Let's say on the turn you hold a NFD and villain bets pot.

Pot is $7.50 before villain bets, now villain bets $7.50 and of course you are facing a bet of $7.50 and the pot is $7.50.

You calculate that you have 14% equity to hit your NFD, not 18% bc you figure villain has a set and you don't have 9 clean outs.

How do you calculate, precisely, how much money you need to make on this call to break even?

I know the equity to call is 33% bc it's a PSB. I know I have 14% equity to hit my draw.

But I have no ****ing idea how to determine the amount I need to earn to make the call breakeven EV .

Thanks to anyone who can do this.

So you want to figure out how big the final pot needs to be for your call to break even. You can use the normal EV equation.

EVsingleevent* = p(event)*payout of event

EVtotal = sum (EVsingleevents)

Basically your total EV is the summation of the individual EVs of each event that might happen.

In your example event 1 is we win the pot after our call (P) plus any additional bets on the river (I) and that happens with probability .14 and* event 2 we lose our 7.50 call. Since we are looking at river play we ALWAYS lose that call when we don't hit so there is no probability factor that goes with it.

So our EV total would look like this:

EVtotal = .14*(P+I) - 7.5

Now in most games there will be rake (R) so we can factor that in by subtracting it from our winnings:

EVtotal = .14*(P + I - R) - 7.50

Now since folding is 0, we need to have at least 0 total EV for calling to be as good as folding, so we will use an inequality to solve for I:

EVtotal >= 0
.14* (P+I-R) - 7.50 >= 0
.14*(P+I-R) >= 7.50
P+I-R >= 53.57
I = 53.57 + R - P

So any rake can be represented as a percentage of the pot (even flat rakes) so let's make a substitution where R = x*pot and 0 < x <= 1. Since the final pot will be the raked pot R = x*(P+I) here. We can probably safely cap x to say .1 or .15 because even at those levels you should probably not be playing in the game due to rake. Any way let's choose x=.05 just so we can finish our example:

I = 53.57 + x*(P+I) - P
I = 53.57 + (x-1)*P + ×*I
(1-x)*I = 53.57 + (x-1)*P
(1-.05)I = 53.57 + (.05-1)*P
.95*I = 53.57 - .95*P
I = (53.57 - .95*P)/.95

Since we know P = 7.50*3 = 22.5

I = (53.57 - 22.5)/.95 = 31.07/.95 = 32.71

Check our work:

.14*(22.5+32.71) - 7.50 > 0
.14*(55.21) - 7.5 > 0
7.73 - 7.5 > 0
.23 > 0

So I think that is right. It makes sense to me any way.

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So you are saying we have to make $32 on the river to make the turn call just breakeven?

That math I'll have to read it a few times - Is there no shortcut formula that can get us very close - excluding rake and what not? To just ball park it?

Given the assumptions, your model looks good but you made a slight error in solving for I. The mistaken equation should be I = 53.57/.95 – 22.5 = 33.89. Then following through you will get 0 >= 0.

I rarely include rake in models I develop but your doing so may make me change my mind.

OP here is a short cut formula:

A much simpler equation for solving implied winnings is the following:

I - rake= C$*(Card Odds – Pot Odds)

where C$ is the call amount (7.50),

card odds = 1-eq/eq = 0.86/0.14 = 6.14

and pot odds = pot after villain bet/ call amount=15/7.50 = 2

Then I – rake = 7.5*(6.14 -2) = 31.05. Estimating rake to be about $2, you have I= 33.05, close to your result.

The model does assume that if you hit the flush, you will always win which obviates accounting for reverse implied odds -- hitting your draw, betting and losing. OP avoided this by reducing the outs by 1.

To include reverse implied odds, you can introduce terms that represent (win given hit), and (lose given hit) and then you interpret the equity term (the 0.14) as the probability of a hit. For this example, unless hero has the flush suit Ace, he could lose to a higher flush if a flush card falls on the river. A further extension is to introduce the probability villain will call given you bet, and for flush draws, it is quite possible to be less than 100%.

I think this should work:

(Equity you need/Equity you have)*Pot after you call

(.18/.14)*22.50 = 28.93

Basically think of the equity you need to make a break event call as a proportion of the equity you have. In this case you need roughly 128% of your current equity so you need 128% of the current pot to make the same call.

We can still calculate rake from here 22.50+28.93 = 51.43 *(.05) = 2.57 + 28.93 = 31.50

Actually just use statmanhal's equation because he is normally right more often than not :-)

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Can anyone else confirm this equation? It seems to work under my OP set up scenario

(Equity you need/Equity you have)*Pot

like I said, I'm only interested in a ballpark number - If it can get me CLOSE I don't care about the exact. Because I'll have to do it real time in real situations at the table , etc.

This number just feel really wrong! Please tell me if it's the amount needed on the river to justify the turn call, or if it's the total pot amount needed in order to justify the call!

So do I need to win an extra $31 on the river??? Or is it only like $9???

Because if I call a pot bet on the turn, with 14% equity, this means the pot on the river is $22.50 in my scenario!

So with NFD, I have to overbet the pot or have villain bet/call my river jam because the amount I need to win is clearly greater than the total pot size on the river!

This is so counter intuitive to me I need an answer to this question please.

I - rake= C$*(Card Odds – Pot Odds)

where C$ is the call amount (7.50),

card odds = 1-eq/eq = 0.86/0.14 = 6.14

and pot odds = pot after villain bet/ call amount=15/7.50 = 2

________________________

We can use simply I=C$*(Card odds - Pot odds) , yes?

I am not following the the 3rd line of card odds = 1-eq/eq=0.86/0.14=6.14

Where did you get 1-eq/eq from? Why did you do 1-eq/eq=.86/.14? What is the 1- part of it? That seems to be missing.

The pot odds I understand 15/7.50=2 makes sense.

So it would be I=$7.50(Card odds-2), but what is card odds? That is the part I don't understand.

So in the end it should be

I = $7.50(6.14-2) OR I=$7.5*4.14 = 31.05

Also thank you for the time, I am assuming that the answer of $31 is the amount I need to win

So when someone says "Yes I think you should call" they probably have no idea that I need to win $31 more just to break even.

My common sense "guess" would have been at most $15 or so but $31 really just amazes me

(size of bet)/(size of pot+size of bet+X)=0.14(in this case if we dont lose any money ever otr)
7.5/(15+7.5+x)=0.14,x=31.We can check ev
EV(call)=0.86*(50-7.5)+0.14*(50+15+x)=50,x=31

If you lose same when you hit your non-clean out as you would win when you hit your good outs.Then you can do the same thing just your equity is 12%.

Its true that 31 $ is lot but that is because his range is set,so your A high has no SDV and A is never an out which is not the case most time in real game.

Yes ok I understand now.......usually facing a normal sized bet an A out is clean or they could have weaker flush draw, but this villain donk potted the flop and turn multiway so I figured it's probably just sets - when the K hits the turn he pots it again.

So if I use this equation in situations where I have let's say 20% and the bet size is 75%, then it should be significantly less.

That formula converts your actual equity into odds. Statmanhal is using cards odds as a shorthand for the odds your hand actually needs to make a break even call.



You can convert between probabilities and odds. Odds is just the ratio of probabilites or relative frequency of out comes.

So if you have something that is 2 to 1 you can read that as "for every 3 occurrences of some event, outcome 1 is twice as likely to occur as outcome 2". To get the probability you would just add up the total (2+1) and divide each number by that total. So one event occurs with probability 2/(2+1) and 1/(2+1).

To convert probabilites to odds you need to calculate the probability of each event occuring. Since we know that the probability you win is .14, then we need to know the probability you don't win to convert to odds.

Now we know that in probability the total sum of probabilities need to add up to 1 (or 100% if expressed as a percentage). So since we only have 2 outcomes here we can calculate the probability you don't win which:

.14 + q = 1
q = 1 - .14
q = .86

So now convert to odds:

.86/.14 = 6.14

So it's 6.14 to 1 odds you lose the hand.

Again it's just a short hand expression for your equity expressed as odds.

So in the end it should be

Yes that's just the extra money you need to make on the river not including the pot after betting on the turn. You can check yourself by plugging into the EV equation.

.14*(31.05) - 7.50 = -3.15
As opposed to
.14*(22.50+31.05) - 7.50
7.497 - 7.50 = -.003

Since we have some rounding errors in some places it's not exactly 0 but close enough.

Very simple way I use in-game.

Decide how big you will bet if you get there.
Estimate how often villain will call you
add that percent of the bet you will make to the current pot size and see if you have the right pot odds.

ex;
there's 100 in the pot on the turn
villain bets 50
you decide that you will bet pot sized on the river if you get there (that will be 200, the pot, villains bet, your call) if you think about half of villains range is strong enough to call you then you take half of the 200 you intend to bet = 100 and add it to the current pot
so,
the 100 pot plus the 50 bet is 150 plus half of the bet you will make if you get there is 100 more
so that means you expect to win about 350 when you get there

divide that amount by the amount you have to risk is 350/50=7
count that as seven to one implied odds

If you are greater than 1 in 8 (seven to one dog or better) then you can make the call.

I understood the formula, but one doubt is, if I'm on the flop and villain's bet, Do I use equity until the river or just equity to see a turn card ??

In doing an implied odds analysis, the usual idea is to justify making a -EV decision now with the hope of stacking villain on the next street or streets if you hit your strong draw. Therefore, stacking would mean there is only one more bet to make; flop to turn/river, or turn to river, so there would be only one showdown equity and you account for you or villain folding some other way.

A fairly complete implied analysis should consider current bet and EV, stack sizes, future bet size, probability of hitting your draw, probability of winning if you do hit (for reverse implied odds), and probability of villain calling if you do hit and bet. It assumes you fold if you don't hit. As you can see, it can get a bit complicated to say the least.

In my Hold ‘em Mathology blog on Tumblr, I posted a series of articles on this subject that includes all of these elements and show results for draws for sets, flushes and straights. The results are stated in the implied odds you need to make a current -EV call. They can be easily converted to the minimum size of the future bet you need to justify the call.

htthttps://holdemmathology.tumblr.com/post/182944722325/an-advanced-implied-odds-model-part-1p://

But EV accounts for the times you hit and get paid. You wouldn’t knowingly make a -EV call.

With 14% equity you need about 6:1 pot odds. You’re getting 2:1, so you need to win another 4 bets on the river on average.

I didn't get it, if I'm on the flop and villain bets I'm not always have the showdown equity because he may bets again on the turn, so it wouldn't be more realistic to use my equity realization then showdown equity ? I think showdown equity is more if us went all in, no ?
Other think is sometimes he fold to our bet on the river and we don't hit the draw too.

Realized equity adjusts a showdown equity for either hero or villain folding.

If not an all-in bet or river bet, implied odds applies only to the next street and the showdown equity is applicable if the implied odds model includes villain fold probability. It also includes a hero fold for it is assumed that if hero doesn’t hit his draw he will fold to any aggressive villain action. Sure, you can consider other cases such as a check-check or hero bluff raise but that leads to much more complexity to a model that is already pretty complex and is probably not worth doing if unlikely to occur.