Calculating Bluff-equity And Breakeven Points

[Tactical Bear 3]

NOTE: I posted this a while back, and I still think the exercise has validity. If you can't do this, then you need to learn how to do it. Before trying to figure out the answer, take an "off the top of your head" guess, just to see how close you are. When I was playing LHE seriously, I would make a note of any decisions that I thought might be close, and then do the math afterwards to see if my decision was correct, incorrect, or close one way or another. I think that's a VERY important part of playing poker professionally or semi-professionally.If you remember doing this, please let people who have never seen it before give it a shot. If you are very good and surely know the answer, PM it to me. 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.

[DinkDonk 1]

PM sent. Good post. For the record, I screwed up how many unseen cards there were, but the same logic applies and the answer should be close anyway.

[Tactical Bear 3]

For the record, DinkDonk got the answer wrong, and he's obviously a very smart, thinking, math-competent LHE player.I want you guys to try this, because I remember the results last time were surprising to a lot of people

[DinkDonk 1]

For the record, DinkDonk got the answer wrong, and he's obviously a non-retarded slightly better than break-even LHE player.I want you guys to try this, because I remember the results last time were surprising to a lot of people

Agreed. I've actually done the same math before several times and still screwed it up. I'll go through again and send a new PM.Also, FYPEdit- NVM I know what I did wrong.

[shpaget 0]

I'm going with 3.8%.My convoluted logic - which is probably wrong - has been sent via PM.

[Tactical Bear 3]

3.8% is incorrect. Keep trying guys. If you limit hold'em gurus don't know the answer, how are you going to keep your STREET CRED?!

[ReraiseAllIn 0]

I interested to see what the correct answer is. I don't consider myself a limit hold'em guru, I just want to know how I am setting up the equation wrong as I also got an answer around 3.8%. What kind of timeframe should I be expecting until the proper math and solution is posted?Thanks for posting this, as it is definetely very interesting.

[Tactical Bear 3]

I am going to wait a little while before posting answers in this thread, but I'll PM anyoen who has expressed interest/frustration my solution

[Polsk33AllIN 0]

maybe im retarded but just looking at it im thinken that he has to fold about 60% of the time.

[outsider13 0]

I guessed (emphasis on guess). And I pm'd to mask my stupidity :)Okay, re-thought this an I was way off. Somehow on my 3rd try i came up with needing to hit 74% of the time to break even. I give up

[Shark527 0]

My first guess was around 40-45% and I was wrong.

[Tactical Bear 3]

maybe im retarded but just looking at it im thinken that he has to fold about 60% of the time.

I don't mean to pick on this particular poster, but any guess that is higher than 1/6.5 is... well, it indicates a complete and total misunderstanding of the nature of poker. Even if we have no equity -- we are drawing stone dead -- your opponent has to fold no more than 1/6.5 times to make the play breakeven. Think about it this way:5.5 times you bluff, and get called and lose the BB you put in on the turn. The next time (the 6.5th time) you bluff and he folds, netting you the 5.5BB in the pot, and meaning you break even. ANY guess that starts anywhere higher than about 15% means you need to bone up on your basic, basic, basic poker math.I'm not posting this to be a dick -- I mean, I am kind of a dick, but that's not what's going on here -- but it's scary that people who play poker even semi-frequently and post on a well-patrolled message board can forget this very, very basic concept.

[Polsk33AllIN 0]

One thing i did misunderstand was i thought that a b et on the turn would be 2BB in a limit game. But id still be off

[MovingIn 0]

Check your PM. I noticed your problem puts a number on everything except the odds that we are drawing dead. How can we know the likelihood that we are drawing dead if we don't know exactly what our hand is and what we are drawing to?

[BaseJester 1]

Check your PM. I noticed your problem puts a number on everything except the odds that we are drawing dead.

Yes it does. It sets the probability that we are drawing dead at zero.

How can we know the likelihood that we are drawing dead if we don't know exactly what our hand is and what we are drawing to?

It's a given in the problem.

[MovingIn 0]

Yes it does. It sets the probability that we are drawing dead at zero.

I gave an answer that Wang told me was incorrect because I did not consider the odds we were drawing dead. If the odds are zero, then why would he say that? Or is he just screwing around with us for his amusement?

[shpaget 0]

I gave an answer that Wang told me was incorrect because I did not consider the odds we were drawing dead. If the odds are zero, then why would he say that? Or is he just screwing around with us for his amusement?

I can't comment on what he may or may not have said to you in a PM.All I can say is in the original post he clearly states that you have 18 live outs.

[BaseJester 1]

I gave an answer that Wang told me was incorrect because I did not consider the odds we were drawing dead. If the odds are zero, then why would he say that? Or is he just screwing around with us for his amusement?

( ) Makes sense to me.(*) What?

[BigDMcGee 3,352]

I gave an answer that Wang told me was incorrect because I did not consider the odds we were drawing dead. If the odds are zero, then why would he say that? Or is he just screwing around with us for his amusement?

LOL if he told you that, he's fcking witn you, because if you have 18 live outs, you cant' be drawing dead. This isn't some esoteric riddle or something.

[MovingIn 0]

Okay. He needs to pop in and explain himself further.What I don't understand is why he keeps bringing up the odds we need to bluff successfully when we're drawing dead... if we're not drawing dead in this problem. Why does that even matter? It's two completely different scenarios.

[BaseJester 1]

Okay. He needs to pop in and explain himself further.What I don't understand is why he keeps bringing up the odds we need to bluff successfully when we're drawing dead... if we're not drawing dead in this problem. Why does that even matter? It's two completely different scenarios.

I think I see what happened here.You gave an answer greater than 15%. That can't be right, because of the explanation in post 12 . Mr. Bear reiterated this in the PM. If he folds more than 15% of the time, then we don't even need cards to make a profitable bet. Since we have outs when called, he can fold even less than that for us to break even. We have outs, so he can fold less and we still break even.

[shpaget 0]

Okay. He needs to pop in and explain himself further.What I don't understand is why he keeps bringing up the odds we need to bluff successfully when we're drawing dead... if we're not drawing dead in this problem. Why does that even matter? It's two completely different scenarios.

As far as I can see, what Bear has said (and he is correct) is that "EVEN IF" we are drawing dead, we only need villain to fold every 7 hands, or twice every 13 hands, for us to break even....so, if you come up with a number higher than 15% you must know you are wrong.15% is the answer if we have 0 outs....as our number of outs goes up, this percentage drops.If you came up with 3.8% like I did you likely did the same mistake I made...double counting your equity on the turn.

[Tactical Bear 3]

As far as I can see, what Bear has said (and he is correct) is that "EVEN IF" we are drawing dead, we only need villain to fold every 7 hands, or twice every 13 hands, for us to break even....so, if you come up with a number higher than 15% you must know you are wrong.15% is the answer if we have 0 outs....as our number of outs goes up, this percentage drops.If you came up with 3.8% like I did you likely did the same mistake I made...double counting your equity on the turn.

Yeah, this. Given pot-size, the highest the number could ever be, even if we have no other information, is the situation in which we're drawing dead, in which case the answer would be about 15%. More equity in the pot means our bluffs are less costly which means that %age will go down.Here's how I solved the problem:If we're called when we bet on the turn, we have negative equity for that bet. 18/46 times we end up winning a bet, and 28/46 times we end up losing a bet, so the cost of a called turn bet is 10/46BB, or about .217BB. When we bet the turn and he calls, we lose .217BB. We know what we stand to lose if he calls, but what do we stand to gain if he folds? The answer is NOT 5.5 BB. If we check behind, we have equity in this pot, and are going to win it 18/46 times. Our equity in the pot is (18/46)*(5.5BB) = 2.15BB. To determine what we gain from a successful bluff, we must first subtract our equity from the pot to determine how much our equity improves. In other words, we're only bluffing at HIS share of the pot. So: 5.5 -2.15 = 3.35BB. When he folds, we gain 3.35BB. Now we know both (cost) and (benefit), so we can just do a little division to figure out a breakeven point. (cost of unsuccessful bluff)/(reward of successful bluff) = (% of time bluff must be successful to break even)(.217BB) / (3.35BB) = .065, or about 6.5% of the time. Tomorrow I shall post a graph drawn by one David Nicoson, unless somebody else wants to track it down and post it first.

[David_Nicoson 1]

[BigDMcGee 3,352]

I don't know about you, but that makes me want to bluff more.