fold equity

What is the easiest way of calculating, the percentage of time a villian would have to fold in order to show a profit. When you know taht when your called your going to be behind.

i.e AQ flush draw on the turn. You have a 800 stack with 400 in the middle? what % of the time, would i need him to fold to show a profit, assuming he is drawing dead to the nut flush. I think this is 50%+. I can get the first part easy enough.... 66%+ and u'd show an intermediate profit. yet i can't correlate this very well with the outs of my hand.

Anyone, have a quick fire, simple way of working this out correctly? or can you show me the simple math behind it. It would hlep me alot.

Thanks.

you need to have more iformation especcially the board cause that dictates his hand range. i ll show you a pre flop way to calculate it so then you understand the math. One thing is when you are making plays like this its not so much what you have for a hand but his hand range.

you have to have his hand range for example lets say he calls with all pairs above 77, AJs-AKs,AK,AQ.
ok so now we have his hand range all pairs above 77 X 6 ways to make each hand 7X6 =42
AJs-AKs X 4 ways for each hand minus 1 AQs = 11
AK, AQ X 16 ways to make it minus all hands we have already accounted for =18

Now that we have our hand ranges complete we add them up 18+11+42=71

now take hand range and divide by 1326 total hand combinations 71/1326=.05354

you you take that number and subtract that from one and multiply to the power ^ of the number of people left to act (1-.05354)^1 player left to act =.946

so now you take that number and multiply that by what you stand to win if they fold .946 X 1200=1135.2

as long as our final number is larger then our beginning then it is a profitable play in the long run.

probly sounds like chinnese coming from me so if want want to watch a whole 30 min video of this concept for free join pro poker school and watch sheets advanced hold-em concepts vol 1

Overview

The smaller your bet, the less often they have to fold for it to be worth it. For example, if you bet half the pot and you have NO chance of winning if called, they only have to fold 1/3 of the time for it to be a +EV play. If you have a 50% chance to win, then it is a +EV play unless they NEVER fold.

Example (some math involved)

More realistically, say you have a 20% chance to win and you bet 400$ in to a 400$ pot. Then when they call you, you have an EV of -160$ (1 of 5 times you win 800 and 4 of 5 you lose 400). When you fold, you have an EV of 400$ (you always win 400$).

Let x be the probability they call, and y be the probability they fold. Therefore, y*400 + x*-160 is your EV. Seeing where this equation is 0 tells you when you break even, and thus the largest amount of times they can fold before the play becomes -EV. So we can set the equation equal to 0 and do some basic algebraic manipulation:

y*400 + x*-160 = 0
y*400 = 160*x
x = 2.5*y

So when they call 2.5 times for every 1 fold you break even. Any more and you are making money. In terms of percentages, they must be folding at least 28.57% of the time for it to be +EV. [Note: 28.57% = 100%/(2.5+1)]

Limitations

Obviously, in a real poker situation you don't know your odds of winning, but you can make educated guesses (this can only really come from experience). This is also an oversimplification because it neglects any betting on future streets or a possible raise - this only accounts for them deciding to call or fold on one street.

Cheers guys,

I'll look into these scenario's this evening. And i'll watch that video at pro poker school. Thanks for sharing it. ahah algebra..it feels like i'm back at school

Can you please explain what the beginning number is? I feel like you must have missed something because you have to take into account how big your bet is in relation to the pot size. And does the 1200 number represent 'what you stand to win'?

Another thing - you are assuming that you have zero chance of winning if they call, which is not a valid assumption preflop. And technically, you have to make a slight adjustment to the formula above because if player 1 doesn't have one of the hands listed above, it increases the chance that player 2 does. But the difference will be small enough that it shouldn't make any practical difference.

Last thing - why do you subtract one for AQ suited?

This might be a little harsh, but I think this needs to be cleaned up and cleared up a lot before it's very applicable.

Do you do all this in your head before every hand because if so I just need to quit now if this is what the majority of the poker palyers do. Wow!!!

wow that was the most complicated thing i have read and comprehinded in awhile. but i dont do any of that. at least not on purpose. basicly if im going to chase a river card to make my hand the pot has to be able to increase my stack by no less than 20%. and that is after subtracting the chips i put in it. if i have 100 in chips the pot has to have at least 20 chips that someone else put in. it is pot odds sure just altered a little. i dont count my chips as part of the pot because i fully intened to get them back at the end of the hand.

i don't calcalate this in my head sheets explains it much betterin at pro poker school which is free to join and has about twenty video but the best ones are sheets on advanced hold-em. i have created a spread sheet that does this for me. the concept that i was trying to explain is that you always should be putting your opponent on arange of hands. by doing that you can find your equity in the hand if you push. its based on the poss of hand combination and what you stand to win. i see if i can break the math down a lil better but what sheets calls it is if your goin to put your chips in the middle and you wantto know if your making the profitable play based on your opponents range of hands.

the very first thing to know is their is 1326 poss hand combinations to make.

then next thing you have to due is put your opponents on a range of hands in the example above i did that and subtracted one AQs because that is what we hold so that is one less poss hand our opponents can get.

once you have the hand range you divide that by 1326 which is every poss combination. hand range/1326=percentage that the opponent will have on of those hands

the second thing to do is calculate the percentage that your opponents will fold based on the hand range. you have to subtract your above percentage from 1 and then multiply to the power of remaining players to act. (1-%of hand range)^players left to act=percentage that the table is goin to fold based on hand range and number of players left to act

the last thing you do is you take your stack that your pushing all in with and add that to whats in the middle, this is what you stand to win if everyone fold. you then take that total win amount and multiply by percentage that table folds and that will give you your equity in your hand. (your stack+pot)X% calculated from 2nd step

i'll use the example from above and go through all the math only we will say we are 8 handed on the button and its been folded around with only the blinds left to act. we have 50,000 and blinds are 2,000,4,000 with 500 ante. so before any action their is 10,000 in the pot 1/5th of our stack.

71/1326=0.0535
(1-.0535)^2=0.895
(10,000+50,000)x0.895=53,751.7

and as long as our final number is greater then our starting stack it is a profitable play in the long run.

based on this theory it doesn't matter what our hand is because we are calculating our equity in the hand based on an opponents hand range for them to fold. i dont know if this helps in the explanation i deffinently recomend joining pro poker school for free its a great site and where else can you watch sheets break down advanced concepts like this for free. and to answer do most player do this the answer is no but alot of the top online mtt players who do this as their job, do. which is why you sometimes see top players push all in with 62off and get called, thier are using their position and hand ranges from their opponents from the information that have tracked and then making the best profitable play sometimes their wrong which is why you see that 62off but most of the time their are right because by their calculations it is a profitable play in the long run which is all they car about. the cards will always even out for everybody so the ones who can capatalize on better situations and extract more money are going to rise above the rest. but the best thing about this is if your wondering is it more profiatable to push or raise then you will get your answer by doing this math.

P.S. Watch the video its advanced concept volume 1

Great thread but I think I'll have to read it over several times to understand it. I found the video from another post just this morning. Looks like I'm back in school.

yeah sheets breaks it down better because he has the visual aids to walk you through it.