stars

#17 Zach6668

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Posted 13 August 2007 - 02:03 PM

So it's 50% - 18/46 = required fold equity?Bleh, it doesn't take into account the extra 18/46th of a bet that you get from his call.
QUOTE (serge @ Tuesday, May 12th, 2009, 7:20 PM) <{POST_SNAPBACK}>
LETS GO PITTSBURGH
QUOTE (Acid_Knight @ Monday, March 10th, 2008, 4:15 PM) <{POST_SNAPBACK}>
Zach is right about pretty much everything.

#18 therrinn

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Posted 13 August 2007 - 02:21 PM

View PostZach6668, on Monday, August 13th, 2007, 5:03 PM, said:

So it's 50% - 18/46 = required fold equity?Bleh, it doesn't take into account the extra 18/46th of a bet that you get from his call.
Getting warmer.

#19 Zach6668

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Posted 13 August 2007 - 02:23 PM

Yeah, I know what it is in theory, but like I said, I've become math-retarded since I left high school, and maybe after 1st or 2nd year of Univeristy.And I'm thinking of going into engineering... durrrrr.
QUOTE (serge @ Tuesday, May 12th, 2009, 7:20 PM) <{POST_SNAPBACK}>
LETS GO PITTSBURGH
QUOTE (Acid_Knight @ Monday, March 10th, 2008, 4:15 PM) <{POST_SNAPBACK}>
Zach is right about pretty much everything.

#20 Shimmering Wang

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Posted 13 August 2007 - 02:24 PM

View PostZach6668, on Monday, August 13th, 2007, 6:03 PM, said:

So it's 50% - 18/46 = required fold equity?Bleh, it doesn't take into account the extra 18/46th of a bet that you get from his call.

View Posttherrinn, on Monday, August 13th, 2007, 6:21 PM, said:

Getting warmer.
Give us the answer, then, therrinn. Hint: '50% - 18/46" really isn't all that close to the proper approach.Wang




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