Hi.

I am currently learning how to calculate my pot odds, and something seemed strange concerning how we do it.
Let's consider a simple situation :

POT is 100 (HERO put 40 in the pot, VILLAIN1 put 40, VILLAIN2 put 20 and folded)
VILLAIN1 bets 50.

1) Classic approach: every book says our pot odds are 25% (we can lose 50 by calling but we can win POT+VILLAIN1 bet = 150)

But when we win (hopefully) the pot, some of it comes from our own stack (40 in our case), so that's not really a gain.

2) I would therefore say, if we call, we can win 60 (money in the pot put by other players) + 50 (villain's bet) = 110 and can lose 40 (what we put in the pot) + 50 (our call) = 90, so our pot odds would be 90/200=45%, which is obviously higher.

Could somebody explain why the first approach is the true one? It is moreover totally asymmetric, which is strange.
In the first approach, if we win 25% of the time, we are clearly not neutral$ on average because we have 90 of our money in the pot, and win 110 when we win..

That money is no longer "ours". It's already lost, and belongs to the pot now.

If we fold, we lose those 40 as well.

Yeah but let's imagine the pot is 100 (50 from us, 50 from villain), villain bets 50, we call. We have EV>0 if and only if we win >50% of the time (clearly), but our pot odds are 25%, so they make no sense

In one sense, EV is a somewhat arbitrary number that is used to help make the best decision. It can be defined as the change is stack size as a result of a betting decision. The baseline can be the stack size at the start of the hand or just prior to the decision or any other point as long as it is used consistently.

In OP’s case assume that decision is to call or fold. OP wants to include the 50 he initially put in the pot as a loss if he calls and loses and not include it if he wins. Therefore he is using as a baseline his stack before the hand is dealt. Fair enough. Assume a 25% win rate. Then his EV = 0.25*50-0.75*100 = -62.5. Okay – what is his EV with a fold decision? It would have to be the negative of the 50 he first put in so folding is 12.5 better than calling.

Now let’s do the EV with the stack size baseline being just before the decision. EV is then

0.25*100 – 0.75*50 = -12.5.

The fold EV is 0 for folding doesn’t change the baseline stack size. Again a 12.5 plus for folding over calling. With a consistent baseline you can consider past investments as belonging to the pot with the baseline stack size being just prior to the decision.

Sorry for such a long explanation. ZKesic’s responses are good enough.

Pot odds are used to compare the EV of calling to the EV of folding.

To make it simple, I'll use the example you posted:
You're saying that if we call with 25% equity here, we'll on average be losing 50, right? That's correct. So calling is -EV.
However, how much do you think we're losing if we fold? Also 50, right? So folding is just as -EV.

Ok thanks my mistake is clear now: I believed pot odds were used to determine positive EV instead of call vs fold, that's what makes the difference