Before asking my question I will give the definition of pot odds and effective odds so any reader unaware of these terms can be picked up to speed and benefit from any discussions from this post.

Pot odds:
The ratio of the current pot to the bet you need to call
ex: pot is $100, opponent bets $100. Now the pot is $200 and you need to call $100 to stay in. Thus your pot odds are 200:100. People use the reduced version so its 2:1

Effective odds:
The pot odds when factoring your opponent's future bets.
ex. flop comes and your opponent bets $100 into a $100 pot. Your pot odds are 2:1 but you believe your opponent will bet the turn for another $100. So in reality you need to pay $200($100 now and $100 on the turn) to win $300(current pot($100) + opponents flop bet($100) + opponents turn bet($100)). So the effective odds are 3:2 or more commonly 1.5:1
Note for those confused as to why the pot isn't $400 on the turn in these calculations it's because you haven't actually put in your money yet. Yes its true that when the turn comes you will have called so in reality the pot would be $400, we don't include it because we are using effective odds to assess what our risk to reward ratio is. We want to know how much we will GAIN, thus we shouldn't include the money we will invest to see the turn.

Since pot odds don't factor in future bets, they aren't useful in determining a profitable call with more than one card to come. Why? Because as we saw in the definition of effective odds if I have drawing odds of 1.8:1 after the flop, initially it was profitable to call because the pot odds were higher, 2:1. However after further consideration using effective odds we realized our pot odds are actually 1.5:1 thus making it a non profitable call....Or so they say.

My Question:
Fundamentally pot odds don't work with more than one card to come because your drawing odds are your chances of winning BY THE RIVER, so those chances are only true if you plan on seeing every street to the river. And unless your opponent plans on checking until the river your going to have to make more calls in the future. This is why we consider future bets in determining our true pot odds(effective odds)...but I don't get why...

Here is my confusion. Why should we care what happens on future streets? It seems overly complicated calculating effective odds because we need to guess how much our opponent will bet in the future. There's no real way to know with accuracy in my opinion. Why not simply use the drawing odds of hitting on the turn only, rather than the total drawing odds? This makes sense to me. Its the flop, I want to see the turn, so I'm deciding if paying to see the turn card is worth it. Why would I factor in the river at this point. When the turn comes I can decide what to do about the river at that point in time. This makes sense to me because when the river comes the drawing odds will have changed. Perhaps my opponent's outs have increased, perhaps mine have increased. It makes sense to see the cards and decide at that point.

Poker is complicated. Pot odds are easy to calculate. I haven't heard much of effective odds, but I have heard of implied odds, which is basically the same concept.

It's pretty simple why we care about the implied odds and not just immediate pot odds. Because sometimes you don't have direct pot odds to call a bet, but if you almost have odds, you likely have the implied odds to make continuing profitable.

Let's say you have AhJh in position on the turn and the board is KsTh7h2d. The pot is 100 and you have 400 behind. Out of position bets $100. If you're behind, you have 10 outs to the nuts (not including a board pairing heart, and technically there could be less if your opponent blocks some outs). You may have as many as 15 outs if your ace is a live out along with board pairing hearts and 18 outs if your J is a live out (like if villain is bluffing with the best hand with a hand like T9, 87, 76, etc.)

Let's say you have 15 outs. 15 out of 46 cards is about 32% (technically it is 15 out of 44 cards since your opponent has 2 cards himself, but he could also have a hand like KQ so one of your Q outs may not be live). You don't actually have the pot odds to call a pot size bet here, since you need 33% equity to call. But as a heuristic, you know you are going to have the implied odds to call, because you ALMOST have the pot odds to call, and if you can win more money some of the time (possibly all of the money some of the time), then you know your call on the turn will be +EV.

If your equity is 32%, if you only had $100 left on the turn to call off into the $100 pot, your EV would be $-4 (because althea pot will be $300 if you call and you win 32% of the time, so your expected value is $96 minus the $100 you put in times call). But let's say after you hit 32% of the time when, you actually win all of the money (the entire $400 stack plus the $100 in the pot on the turn) 33% of the time, and the rest of the time you only with the $300 pot. Now your EV is +$17.

And things can get vastly more complicated than this. When you're on the flop or turn, you have to factor in your ability to bink and get paid on turn or river, or pick up a backdoor on the turn, and you have to factor in the possibility thst sometimes you have the best hand with a hand like AJ calling the flop, and sometimes you won't have the best hand, but you will get to bluff later to steal the pot and that will be a source of EV for you.

In reality, it is EV we care about, not pot odds or implied odds, but as you alluded to, this is very difficult to calculate. The more you study the game and apply your studying when you put in your hours ro play, the more you will be able to identify the spots where you will be able to call a bet on an earlier street with or without the direct pot odds, because you know you can get paid off if you bink or you may be able to bluff on a later street. Furthermore, you can identify spots where you can even raise bets as a bluff, such as when an opponent is cbetting the flop too frequently with air and maybe you have a hand like a gutshot with 1 over and a backdoor flush draw on the flop, so you check raise him. You know it is profitable because sometimes he just folds and you win, and when he calls, sometimes he folds a later street, or you improve on a later street and you win a very big pot. Ultimately you want to get to that point in poker. Learning pot odds is like the first step, and implied odds is sort of the next step in eventually crossing that bridge.

Thank your for your reply! This was helpful. After some time learning more I came to realize "effective odds" is just a term David Sklansky coined that is never really used in the poker community so most people don't know what it is. In Theory of Poker, it basically states that effective odds what your "real odds" are. Meaning to say, if your post flop with 2:1 drawing odds and your opponent is very likely to bet the turn, its best to factor in the future bet into your post flop decision. When adding the turn bet when I'm calculating the pot odds postflop it would of course worsen then odds.

Ultimately this is just a really confusing way to say, "Although you have the right pot odds on right now, consider what your opponent is likely to do in the future because it may make your call less profitable than you realize". This is similar to the gist of your reply.

This leads me to the root of my confusion. How should I calculate odds with more than one card to come? For example, if I have 4 cards to a flush on the flop(9 outs), my odds using the 4 2 rule is 36% by the river. But using these odds doesn't seem quite right because that's assuming I see the river card and there's a good chance I won't see it given my opponent can bet again on the turn and force me to fold. Should I instead call postflop using only my turn odds of 18%? This also seems counter intuitive because preflop the starting hand equity is based on assuming you go to showdown. It seems more correct to be consistent with how I calculate my odds. Meaning I should continue to use my full equity, in this case 36%, to inform my decisions.

You can't reduce it implied odds to a comparable number to direct odds. What ultimately matters is EV. Solvers are good at calculating EV im non-all in scenarios on early streets. Humans are not.

What a solver does is calculate what the maximum exploitative strategy is for both players and calculate an EV for each action you can take, check, call, bet, raise (fold is always 0 EV). It's not really practicable for humans to calculate the EV in a spot for each action because you have to take into consideration every hand in your opponent's action, every card that can come out on future streets, and every future action you and your opponent can take. Sometimes you call flop out of position and turn checks through. Sometimes you face a 2/3 pot bet on the turn when you don't hit your draw. Sometimes you face a 150% pot bet without hitting your draw. Sometimes you hit the turn and it checks through and the river pairs the board, and you bet and villain jams on you.

You can kind of calculate your EV using some rough assumptions on each street of the possible directions the game tree can go. For example, you can say 9/47 cards on the turn complete your draws, while 36/47 don't, so maybe 36/47 of time when the draw doesn't complete, you face a 2/3 pot bet 50% of the time and it checks 50% of the time, then figure if you call the 2/3 pot bet or fold, basically do this for every scenario, probability weight them, and approximate an EV.

But again, this isn't really practicable. It may be a useful exercise to do for a spot or 2 in excel for the sake of studying so you can understand the mechanics of EV and implied odds, but this is in general not an efficient way to study.

As a rule of thumb, if you almost have direct odds to call, you likely have the implied odds to call, especially when you are in position, especially when sometimes you actually have the best hand (IE with A high), especially when the turn can check through and you can get a free card at a reasonable frequency (IE villain is less aggressive).

You're never really going to be able to calculate EVs on the fly. At a certain point if you really want to improve at understanding better when and how to continue (call vs raise) when you may or may not have direct odds, you probably want to study using solvers and/or tools like GTO Wizard. Or don't. It's a matter of how much do you want to improve and how interested you are in studying using solvers.

For me personally, even when I had a day job, I have always found studying with solvers to be really fun and interesting, and it has given me a great return on investment. Now that I have been playing poker full time for a little over a year, studying with solvers is a no brainer- clearly worth it to develop and maintain an edge.

Reference hand from last night that contributes to this discussion somewhat:

Folds to me on BTN and I haz J J and open 10 at 1/3, SB fish and BB OMC call. Flop As 7s 2c SB open folds x x Turn 9s OMC bets 20 into 30 I CALL getting 5:2 with a 4-card FD and 2 Jacks 11 outs one time ~22% but need 28.5% to break even so need to win 30$ OTR to make profit.

Thought about it after, would OMC ever pay off 30$ on a 4 flush? He sometimes even has a higher spade. And he always had at least an A.

Haven't read Sklansky's book in a few years. Don't remember effective odds from the book, and probably wouldn't understand the concept well enough.

Pot odds are simple enough, but seem to matter most on the river. Prior to the river, we're mostly thinking about implied odds.

That's not to say it's not worth considering what our opponent may do on the next street. It absolutely is worth considering. If an opponent c-bets the flop, we should think about whether or not he'll bet turn, and for what size, and if we'll be able to continue. Having some sense of what our opponent is going to do on a future street helps when deciding whether or not we should continue on the current street.