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Calculating Bluff Equity And Breakeven Points


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#21 Shimmering Wang

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Posted 13 August 2007 - 02:25 PM

View PostZach6668, on Monday, August 13th, 2007, 6:23 PM, said:

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.
If you know what it is in theory, you should be able to put all the numbers on a piece of paper, or at least give us a general idea of how to find the answer.Wang

#22 Shimmering Wang

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Posted 13 August 2007 - 02:26 PM

If anybody wants a hint or a solution, just send me a PM....Wang

#23 Zach6668

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Posted 13 August 2007 - 02:27 PM

View PostShimmering Wang, on Monday, August 13th, 2007, 6:25 PM, said:

If you know what it is in theory, you should be able to put all the numbers on a piece of paper, or at least give us a general idea of how to find the answer.Wang
No damnit!I'm just trying to save face by pretending I know!I've built up a reputation over the years.Stop ruining it!:club:
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.

#24 opie

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Posted 13 August 2007 - 02:29 PM

There are 3 cases:1. Check / Check2. Bet / Call3. Bet / FoldQuestion - How often does the fold in case 3 happen to make the bet you make in cases 2&3 the same value as not betting, which is case 1.1 is easy to figure. We win 5.5 BB in 18/46 cases, or an EV of 2.15BB, and lose nothing (since we made no more bets) in the other 28/46 cases.2. We win 6.5 BB in 18/46 cases, for 2.54 BB, but lose the 1BB we bet in 28/46 cases, or -0.60BB, for a total EV of 1.94BB.3. We win 5.5BB every time in this case.So, how often is case 3? Call it X, and solve 2.15 = X(5.5) + (1-X)1.94.Distributing X gives us: 2.15 = 5.5X + 1.94 - 1.94XSimplifying: 0.21 = 3.56XX = .21/3.56 = 0.059.6% of the time.Peace,Opie

#25 psujohn

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Posted 13 August 2007 - 02:37 PM

I have a feeling like I'm over simplifying this but ...If our bet is called we'll win 18/46. This means out bet has a .39 BB expectation. Let's call that .4For out bet to be profitable we need to make up that other .6 of a bet. Since our hand is never good we need to win 5.5 x X% = .6 or X% = .6/5.5 = just under 11%. Hmm. That's not quite going to work is it..11(5.5) + .9(.39) != 1So to start over with the ev equation and work backwardsX% of the time we'll win 5.5BB. 100-X% of the time we'll win .39 BBX(5.5) + 1-X(.39) = 15.5X + .39 - .39 X = 15.11X = 1 - .39 = .61X = 12% ???That's mysteriously close to the wild guess 13 answer.I left my incorrect thinking in there as an exercise for the student.Edit: Opie - I think your step 2 is incorrect. By your calculation betting is +EV even if we're always called and that's clearly not true. The EV of that bet is only the additional amount that you win based on that bet or .4 BB. That bet doesn't help (or hurt) us win the $$$ already in the pot.

#26 Shimmering Wang

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Posted 13 August 2007 - 02:44 PM

View Postopie, on Monday, August 13th, 2007, 6:29 PM, said:

There are 3 cases:1. Check / Check2. Bet / Call3. Bet / FoldQuestion - How often does the fold in case 3 happen to make the bet you make in cases 2&3 the same value as not betting, which is case 1.1 is easy to figure. We win 5.5 BB in 18/46 cases, or an EV of 2.15BB, and lose nothing (since we made no more bets) in the other 28/46 cases.2. We win 6.5 BB in 18/46 cases, for 2.54 BB, but lose the 1BB we bet in 28/46 cases, or -0.60BB, for a total EV of 1.94BB.3. We win 5.5BB every time in this case.So, how often is case 3? Call it X, and solve 2.15 = X(5.5) + (1-X)1.94.Distributing X gives us: 2.15 = 5.5X + 1.94 - 1.94XSimplifying: 0.21 = 3.56XX = .21/3.56 = 0.059.6% of the time.Peace,Opie
Ship it ALLLL to Opie. You guys are banging your heads against the wall, and this clown with 75 posts makes you all look afoolHere are the two ways I came up with to figure the answer. Our answers might be slightly different, due to rounding error.This is the way that's really intuitive for me:There are 5.5BB in the pot. 18/46 of that is ours, and 28/46 is our opponent's. That is to say:Our Equity = 2.15BBOpponent's Equity = 3.35BBWhen we're bluffing, we are ONLY bluffing at our Opponent's share of the pot, right? Part of that money is ours. So when I think about it, I thinK- What am I bluffing at?- How much does a bluff cost me?We've already figured the first part, so let's figure the second. How much does it cost to fire a bluff here, with 18 outs? Easy. The cost of a bet is simply My Equity - Opponent's Equity. 18/46 times I win 1BB when he calls and I get there, and 28/46 times I lose a BB when he calls and I don't get there. Simply, the EV of a called bet here is -10/46BB, or about -.218BB.For me, the easiest way to visualize the situation is as follows:"How many times can I bluff at my opponent's share of the pot and get called before I spend EXACTLY the amount of money in my opponent's share of the pot? In otherwords, how many times will he have to call me for a single successful bluff to make up for it?"Easy:Opponent's Equity/BetCost3.35BB/ (10/46) = 15.4So I can bet 15.4 times before I bluffed off his share of the pot. He folds to the next bluff -- the 16.4th -- and then we're dead even.So, he has to fold 1 in 16.4 times. Or about 6.1% of the time. I have a second, more simplified model that I sent in a PM to Peter. It's probably going to be more intuitive for most.WangEDIT- The whole point of this exercise was to show that bluffing with a lot of outs is often the BEST PART of having all those outs. There aren't many situations anymore where I don't fire the turn if my opponent isn't a total calling station. There are obviously more considerations, like being check/raised, not knowing how many outs are good, meta-game stuff, etc., but let this be a small lesson for you.

#27 Shimmering Wang

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Posted 13 August 2007 - 02:49 PM

View Postpsujohn, on Monday, August 13th, 2007, 6:37 PM, said:

Opie - I think your step 2 is incorrect. By your calculation betting is +EV even if we're always called and that's clearly not true. The EV of that bet is only the additional amount that you win based on that bet or .4 BB. That bet doesn't help (or hurt) us win the $$$ already in the pot.
Nope. Compare his calculated equity when we bet (1.94BB) vs the equity of checking (2.15BB). The difference, there, is the EV of betting vs checking (obviously a negative number).EquityBet - Equity Check = 1.94 - 2.15 = -.21BBBetting costs us about .21 BB when we're called, and is (obviously) -EV.Wang

#28 therrinn

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Posted 13 August 2007 - 03:09 PM

Psujohn, you were on the right track, just got a little mixed up with some of the things you were equating.I rounded, and assuming I didn't **** up any of the algebra, here's the answerLet p(x) = probability of your opponent folding i.e. your semi-bluff works.If you bet and your opponent calls, your EV:18/46*6.5bb -28/46*1bb = 2.54bb -0.58bb = 1.96bbIf you bet your opponent folds, your EV:5.5bbIf you take the free card, your EV:18/46*5.5bb = 2.15bbSo, if you want to know how often your semibluff has to work for it to be break even, you set your EV from a free card equal to your EV from betting, and solve for p(x):2.15bb = p(x)*5.5bb + (1-p(x))*1.96bb2.15 = p(x)5.5 + (1-p(x))1.962.15 = 5.5p(x) + 1.96 - 1.96p(x)0.19 = 5.5p(x) -1.96p(x)0.19 = 3.54p(x)p(x) = 0.0537If your semibluff here works more than about 5.4% of the time, it is +EV

#29 opie

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Posted 13 August 2007 - 03:49 PM

View PostShimmering Wang, on Monday, August 13th, 2007, 6:44 PM, said:

Ship it ALLLL to Opie. You guys are banging your heads against the wall, and this clown with 75 posts makes you all look afoolThe whole point of this exercise was to show that bluffing with a lot of outs is often the BEST PART of having all those outs. There aren't many situations anymore where I don't fire the turn if my opponent isn't a total calling station. There are obviously more considerations, like being check/raised, not knowing how many outs are good, meta-game stuff, etc., but let this be a small lesson for you.
Yeah, I guess I am a "clown" - because I should post more. I'll try. I'm good at math - it is poker that I need to learn better!Thanks for the fun math puzzle, Wang. But more importantly, thanks for the valuable poker lesson! I guess it is related to the statement - the aggressive player more often wins the pot.Peace,Opie

#30 Shimmering Wang

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Posted 13 August 2007 - 04:08 PM

View Postopie, on Monday, August 13th, 2007, 7:49 PM, said:

Yeah, I guess I am a "clown" - because I should post more. I'll try. I'm good at math - it is poker that I need to learn better!Thanks for the fun math puzzle, Wang. But more importantly, thanks for the valuable poker lesson! I guess it is related to the statement - the aggressive player more often wins the pot.Peace,Opie
No offense meant by the little "clown" remark. It was more a barb directed at the regular posters here who I enjoy poking at, from time to time, even though I'm pretty sure most of them have higher equity than I do at most any table.That being said, you should post here, more. I hardly do anymore, but you seem to have a pretty solid understand of some the underlying concepts involved. Some pretty good, winning cardplayers don't possess the basic tools you seem to. What games do you play, and where? Bring a little something to the table, Clown.Wang

#31 aim786

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Posted 13 August 2007 - 04:39 PM

> x*(5.5)+(1-x)*(18/46*(5.5+1)-28/46*(1)); 3.565217391 x + 1.934782609> 18/46*(5.5); 2.152173913> solve(3.565217391*x+1.934782609 = 2.152173913,x); 0.06097560966That's how I'd solve it, which is pretty much exactly what opie did. You should start posting more man, we need more math guys around here!

#32 opie

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Posted 13 August 2007 - 05:04 PM

View PostShimmering Wang, on Monday, August 13th, 2007, 8:08 PM, said:

That being said, you should post here, more. Bring a little something to the table, Clown.

View Postaim786, on Monday, August 13th, 2007, 8:39 PM, said:

You should start posting more man, we need more math guys around here!
OK. I'll try. I've actually been looking for an interesting hand to post for quite a while and haven't been able to find one. Some of the sort of interesting ones are because I didn't use my normal strategy based on a read of an opponent. But it takes so long to describe why I had that read (unless I use PT stats, which I haven't set up yet). Another interesting type of hand is when multiple players raise at different points in a hand, but if I'm in a game that aggressive, I play very tight and my decisions get a lot easier and the hands I'm in aren't post-worthy. I'll keep looking.Peace,Opie The Happy Clown :-)

#33 Shimmering Wang

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Posted 13 August 2007 - 05:20 PM

View Postopie, on Monday, August 13th, 2007, 9:04 PM, said:

OK. I'll try. I've actually been looking for an interesting hand to post for quite a while and haven't been able to find one. Some of the sort of interesting ones are because I didn't use my normal strategy based on a read of an opponent. But it takes so long to describe why I had that read (unless I use PT stats, which I haven't set up yet). Another interesting type of hand is when multiple players raise at different points in a hand, but if I'm in a game that aggressive, I play very tight and my decisions get a lot easier and the hands I'm in aren't post-worthy. I'll keep looking.Peace,Opie The Happy Clown :-)
Just find one where you think there's a close decision, or where an opponent takes a line that confuses you, or you feel like you called down but it didn't feel right or that you were losing value. Or post a boring one so I can contradict Zach.

#34 Actuary

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Posted 13 August 2007 - 05:43 PM

before reading repliesPot 5.5 18 outs x = % he folds (1-x) = % he calls we win 18/46 times he calls we win 6.5 when he calls and we hit we lose 1 when he calls and we miss we win 5.5 when he folds -1 * (1-x) * (28/46) + 6.5 * (1-x) * (18/46) = 5.5 * (x) -1 * (1-x) * 28 + 6.5 * 18 * (1-x) = 5.5 * 46 * (x) 89 * (1-x) = 253 * (x) 89 = (253 + 89) * (x) x = 89 / (253 + 89) x = 0.260234

#35 opie

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Posted 13 August 2007 - 05:51 PM

View PostShimmering Wang, on Monday, August 13th, 2007, 9:20 PM, said:

Just find one where you think there's a close decision, or where an opponent takes a line that confuses you, or you feel like you called down but it didn't feel right or that you were losing value. Or post a boring one so I can contradict Zach.
OK, here's one I thought about posting from a $4/$8 live game in Atlantic City earlier this summer.I am in cut-off with QQ.2 limpers, I raise, button calls (huh?), SB folds, BB calls, 2 limpers call. 5 to the flop (actually probably below average at the table for players to the flop - there were a few bad players who limped most hands)Flop: 9TJ (I don't recall suits, let's say rainbow)Not a great flop for me, but not bad - I have an overpair and a straight draw.Check, Check, Check, Opie bets, Button raises (hmmm), BB re-raises (wow!), fold, fold, Opie ...???My answer at the table was to call the 2 bets, figuring I still have a straight draw even if I am behind, which I probably am (guessing someone had TJ, but otherwise confused). Button called (luckily he didn't reraise).Turn: blankBB bets, Opie (fearing a reraise from button and being stuck in between 2 raisers, and realizing I'm probably behind) folds, ...As the hand turns out, that the fold saved me money, but perhaps I should have folded to the flop check re-raise? Button had 78s for the straight, BB had JJ for trips. The only way it could have been worse was if someone had KQ. It turns out I did have 7 outs (minus the full house possibility for the BB), but I had to call 2 bets with a chance button would cap it for another.But here's the thing - it depends on the opponents. The BB was a quiet guy, so his raise was intersting. But the BB was an older lady who was a regular and definitely knew what she was doing. Without a read, maybe (but doubtful) that my call of 2 bets was OK. But with the read I had, it should have been an easy lay-down - it only took me 2 days of thinking about it to realize it!See? Was that interesting enough to post? I initially thought so, but eventually figured out the answer, which is hard to understand without knowing the opponents.Peace,Opie

#36 Zach6668

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Posted 13 August 2007 - 06:07 PM

Make a new thread with it, you donk.
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.

#37 Actuary

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Posted 13 August 2007 - 06:12 PM

View PostZach6668, on Monday, August 13th, 2007, 6:07 PM, said:

Make a new thread with it, you donk.
Hope Wang returns..I was playing PLO STT at the time, but I'm so far still liking my answer.soon I'll look at Opies

#38 Zach6668

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Posted 13 August 2007 - 06:13 PM

Wang already answered it.Also, AIM786 I SEE YOU READING GET ON MSN SOMETIME YOU DONKEY.
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.

#39 aim786

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Posted 13 August 2007 - 06:20 PM

View PostActuary, on Monday, August 13th, 2007, 6:43 PM, said:

before reading repliesPot 5.5 18 outs x = % he folds (1-x) = % he calls we win 18/46 times he calls we win 6.5 when he calls and we hit we lose 1 when he calls and we miss we win 5.5 when he folds -1 * (1-x) * (28/46) + 6.5 * (1-x) * (18/46) = 5.5 * (x) -1 * (1-x) * 28 + 6.5 * 18 * (1-x) = 5.5 * 46 * (x) 89 * (1-x) = 253 * (x) 89 = (253 + 89) * (x) x = 89 / (253 + 89) x = 0.260234
Actuary,There are 2 sides to the equation. One side should represent when you check behind on the turn, the other should represent when you bet. Therefore, the equality you made should actually be on the same side, with the other side containing an equation to show the EV from simply checking behind on the turn.

#40 Actuary

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Posted 13 August 2007 - 06:22 PM

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

Wang already answered it.Also, AIM786 I SEE YOU READING GET ON MSN SOMETIME YOU DONKEY.
no dummyI wanted him to see mine...but alas, Aim has responded.Looks like a set up problem, I need to look over what he said




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