Little critique of pot odds

[jackvance]

It's a little side-thinking of mine, but the strategy article about pot odds is actually a bit misleading once you get deeper into it. It doesn't give any false information, but it's rather missing some important clarifications.

Part 1.
1. The first thing I have to say is implied there, I just want to reiterate this to be complete. Let's say you correctly estimate your odds to win at 25%, and you have to invest 25% into the pot (as your opponent raises you exactly 1/2 pot), is it a good idea to make this call? Sure. If I always do this, will I be a winning player? Nope. You'll be a break-even player. But this is pretty self-evident.

2. So let's say I always piously calculate my % to win from my outs, and make sure I have to invest just a bit less than them into the pot.. will this make me a winning player? Nope! Why not? Because the pot odds you calculate here are actually the best case scenario!

Why? Here are the reasons:

- Some of these outs might not be in the deck anymore. They might be in your opponent's hand, or in the hands of other players that already folded. So maybe you'll be chasing a 2-edged straight and think you have 36% to win, but in reality all but one of your outs are in the hands of people that already folded! So your chance to win here would be 8%. And you have no way of knowing this.
=> In principle, you could calculate a more wholesome pot odds theory in which you take the chances that you have less outs than you think and use them as weights to make a more correct weighted average of your chance.. but this'd be largely impractical ofcourse. I for one don't feel the need to calculate this, as it seems superfluous. So just remember that the number you calculate is a little bit of an exaggeration of your real odds to win because of this reason.

- Poisoned outs: You are chasing a straight with a 5 in your hand on a board showing 678, so 4 and 9 are the cards you want. But what you don't know, is that your opponent is holding a T. So half of your outs are actually poisoned! Even if you hit them, you still lose. An absolute worst case scenario here would be that you're paying to chase a flush that your opp has too, pocketing a higher card. So just remember that this possibilty adds a bit more of an exaggeration to your calculations than what your real chance to win is.
Another example here would be when your opp is holding a pp, the board is paired, and you're chasing a flush. Now you have one less out that you don't know about, because one of your outs gives your opp a boat, beating your flush.

- your opp has outs too. This is the case if we calculate across turn and river. Take the previous example again. Aside from the one poisoned out, even if we hit a real flush-out on the turn, our opponent has 2 more outs of his own, which would be the third card of the one that is already pairing the board, because this would give him a boat.

- you might have forgot about some outs. Granted, this can work both in your favor and against it; Just remember that an in-the-heat-battle estimation of your outs might be off. An example would be:
You're holding A7, your opp AK, and the board is A789. So you only give your opp 3 outs to win (the K).. but actually he has 9 outs! Because an 8 or a 9 would make the board pair higher than your pair, and he'll win with his high card K.

- decimal odds: these can generally be ignored, because they work both ways and don't add all too much to odds that in practice are approximations anyway. An example would be that you're holding A7, your opp AA, and the board is 225. Pretty crappy situation, but turn and river giving you two more 7s could still make you win. These kinds of decimal odds should best be ignored.

To conclude: When calculating pot odds, even if you do it correctly, be sure to take a large enough margin. Ie, don't call a pot-size raise to chase a flush because you think your 33% pay is less than the 36% to hit. Not only do you want to be a winning player rather than a break-even player; You actually have less of a chance to win in practice than you think.

Part 2.
But this sounds horrible! Is there nothing that works in my benefit here? Luckily, there is. Two things actually. The first we hear about all the time: implied odds.

I think everyone knows what this means. It probably takes an experienced poker player to correctly assess this value however. Basically even if you pay too much for your chances to win, it might be a winning strategy afterall because in the case you hit, you might make a bigger profit afterwards than the pot you calculated your odds on. In the best case scenario, you destack your opponent. Don't, however, fall into wishful thinking and assume you can destack your opp everytime you hit. He might catch on to the fact that you hit; Or he might not value his hand high enough in the first place to put a lot of money on it.

But there's something else working in your favor. Something that increases your chances to win. You might already have the best hand without knowing it! This is usually the case if your opponent is bluffing. It might also be that he's an idiot who overvalues his hand. Like this one time I called my opp's raises, chasing my flush. I didn't hit.. but won with high card ace anyway! (all the more reason why weak bluffs suck) Another scenario could be where you call a raise to chase your flush, but that raise came from an opponent who was chasing his straight with nothing in his hands either. Or you have a pair and a flush draw at the same time. Not only do you have 9 outs for a flush, 2 outs for a set, 3 outs for 2 pair (all in the best scenario ofcourse as we learned earlier), your pair might actually be the best hand already!

Now, the fact that you will win with high card isn't that great ofcourse, but more generally, chasing your pot odds, you could suddenly notice your opp was bluffing or overplaying his hand, because he backs down. Had you not had a hand to chase, you would never have stuck in there and figured this out.


Hm this turned out bigger than I intended.
Comments/suggestion/critique welcome

[DWayneBos]

- Some of these outs might not be in the deck anymore. They might be in your opponent's hand, or in the hands of other players that already folded. So maybe you'll be chasing a 2-edged straight and think you have 36% to win, but in reality all but one of your outs are in the hands of people that already folded!

I am certainly not the one to comment here, as I am not a math-wiz and a newish poker player, however..

I am pretty sure the fact that a card may have already been dealt, in and of itself, does not effect counting your outs. Your outs could also be at the bottom of the deck, but you don't know that either. So, in the absence of information to the contrary, you must (from a statistical and probability standpoint) consider all cards you cannot see as being possibly the next card to be dealt.

So, when you have 5 outs after the flop, you can't see 47 cards so your odds of hitting one of those cards on the next card is about 10%.

Now, if you KNOW other cards.. maybe someone folded and showed their cards, I guess you could adjust your calculation then, somehow.

[ed]

I might be no expert, but your idea about "outs not in the deck anymore" is just plain wrong unless you have reason to believe opponents are holding or have folded the specific cards you need.

If you want to take into calculation that opponents could have been dealt the cards you need, you also have to take into calculation that opponents could have been dealt other cards! See the problem here? It of course evens out, making the argument air.

An example where you have reason to believe opponents could be holding the specific cards you need:
You hold KQ. Pre flop there's a raise and several callers (maybe even a reraise). Flop is JT5. You need a 9 or an ace for the nut straight, but pre flop action have told you that it's very likely that one or more aces have been dealt to opponents.

[jackvance]

Right.. ok thx for the feedback. Well, there definately IS a difference, mathematically, but you guys are right that it isn't significant.

In principle, the mathematically 100% correct way to calculate pot odds would be to count the odds that 1-all of your outs have been dealt to your opponents, and use these odds as weights on the pot odds calculations. Hope that makes sense.

But if I think about it, then indeed the situation is that you get a little better pot odds in the cases they aren't hoarding many of them, and in the cases where they áre, the weights are rather small (because it's quite unlikely that all your outs will have been dealt out already).

So I ran it through the simulator. Let him play out hands with 0, 2 and 4 opponents who could possibly hoard your outs.. and the difference indeed seemed abysmal. At most 0.1%. So yeah, scratch that point on my list.

Btw, as a side note, most of this is probably old news to the vets. It's more a "newbie realization" kind of post, that's why I put it in this forum too, I'm not trying to preach the gospel here. Could maybe (hopefully) help some other beginners who have problems with pot odds and what they really represent, give them insight in the matter. Like the last example I gave, how you could stumble upon a bluff chasing your odds.. probably won't apply at all on the higher levels since they won't throw bluffs around that give you pot odds to chase your draws.. Mostly lower stakes stuff.

[DWayneBos]

Ok.. So explain to me why cards witch were shuffled in the second 1/2 of the deck, and therefore will not be played in this hand are differnt from cards dealt to others at the table, in terms of calculating odds. They are as inaccessable to you as those in your opponents hands, right?

I really think that statistically, any card you can't see can be an out, for pot odds purposes.

[sejje]

What they're saying is if you're not counting outs because they're in other people's hands, then you have to lower your ratio of outs:cards remaining when they're not in other people's hands.

Regardless, calling with perfect pot odds won't make you a "break-even player." You'll be winning bets after you hit. I make my hand quite often and still get paid afterwards.

Yameen?

[jackvance]

Ok.. So explain to me why cards witch were shuffled in the second 1/2 of the deck, and therefore will not be played in this hand are differnt from cards dealt to others at the table, in terms of calculating odds. They are as inaccessable to you as those in your opponents hands, right?

I really think that statistically, any card you can't see can be an out, for pot odds purposes.

Good point. I can't readily find an answer. That would mean my super-big calculation, if carried out, would come to the exact same solution. (different model, same universe, same results)

Regardless, calling with perfect pot odds won't make you a "break-even player." You'll be winning bets after you hit. I make my hand quite often and still get paid afterwards.

Sigh.. you're not following my train of thought. Which is not a blame by the way. I did a modular research on each aspect on its own, you're talking about the big picture etc bla bla. Forget it, I feel bad enough as is about making this post, maybe I should delete it or something.

[ed]

A lot of your original post is very good, it's just that your "outs not in the deck" theory is plain... wrong. This only makes up a small part of the post tho, and there's a lot of other good things in there.

[krimson]

- your opp has outs too.

This is not really an issue unless you are calling AI (or close to AI) on the flop. If there's money left behind, you hit your draw on the turn and are worried that your opponent has a redraw you can bet out to protect your hand.

[TLR]

There are basically 3 main points in your article that needs addressing
1. "Some of the outs may not be in the deck anymore" - this is totally irrelevant - when you calculate your outs each of the 52 cards is in one of 2 states - known (i.e. your hole card or community card) or unknown - all the unknown cards are equal. I will give you a matematical example to clear it.
Lets say you have 1 out a 7 of spades in a 9 people game after the flop.
'standard' pot odds theory 1/(52-5) = 1/47
another way of looking at it.
The chance of this card to be in the 16 other hole cards + burn card = 17/47 then you have 0% to win
0*(17/47) + (1/30)*(30/47) = 0 + 1/47 = 1/47.

The other major part of your article refers to a situation when you dont know how to calculate your outs.
Pot odds assumes is a standard mathemical calculation based on the assumpion you know what are the villian's cards, ofcourse in reality you dont know that, but putting your opponent on a hand (or range of hands) is a prerequisite for pot odds calculation

[TLR]

There are basically 3 main points in your article that needs addressing
1. "Some of the outs may not be in the deck anymore" - this is totally irrelevant - when you calculate your outs each of the 52 cards is in one of 2 states - known (i.e. your hole card or community card) or unknown - all the unknown cards are equal. I will give you a matematical example to clear it.
Lets say you have 1 out a 7 of spades in a 9 people game after the flop.
'standard' pot odds theory 1/(52-5) = 1/47
another way of looking at it.
The chance of this card to be in the 16 other hole cards + burn card = 17/47 then you have 0% to win
0*(17/47) + (1/30)*(30/47) = 0 + 1/47 = 1/47.

The other major part of your article refers to a situation when you dont know how to calculate your outs.
Pot odds assumes is a standard mathemical calculation based on the assumpion you know what are the villian's cards, ofcourse in reality you dont know that, but putting your opponent on a hand (or range of hands) is a prerequisite for pot odds calculation

[TLR]

There are basically 3 main points in your article that needs addressing
1. "Some of the outs may not be in the deck anymore" - this is totally irrelevant - when you calculate your outs each of the 52 cards is in one of 2 states - known (i.e. your hole card or community card) or unknown - all the unknown cards are equal. I will give you a matematical example to clear it.
Lets say you have 1 out a 7 of spades in a 9 people game after the flop.
'standard' pot odds theory 1/(52-5) = 1/47
another way of looking at it.
The chance of this card to be in the 16 other hole cards + burn card = 17/47 then you have 0% to win
0*(17/47) + (1/30)*(30/47) = 0 + 1/47 = 1/47.

The other major part of your article refers to a situation when you dont know how to calculate your outs.
Pot odds assumes is a standard mathemical calculation based on the assumpion you know what are the villian's cards, ofcourse in reality you dont know that, but putting your opponent on a hand (or range of hands) is a prerequisite for pot odds calculation

[ekillian]

OMG Jack you put a lot of effort into being dumb. Learn before you teach. Fuckin A I couldn't even get through taht and I know you must've felt so smart typing it. Damn.