ChunkyMonkey

My equity is 45%. So that means if we played this hand loads of times, I will win 45% of the time.

I'm nitpicking, but it means you only expect to win 45% of the time. There is no guarantee of course. You'll also need a "reasonable sample" before it converges to an average of 45% but yes.

To make the call my pot odds are 1:3 or 25%. Now what do these pot odds mean??

The pot odds don't care if you've made the call or not, they just are 25% and that's it. Here is exactly what these pot odds mean, nothing more and nothing less: you must pay (risk) 1 for a chance to win 3. That's it. The final pot is 4, and 1/4=25%. Your risk of 1 represents 25% of the total pot.

Does it mean if I make the call, I win 25% of the time.

No, whatever happens after you make the call depends entirely on your equity, not on your pot odds. Your equity determines how often you win (45%). Your pot odds alone have no bearing on whether or not you'll win or lose, they are independent from equity. Now imagine making the call loads of times. Obviously each time you do that you're throwing the 1 into the pot of 3 and you aren't winning every time. That doesn't feel nice on its own, but then you remember how 45% of the time you actually win the 3 (plus your 1 investment) and on 55% of the time you only lose the 1. So on average, for each time you play that exact situation, your ev is +0.8.

The only thing I dont get it is how the pot odds connect to equity. Lets say an opponent bets big creating bad pot odds

I understand why it seems that way, but pot odds are only ever good or bad relative to our equity. You can't just say your opponent bets big creating "bad pot odds" because what makes them good or bad is our chance of winning.

I know if the flush hits I likely I win, surely I need to call because otherwise he can just run me over. In theory, the opponent could constantly bully me out of pots with big bets

This logic is faulty and can be used to justify never folding anything, because "there's a chance you can win". A chance to win (i.e. nonzero equity) is not a justification for calling. Only your EV matters. That is why you wouldn't play a coinflipping game where you pay me $2 if it's tails and I pay you $1 if it's heads - you will lose over the long run. This is entirely down to the pot odds offered combined with your equity, which is what EV shows you. If you are unfamiliar with calculating your EV, you should give it a go and try out different scenarios. It really is the only way to see why this is important.

I feel like this might be the issue then. What does it mean to think you can beat the game? I hope not just a feeling, or just winning for the last 10,000 hands.

Take the classic flush draw on the turn scenario for example. Imagine the pot is $37.83 and your opponent jams for another $12.17 and shows you he has a straight with no blockers. The pot is a nice round $50 now, and you only have to call $12.17 for a shot at winning the $50, but unless you hit on the river you're dead. Should you call it? It doesn't matter that this is contrived - you have 19.57% equity and a decision to make.

The only way you can know that this is a game you can beat is if you can correctly make use of the pot odds in this scenario to make a +EV decision. You can't just look at your hand and say "I don't have a made hand, so I fold", because that means you will never get to hit your flush draw and your opponent can bet $0.25 here and you'll always fold, because you don't have a hand. You also can't look at the bet of $12.17 and yolo call just because "it's cheap", because you haven't defined what it means to be cheap. It is your pot odds that define what is or isn't cheap. Therefore you must weigh up your equity with your pot odds and see how much you'd make on average, in the long term. Or in other words, calculate your EV.

I strongly recommend writing out some example scenarios and calculating your EV in each to see how your pot odds have a direct impact on your EV. It is the only way to clear things up.

P.S pls dont take my comments as me saying your wrong. I know I'm misunderstanding something. I'm just writing my full thought process, hoping someone can see my misunderstanding.

No worries, I completely understand the feeling.

Pot odds well to me at least, seem to be just odds. Odds tied to nothing (no hand).

That's correct - they are not tied to anything other than the pot. As I mentioned above, they are a standardised expression of your risk relative to the size of the pot: how much do you need to pay to play? On their own they mean nothing.

Let me ask then - if we play a game where you risk only $1 to win a whopping $3, should you play or not? No other details about the game.

why would that have any affect on my strategy

Because equity alone isn't enough to make a decision when doing so requires you to take a risk. You want to know how much you win when you do win, and likewise how much you lose when you do lose. If you don't risk anything, then everything is +EV because you don't lose anything for trying. But that isn't poker.

Think about this: If we play a coinflipping game where I pay you $1.00 every time a fair coin comes up heads, and you pay me $1.10 every time it's tails, would you like to play? Look at the EV for it: EV = (equity * gain) + ((1-equity) * -risk). The coinflip is EV = (.5 * $1) + (.5 * -$1.10) = -$0.05.

What about a roll of a die? I give you a $1 if it comes up 6, otherwise you give me $0.19. How do you know whether it's worth taking my bet? We clearly can't just look at our 1/6 equity and decide because we need to know our risk and how much we gain if we win.

If my opponent never bluffs in a particular spot regardless of good or bad pot odds, I should fold. Likewise if my opponent has a tonne of bluffs in a spot regardless of the pot odds I should be calling

But this isn't a fair comparison. If your opponent never bluffs in a spot, you should fold because you figure that your equity is 0%. As I said above, if you have 0% equity, no pot odds in the universe can justify a call. But you should only call "regardless of pot odds" if you have 100% equity. If you don't have 100% equity, what you really mean is that you win often enough against his range to make calling profitable. How do you do that? You factor in pot odds. This is what lets you decide whether to call given your equity.

It ultimately comes down to EV. If it's not clear still, I suggest opening up excel or some other office, putting in some numbers, and seeing what happens when you tweak the dials of risk and equity, and especially what happens when your pot odds % approach your equity.

Pot odds are a standardised expression of your risk relative to the size of the pot. Having to call $1 for a pot of $2 has the same pot odds as having to call $500 for a pot of $1000.

They tell you how much you have to risk relative to how much you stand to gain. This is meaningless until you combine that information with equity because you can't tell if pot odds are "good" until you know how often you win or lose.

In the extremes, with 100% equity any pot odds are favourable; with 0% equity no pot odds are good enough to justify continuing.

Most cases are in between that. When your pot odds equal your equity the EV is 0. When your pot odds are smaller than your equity (e.g. 33% pot odds vs 40% equity), then the EV is positive because you risk less. When your pot odds are larger than your equity, your EV is negative because you risk more.

This idea of risking more or less is a bit clearer when you think of equity shares. If you take your equity and multiply it by the pot size, this gives you your "equity share" of the pot. If that equity share is larger than the amount that you have to risk, then it is good because your hand is worth a larger % of the pot than the amount that you have to risk. If not, then your hand is worth a smaller % of the pot than you have to risk.

Your equity share is both the % of time that you win the hand as well as the % of the pot that you will gain on average, so you want that to be higher than what you must risk to realise that share.

Note that the perspective "flips" when dealing with ratios (but the maths stays the same). For example, 4:1 pot odds is a larger (higher) ratio than 3:1 win odds (equity), but because 4:1 == 20% but 3:1 == 25%, your equity is larger than your pot odds, so it is good. In other words, when dealing with %'s you want your pot odds % to be less than your equity %; when dealing with ratios you want your pot odds ratio to be greater (higher) than your win odds ratio.

RaoulFlush (sorry don't know how to reply under your specific comment) good point, and I was not initially thinking about how datamined hands could be used to exploit specific players, but rather to inform our understanding of a player pool. But I do find it still quite a gray area: I could datamine 1k hands on someone and it is no different to playing 1k hands, but all of a sudden I am "cheating" when I buy it but not when I play for the hands. Granted your example with 200k hands is far clearer, but it is not beyond possibility that you could play 200k hands against someone (maybe heads up in a small player pool, but I know I'm stretching the argument).

I just hear a lot of talk about "the player pool" as a whole for some quite specific spots, and I feel like most of these claims are unjustified if they are not based on actual analysis of a large dataset. Datamining hands would support these claims, and in my opinion would be the only way to do so.

But this is information that one would obtain by just observing anyway (it is not like we gain some secrets about players' hole cards). What makes it cheating when they are bought but completely ok when we sit and accumulate those same hands via our PT4? Or you mean it is "considered cheating" by the poker rooms?

Re-bumping this, there were some really golden series on that site! I still have some saved and am quite tempted to resurrect Apex Predator, & the thin red line now that I'm coming back to playing. I wonder how relevant they are today?

I keep reading about those issues with improva, blah234, and sthief. Does anyone know what the hell that was all about?

What made hands do we have here? AA/KK/AK/KQs and that is about it unless we are min 4 betting 66 or 44. What draw do we have? Do we 4b much beyond AQs? Maybe A5s?
Probably definitely no 66 or 44, but draws I can imagine we might have A5s if I'm feeling dangerous (I'm probably not).

Regarding postflop betsizing, I guess this is another leak of mine to be playing too prescribed. I picked up the ~1/3 psb in 4bet pots and pretty much never think about betting bigger unless I'm against a complete drooler.

You say jamming non diamond turns. But what then is the plan for the 20% of time when a lovely diamond slaps the turn? Every possible outcome feels difficult.

When you say at the top of my range you are right, I can't actually see myself with a better hand at all in practice. So does this mean that I need to have some more bluffs in this spot preflop (ignoring my silly size)?

Ignoring this specific hand where it seems unanimous that river is a call, I wonder what are the implications of (1) being at the top of my range, and (2) facing a spot where I know the population underbluffs and I'm f'd? Feels I can always justify stationing because I'm at the top of my range, but it seems like a bad justification unless villains are all playing balanced.

I guess we found a leak in my game for not thinking enough about my 4bet sizing :D it is a completely silly sizing looking back.

About the river. My question is, if we have this view of population tendencies (which I think is pretty reasonable), and if I have no other reads on villain, then shouldn't my default be based on the population? Otherwise what is the point of thinking about population tendencies at all if we won't use them when they matter the most (i.e. when we are readless vs a specific villain)?

Interesting. I would have thought that playing 4bet/fold with AQ and JJ would be questionable with the logic being if you're going to fold after a jam you should just call and see.

On a side note, how do you find snowie? Haven't seen people speaking about it much - seems like everyone is using Pio these days.