Odds Vs Possibility

I did a search, and didn't find a thread like this one out there, but if I missed it, point me in the direction, and I'll be there.

I got 4 spades, I have to ask, what are the ODDS I'll catch my flush on 4th or 5th street right? Or is it wrong, am I actually looking for the possibility that I'll catch my flush?

Let me give further example. Suppose I caught two A high flushes(OF SPADES) in a row(Sequential hands, one right after the other) Ok, next hand I get delt Ax of spades. I see two Spades on the flop. NOW, The possibility would be the same, but the Odds of hitting it a third time would be much lower.(Right?)

Say I was dealt A's. SURE The possibilty of being dealt A's 17 more times in a row is equal assuming the deck is shuffled between each hand, but the Odds are extreamly low. JUST LIKE the Odds of being dealt an ace high spade flush three times in a row.

Anyway, my question is simple really(Despite the post length). When I'm told "pot Odds" Is it really possibility or no?(I'm asking sincerly because I don't know.)

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I got 4 spades, I have to ask, what are the ODDS I'll catch my flush on 4th or 5th street right? Or is it wrong, am I actually looking for the possibility that I'll catch my flush?

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Approx 19% for each card to come.

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Let me give further example. Suppose I caught two A high flushes(OF SPADES) in a row(Sequential hands, one right after the other) Ok, next hand I get delt Ax of spades. I see two Spades on the flop. NOW, The possibility would be the same, but the Odds of hitting it a third time would be much lower.(Right?)

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Sounds like you're saying you get 4 to the flush in 3 sequential hands. In which case the odds of completing your flush are the same. If you have 4 of the same suit then you are still 19% to complete on the turn. Then another 19% to complete on the river should you miss the turn.

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Let me give further example. Suppose I caught two A high flushes(OF SPADES) in a row(Sequential hands, one right after the other) Ok, next hand I get delt Ax of spades. I see two Spades on the flop. NOW, The possibility would be the same, but the Odds of hitting it a third time would be much lower.(Right?)

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No. Each event is distinct.

Pot odds has nothing to do with this. Pot odds is literally the odds you're being offered to call, and the probability of hitting your draw is a fixed amount each time.

Well first off, thank you for your responses.

In strict mathmatical terms, odds are distinctly different than possibility. The possibility of getting pocket aces 100 times in a row is equal, each hand is Distinct. But the Odds of doing it 100 times sequentially are Extreamly low. I don't doubt the the poker term "Pot Odds" addresses each hand distinctly. But are we not actually dealing w/ possibility?(Strictly mathmaticly speaking)

EDIT!
Probability, that's the term I meant. Sry.

Not at all.

Chances of getting AA dealt is around 1/200.

Mathmatically the chance of getting AA dealt to you 100 times in a row is astronomical, however if you've had AA dealt to you 99 times, then the chance of getting AA dealt to you the 100th time is still 1/200. Nothing changes that, its a distinct event.

i believe this is called the "gambler's folly". Lets take an example, say we flip a coin 99 times and it comes up heads every time. One might say that the odds of getting heads on the 100th time is fairly low, considering we already flipped heads 99 times before. However, it is actually still 50% to get heads! While this specific sequence of flips s is very rare, the exact same rarity is true for any other random sequence.

I probably can't explain it as well as the person that came up with it can, but this is the jist

edit: applying more to poker and adding to bjaust's explanation, the odds of getting this specific sequence of hands AcAs, then getting AhAc, then AdAs is exactly the same as the odds of getting this specific sequence 7h2s, KdKc, Js8s.

Probability and odds are directly correlated.

4:1 odds implies a 20% chance of an event happening.

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Originally Posted by swiggidy

Probability and odds are directly correlated.

4:1 odds implies a 20% chance of an event happening.

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Ok. Thank you very much. That answer's my question exactly.

And thank you for the input by others to help further explain. I think we were all agreeing on the same thing(I was obviously not stating it in a clear way however.) Thanks.