Hi friends !
Assuming we hold A2hh OOP against an oponent in a single raised pot in cash games and the flop come Kc7h3s and we check.
Villain fire a 1/2 psb which gives us a 25% pot odds.
We have an over card and a backdoor flush and straight draw, which means 21 outs to make our hand improved by the turn assuming Villain hold a simple pair which beat us (3 outs for an ace, 8 for completing a straight draw card and 10 for completing a flush draw card)
Should we calculate our equity OTF by just multiply and add 2% percent like below: 21*2+2 = 44% pot odds which could make our call +EV because Hand Equity > Pot odds ?

If this is not the case, more generally how to evaluate a backdoor draw equity with a simple formula ?

First of all, "pot odds" refers to the odds the pot is offering us, i.e. how much it costs to continue vs how much you can win. You want to compare your odds of winning to the pot odds to decide on a call.

You do *not* compare your odds of "improving" to the pot odds, especially you don't consider gaining a flush or straight draw to be an "improvement"

The typical way to evaluate backdoor draws is to calculate the chance of hitting both cards. The reason you use "about 2% per out" is that on the flop you know 5 cards - your hand and 3 board cards. There are 47 unknown cards so any given card has a 1/47 chance of occurring on the turn. 1/47 is close to 1/50 which is 2%.

To calculate the chance of hitting a backdoor flush you'd say "I have 9/47 cards to hit on the turn, and then I have to hit 8/46 of the remaining" so you'll get a flush
10/47*9/46 = 4%
which is worth a little less than 2 outs.

You're also over-counting because 2 of your straight cards are also flush cards.

I think you'd be better served with using a simpler example to start with and exploring the numbers, i.e. start with just a backdoor flush draw and see what the numbers look like, then maybe add an overcard, then maybe add a straight draw.

First of all thank you for your answer !

If I have well understand, we can't calculate OTF outs on turn AND then on river to figure out if our call is ev+ but assume with "what frecquency" we complete our draw by the river.
More generally we have to add 2 outs (proven by your sum) if we have a flush draw OTF, 1 out if we hold a backdoor straght draw (8/47*7/46 without counting card removal effect) ?

To request to my original question, with just an over card and double backdoor draw we have 6 outs (3 ace, 2 for the BDFD, 1 for the BDSD) to win the pot assuming villain don't improve his hand and simply have an overpair ?

Going further we need to win at least a 30BB pot by the river to breakeven at showdown assuming we opened 3.5BB and get cold called ?
(We have 6 outs on the flop, pot is 8.5 BB and villain bets 4.25BB.
We beat Villain 14% of the time ( 6*2 + 2 ) so by making the sum 4.25 / x = 0.14 i found around 30BB)

You're getting closer but now you actually have to consider effective pot odds, which are the same as regular pot odds except they take into account *all* the money you can win vs all the money you'll pay. These can work both against and for you.

For example... your calculations above seem basically right at first glance, except, what if the guy bets again on the turn? Because you need to see both cards to realize your equity, you MUST take that into account.

But then again, if you miss the turn, you'll fold and if you catch the turn and miss the river, you'll fold. If you catch both, you will probably get to make a value bet.

So you have to estimate, how much will he bet on the turn, and how much will I get to bet on the river?

So your effective pot odds will be more like
(pot + flopbet + turnbet + riverbet) : (flopbet + turnbet)
The first part being what you can win, and the 2nd being what you risk to win it

Even this isn't *exactly* right, because you won't call every turn. It's a worst case scenario. This situation is actually quite complex. If I wanted to figure out the true EV of it I'd need to get out a spreadsheet or write a little program, or at the very least spend some time with pencil and paper.

Once I'd worked it out, I would probably have a good rule of thumb for the future, but honestly, it's not something that comes up a lot, so I haven't given it a lot of thought.

Okay right...
This is the "Implied odds" phenomenom ?

Implied odds are a sub-category of effective odds, as are reverse implied odds. Effective odds are simply:
(total reward) : (total risk)

Immediate pot odds are the same thing, but instead of "total" are just for "this round". Effective pot odds involve predicting the future a little bit. They are most useful, imo, when you use them to find the worst and best case scenario, especially in limit poker.

In limit poker, heads up, you can only be forced to call a single bet each street, and the bet is a fixed known size. So worst case is he bets every future street, best case is he bets zero future streets. True effective odds must be between those.

So if the worst case is good enough to justify a call, then you call. If the best case is not good enough to justify a call, you fold. In between, you play poker.

Reversed implied odds i quite the opposite : how much should we invest in the pot by the river to go to showdown with a medium strenght hand ?

Reverse implied odds are when you have a hand that is too good to fold, so you have the call the river. It ties into effective pot odds when you have a hand that is not likely to improve, but where if you call a bet now, you'll be obliged to usually call another.

So say the pot is 100 and your opponent bets half the pot (50) and you think he'll bet half the pot next street too. If you call then the pot will be 200 so the next bet will be 100. Your immediate pot odds are 150:50 or 3:1

Your effective pot odds will be
(100 + 50 + 100) : (50 +100) = 250:150 or 1.6:1

I understand now..

But we need more equity with our hand if we consider effective pot odds ?
Before with immediate pot odds we get a 25% pot odds whereas with effective pot odds we have 38% pot odds !