question on how often my opponent needs to fold to make a semi bluff +ev

i know i could use a FE calculator but i think those only work when shoving.

Ok I have A FD on the turn and for the sake of simplicity lets say i can never lose if i river my flush. lets also say i'm gonna shove river every time i hit and V will call a river shove 20 percent of the time. my bluff is 3/4s pot and effective stacks are 100xbb and so far pot has 10xbb in the middle. so our bluff is 7.5 thus we will lose 7.5 81 percent of the time and we will win 100 0.038 percent of the time so we lose 7.5 when me miss and win 3.8 when called. if he never fold we lose -2.275.

(100*0.038)-(7.5*.81) I just don't know how to figure how often V needs to fold in this situation to make the bluff 0ev

OTT
pot = 10 bb
Hero's equity = 19%
Hero's bet size = 7.5 bb
Villain's % to call = x
Villain's % to fold = 1 - x
Villain's % to raise = 0%

OTR
When Hero misses draw, Hero x/f.
When Hero catches draw, Hero shoves
When Hero shoves, Villain folds 80%
When Hero shoves, Villain calls and loses 20%
When Hero shoves, Villain calls and wins 0%


So now do the EV calc.
Start by listing all the possible scenarios and the value of each.

Hero bets, Villain folds: 10 bb * (1-x) = 10 - 10x
Hero bets, Villain calls, Hero misses draw: -7.5 bb * x * 81% = -6.075x
Hero bets, Villain calls, Hero hits draw / shoves, Villain folds: 17.5 * x * 19% * 80% = 2.66x
Hero bets, Villain calls, Hero hits draw / shoves, Villain calls, Hero wins: 100 bb * x* 19% * 20% = 3.8x

The sum of all these is the total EV.
10 - 10x - 6.075x + 2.66x + 3.8x = EV

You want to set EV = 0 and solve for x
10 - 10x - 6.075x + 2.66x + 3.8x = 0
10 + (-10 - 6.075 + 2.66 + 3.8)x = 0
10 + (-9.615)x = 0
x = -10/-9.615 = 1.004

So x is greater than 100%, which is a problem. Either I made a mistake somewhere, or there is no possible way for Villain's folding frequency to yield 0 EV.

EDIT: We technically want the EV to be greater than or equal to 0, which means that when we divide by a negative, it becomes less than or equal, so no matter what Villain's folding frequency, x is always less than or equal to 100.4%, so the EV is always positive. [/EDIT]

***
At any rate, the method I've shown you here is what you need to do. Multiply the value of every outcome by the chance of that outcome's occurrence. If you have nested events, then just multiply the frequency of each step through.

E.g. When it goes bet/call (yes/no)/draw (yes/no)
you set it up
value of outcome_1*%call_yes*%draw yes
+ value of outcome_2*%call_yes*%draw_no
+ value of outcome_3*%call_no

Note that %call_yes has 2 outcomes after it, so it is used 2 times.

So they only need to fold a little over 1 percent of the time?

Quote:

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Originally Posted by grumpy64

So they only need to fold a little over 1 percent of the time?

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What? No.

Reread my post.

Quote:

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Originally Posted by MadMojoMonkey

What? No.

Reread my post.

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will do but this is what had me thinking you were saying it was a little over 1 percent

You want to set EV = 0 and solve for x
10 - 10x - 6.075x + 2.66x + 3.8x = 0
10 + (-10 - 6.075 + 2.66 + 3.8)x = 0
10 + (-9.615)x = 0
x = -10/-9.615 = 1.004

on the bottom line does the 1.004 not rep how often they need to fold?

so we need to figure how often he needs to fold to make 2.275? as that is how often we lose if he never folds so if he folds 28 percent of the time our bluff is +ev. is that right?

also this line has me confussed

_1*%call_yes*%draw yes

how can i put %call when i don't know how often they will call?

Quote:

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Originally Posted by grumpy64

so we need to figure how often he needs to fold to make 2.275? as that is how often we lose if he never folds so if he folds 28 percent of the time our bluff is +ev. is that right?

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was just messing around and the above can't be correct

Quote:

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Originally Posted by grumpy64

will do but this is what had me thinking you were saying it was a little over 1 percent

You want to set EV = 0 and solve for x
10 - 10x - 6.075x + 2.66x + 3.8x = 0
10 + (-10 - 6.075 + 2.66 + 3.8)x = 0
10 + (-9.615)x = 0
x = -10/-9.615 = 1.004

on the bottom line does the 1.004 not rep how often they need to fold?

---

Ahh. I see the confusion.

1.004 = 100.4%

Which is why I said the following line, "So x is greater than 100%, which is a problem. Either I made a mistake somewhere, or there is no possible way for Villain's folding frequency to yield 0 EV."

But then, we are actually interested in the inequality, not the equation. This gives us

x <= 100.4%

which is always true. There is no possible range Villain can fold which prevents him from being pwned by this line. His terrible practice of calling river shoves when they're way over a PSB at such an alarming rate is screwing him over entirely.

Quote:

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Originally Posted by grumpy64

also this line has me confussed

_1*%call_yes*%draw yes

how can i put %call when i don't know how often they will call?

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You have to guess at their current range and their raising/folding/calling ranges which come from the current range.

It's always a guess, but you get better and better over time.

Once you have guessed their ranges, then you count the number of combos in their current range. Then count the number of combos in the other ranges.

The %call_yes stat is simply the number of combos they call with divided by the number of combos they currently have in their range.

Same for the other stats.


EDIT: Just like %draw_yes is simply the number of cards in the deck which complete your draw divided by the total number of cards left in the deck.

using some diff numbers to show that i do understand u up to a point
stacks=100xbb
ott pot before action=30xbb 2/3s pot bluff
30x.66=19.8

Let's solve your equation step-by-step.
30−30x−19.8x+2.66x+3.8x=0
30−30x−19.8x+2.66x+3.8x=0
−43.34x+30=0
−43.34x+30−30=0−30
−43.34x=−30
−43.34x
−43.34
=
−30
−43.34
x=0.692201

thing is if x doesn't actually tell me how often they need to fold i don't see how it helps me

Quote:

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Originally Posted by grumpy64

using some diff numbers to show that i do understand u up to a point
stacks=100xbb
ott pot before action=30xbb 2/3s pot bluff
30x.66=19.8

Let's solve your equation step-by-step.
30−30x−19.8x+2.66x+3.8x=0
30−30x−19.8x+2.66x+3.8x=0
−43.34x+30=0
−43.34x+30−30=0−30
−43.34x=−30
−43.34x
−43.34
=
−30
−43.34
x=0.692201

thing is if x doesn't actually tell me how often they need to fold i don't see how it helps me

---

This tells you that, assuming those frequencies, your line is +EV so long as villain folds less than 69.2%. If Villain folds exactly 69.2201%, then this is a 0EV line.


You need to go back and see where the 2.66 comes from. You've changed the value of that outcome by changing the pot and bet sizes.

In your first example, you had a pot of 10 and you bet 7.5, which villain called OTT, so the amount you stand to gain if Villain folds OTR is 17.5. In this example, that should be 30 + 19.8 = 49.8. Then multiply that value by the probability that it occurs. Here, there is an 19% chance Hero makes his draw and a 80% chance that Villain folds to the shove. So 49.8*0.19*0.8 = 7.5696 ~= 7.57

Always list out every possible outcome with the value of that outcome and the chance of that outcome happening. Then multiply the value by the chance to that part of the total EV calculation.
This is actually a very easy thing to create a spreadsheet for, and it will allow you to just change the significant numbers while it does all the calculations instantly.


EDIT: The -19.8 in your example is incorrect, too. That is the amount you lose when you bet OTT, and Villain calls, but you brick OTR and x/f. You will only brick OTR ~89% of the time, so that -19.8 should be multiplied by 0.89 to get -17.622.

The 3.8x is hard to evaluate because your statement of 100bb ESS. Do you mean that you started the hand with that ESS, or that there is 100 ESS in the hand at the point of your decision OTT. Either way... I didn't pay too much attention to it the first time through, and it does matter.


So

30 - 30x - 17.62x - 7.57x + 3.8x >= 0

Note that we want the EV of the line to be greater than or equal to 0

x <= -30/(-30-17.62-7.57+3.8) = 0.508 = 50.8%

When we divide by a negative number the inequality switches direction. We now have that x should be less than or equal to ~51%.

We started with 100xbb

OK, so the 100bb number doesn't directly come up in this calculation, then.

The ESS at the time you begin the analysis, i.e. the turn, is what matters.

Whatever money is already in the pot is dead money and it doesn't matter how it got there, it is not yours. If we want to consider the value of that money, then we need to start at a time before that money got there. When we analyze your hand from the turn, we're saying, maybe what we did to get to this point was perfect, maybe it was junk, I don't care. I only care about how to make the best decision from here going forward, given what information I now have.

This may mean that we're solving for the EV in a situation and no matter how much EV we can get from this line, we lost so much getting to this spot that the whole line from blinds to showdown is -EV. That's OK. We still know that, given where we started, we made the best of it.

***
So in either or both of your scenarios above, tell me how much the ESS is at the start of our analysis. I.e. what is the ESS at the point where you are about to make the semi-bluff?

Then plug that number into the EV calculation and solve for x again.

***
IMPORTANT NOTE: I've gotten a bit tripped up in exactly what x is. I stated in my first post that x is the % that Villain calls OTT. We keep talking about how much Villain folds, so I may have said some backwards things about that greater than or less than sign and whether it means that Villain need to fold more or less than that number.

To be perfectly clear: x is the rate of Villain's calls OTT... and not the rate of Villain's folds OTT.

Ok it seems i have caused some confusion or was perhaps unclear as to what i wanted. Me and V start with 100xbb. Cut to the turn pot has 10XBB. i bet 7.5. Now if V calls and i miss i lose 7.5. this will happen 81 percent of the time as i have a 19 percent chance of making my flush. As i said in an earlier post V will call a shove 20% of the time. So i lose 7.5 81% and gain 100 3.8% of the time. Or is it 90? I know money in the pot isn't ours but u don't u still have to count it as potential winnings? In this scenario we have a 3.8% chance of scooping his entire stack and a 81 percent chance of losing the 7.5 i put in on the turn.

so if he never folds i lose on average 2.275. (100*0.038)-(7.5*.81)=-2.275. I simply want to know the minimum amount V needs to fold for me to make up the difference. so i need to win exactly 2.275 on my turn bluffs to make up the difference.

i know that in a vacuum V needs to fold to my turn bet 42.8X to make it 0ev

Quote:

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Originally Posted by grumpy64

Ok it seems i have caused some confusion or was perhaps unclear as to what i wanted. Me and V start with 100xbb. Cut to the turn pot has 10XBB. i bet 7.5. Now if V calls and i miss i lose 7.5. this will happen 81 percent of the time as i have a 19 percent chance of making my flush. As i said in an earlier post V will call a shove 20% of the time. So i lose 7.5 81% and gain 100 3.8% of the time. Or is it 90? I know money in the pot isn't ours but u don't u still have to count it as potential winnings? In this scenario we have a 3.8% chance of scooping his entire stack and a 81 percent chance of losing the 7.5 i put in on the turn.

so if he never folds i lose on average 2.275. (100*0.038)-(7.5*.81)=-2.275. I simply want to know the minimum amount V needs to fold for me to make up the difference. so i need to win exactly 2.275 on my turn bluffs to make up the difference.

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I'm glad to help. Sorry if I've added any unnecessary confusion.

PLEASE do not start introducing unneeded x's in your posts. It's not 100xbb; it's 100 bb. Not 10Xbb, just 10 bb. We're using the x as a variable and it doesn't count as a multiplication sign in this thread. I'm happy to use another letter if you are attached to using x to mean multiply.

Yes, you count the pot as potential winnings, but the final value of those winnings is NOT 100bb.

You need to know the ESS at the time you begin your analysis. Just knowing the starting stacks and the value of the pot isn't enough due to blinds and antes and any other players that may have VPIP/fold pre-flop. You need to know the state of the game at the point of analysis.

@underline: Your %ages don't add up to 100%, which should be a clue that you haven't accounted for all possible outcomes, or at least that your %ages are incorrect.

Quote:

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Originally Posted by grumpy64

i know that in a vacuum V needs to fold to my turn bet 42.8X to make it 0ev

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Show me.

This list is every possible outcome to your situation.

Hero bluffs OTT, Villain folds:
Hero bluffs OTT, Villain calls, Hero misses draw / Hero loses:
Hero bluffs OTT, Villain calls, Hero hits draw / shoves, Villain folds:
Hero bluffs OTT, Villain calls, Hero hits draw / shoves, Villain calls, Hero wins:

1) Write down the value of each outcome.
2) Write down the % chance associated with each step in each outcome.
3) Multiply the value by any percentages in each outcome
4) Add up all the outcomes (noting that some of them are negative). This is the total EV of your line.
5) IF there is a variable in your equation (I.e. Villain's fold rate OTT), then set the EV >= 0 and solve for the variable.

Quote:

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Originally Posted by MadMojoMonkey

Show me.

---

risk / (risk + reward)
pot has 10 and our bet would be 7.75
7.75/(10+7.75)= around 42.2%

Quote:

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Originally Posted by grumpy64

risk / (risk + reward)
pot has 10 and our bet would be 7.75
7.75/(10+7.75)= around 42.2%

---

Should be {total risk}/{total reward}
7.75/10 = .775 = 77.5%


Normally, when we evaluate the EV of this situation, we're talking about a bet which is called. The 7.75 in the denominator comes from Villain's calling chips, not our own contribution to the pot. Since Villain is not calling, we do not add that value to the reward.


Villain's fold freq is so high because we're assuming that it's a pure bluff and Hero has 0 outs and 0 value if Villain calls.

Quote:

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Originally Posted by MadMojoMonkey

Should be {total risk}/{total reward}
7.75/10 = .775 = 77.5%


Normally, when we evaluate the EV of this situation, we're talking about a bet which is called. The 7.75 in the denominator comes from Villain's calling chips, not our own contribution to the pot. Since Villain is not calling, we do not add that value to the reward.


Villain's fold freq is so high because we're assuming that it's a pure bluff and Hero has 0 outs and 0 value if Villain calls.

---

ok well i got the formula i used from here http://www.splitsuit.com/simple-poker-bluff-math . in big blue letters near the middle of the page he says use risk / (risk + reward)

Crap.

My bad.

Grrr.

I'm not saying your wrong just wondering why your math is different then his

I'm wrong. He's right.

It's obvious that if you make 2 PSBs, and you lose 1 and win 1 that you've broken even.

Quote:

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Originally Posted by MadMojoMonkey

I'm wrong. He's right.

It's obvious that if you make 2 PSBs, and you lose 1 and win 1 that you've broken even.

---

i didn't want to insult anyone. Particularly when u have been nice enough to offer me help.

speaking of poker math why is it so dang hard to find formulas that account for money u can make on the next street. Pretty much every semi bluff and bluff calculation i can find on google assumes you're all in

You're cool. I'm not insulted by you, only by my own self-criticism.

By the way... the following question touches one of my pet peeves, so bear with the semi-rant that comes. It's not about you, so much as the failed education system which tells people that it's OK to be voluntarily ignorant.

Quote:

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Originally Posted by grumpy64

speaking of poker math why is it so dang hard to find formulas that account for money u can make on the next street. Pretty much every semi bluff and bluff calculation i can find on google assumes you're all in

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Well, first off, I told you exactly the math for a full calculation when you are not all-in, and all you had to do was ask. I'm not so sure I see what you mean by the information being hard to find.

BUT, assuming that you have a point which I have simply not observed, I assume that it's mostly because people have been told that it's OK to not be embarrassed if they can't do grade-school math. So people who are fully capable of doing the math say, "it's hard," as if the difficulty of math-thinking is even remotely comparable to the actual difficult things they deal with (and solve) on an hourly basis.

Also, people want to believe that there is some "neat trick" that they can memorize to be good at poker, and when they see a simplified, dumbed down EV calc which assumes they're all in, they shy away from it. So what's the point of showing them a more complicated EV calculation with fewer assumptions when they don't even care enough to try to understand the most simple forms?


E.g. you've still not answered these 5 questions:

Quote:

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Originally Posted by MadMojoMonkey

Hero bluffs OTT, Villain folds:
Hero bluffs OTT, Villain calls, Hero misses draw / Hero loses:
Hero bluffs OTT, Villain calls, Hero hits draw / shoves, Villain folds:
Hero bluffs OTT, Villain calls, Hero hits draw / shoves, Villain calls, Hero wins:

1) Write down the value of each outcome.
2) Write down the % chance associated with each step in each outcome.
3) Multiply the value by any percentages in each outcome
4) Add up all the outcomes (noting that some of them are negative). This is the total EV of your line.
5) IF there is a variable in your equation (I.e. Villain's fold rate OTT), then set the EV >= 0 and solve for the variable.

---

Why is that?

Quote:

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Originally Posted by MadMojoMonkey

You're cool. I'm not insulted by you, only by my own self-criticism.

By the way... the following question touches one of my pet peeves, so bear with the semi-rant that comes. It's not about you, so much as the failed education system which tells people that it's OK to be voluntarily ignorant.


Well, first off, I told you exactly the math for a full calculation when you are not all-in, and all you had to do was ask. I'm not so sure I see what you mean by the information being hard to find.

BUT, assuming that you have a point which I have simply not observed, I assume that it's mostly because people have been told that it's OK to not be embarrassed if they can't do grade-school math. So people who are fully capable of doing the math say, "it's hard," as if the difficulty of math-thinking is even remotely comparable to the actual difficult things they deal with (and solve) on an hourly basis.

Also, people want to believe that there is some "neat trick" that they can memorize to be good at poker, and when they see a simplified, dumbed down EV calc which assumes they're all in, they shy away from it. So what's the point of showing them a more complicated EV calculation with fewer assumptions when they don't even care enough to try to understand the most simple forms?


E.g. you've still not answered these 5 questions:


Why is that?

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yes you did tell me i meant the info isn't readily available. on google and what not.

Quote:

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Originally Posted by grumpy64

yes you did tell me i meant the info isn't readily available. on google and what not.

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... and I offered my opinion as to why that is, but you didn't answer my question.
Specifically, the final line of my previous post.

I suspect that the general answer to your own question coincides with the reason that you have not followed those 5 steps.
(No judgement from me. Like I said, I'm a geek about this stuff.)

For what ever reason, I told you exactly how to do this, but you have not yet (given me any sign that you have) done it.
I suspect this is indicative of a common theme. Whatever your own reasons for not doing this are probably a lot of people's reasons for not doing it.


I mean... there's a lot of guess work when it comes to an actual calculation. You have to guess Villain's ranges for each decision point, and no one likes to know they're wasting time chasing down a solution based on a handful of guesses. However, it is by doing exactly this over and over that you build your skills in doing it. Eventually, you see all sorts of patterns in the calculations and you can make quick educated guesses as to the "ballpark" of the answer w/o doing the full calc. That's when the time spent studying transfers to live skills at the table.

Quote:

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Originally Posted by MadMojoMonkey

... and I offered my opinion as to why that is, but you didn't answer my question.
Specifically, the final line of my previous post.

I suspect that the general answer to your own question coincides with the reason that you have not followed those 5 steps.
(No judgement from me. Like I said, I'm a geek about this stuff.)

For what ever reason, I told you exactly how to do this, but you have not yet (given me any sign that you have) done it.
I suspect this is indicative of a common theme. Whatever your own reasons for not doing this are probably a lot of people's reasons for not doing it.


I mean... there's a lot of guess work when it comes to an actual calculation. You have to guess Villain's ranges for each decision point, and no one likes to know they're wasting time chasing down a solution based on a handful of guesses. However, it is by doing exactly this over and over that you build your skills in doing it. Eventually, you see all sorts of patterns in the calculations and you can make quick educated guesses as to the "ballpark" of the answer w/o doing the full calc. That's when the time spent studying transfers to live skills at the table.

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Ok well i have paid attention to u but one problem i have had is this "Hero bluffs OTT, Villain folds:" I don't know how often V folds the turn. that was the whole point of this thread i want an equation that tells me how often they need to fold.

as far as my math skill i can do some algebra if somebody else came up with the question as far as inventing my own formulas from scratch nope.

Quote:

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Originally Posted by grumpy64

Ok well i have paid attention to u but one problem i have had is this "Hero bluffs OTT, Villain folds:" I don't know how often V folds the turn. that was the whole point of this thread i want an equation that tells me how often they need to fold.

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Start by assign the unknown value (Vill's % chance to fold OTT) as a variable.
(I used x as the variable, but literally anything will do. Use a star or a cat face for all it matters, it's just a place-holder.)

Then do all the 5 steps.

You will have constructed the equation you need to solve.

You will have the EV equation, with 1 variable in it. Now the trick is to solve it for the variable. It should always be a little bit of algebra and no higher math is needed.

Quote:

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Originally Posted by grumpy64

as far as my math skill i can do some algebra if somebody else came up with the question as far as inventing my own formulas from scratch nope.

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If you stick with me in this thread, I can definitely teach you how to set up this kind of equation as pertains to poker math.

It's all rather straight-forward when it comes to EV calculations. The harder stuff comes into play when you want to make predictions based on stats, but we're not even discussing that. In the context of EV, we pretty much always treat a stat as though it is exact. While this may not be perfect, you should be able to see how the imperfections change the result with just a little bit of messing around with the equation.