Basic pot-odds concept question.

Dear Members,

I’m new at No Limit Hold’em and my question is, if someone is playing say a top pair of some kind and the opponent is on a draw either flush or straight, theory says that for the person on the draw, they need “adequate” pot-odds before it’s worthwhile to proceed on the turn or flop or what have you. My questions are, isn’t putting money into that pot as the person on a draw -EV at that point and so isn’t more money bet just putting more money under influence of -EV? Then, when there’s “enough” money in the pot, why would it be a “good” risk to be drawing after a certain point? When the person with the strong pair puts out a large bet to dissuade the person drawing, does it help the person with the pair? does it help the person on the draw or both? And why? My conceptual understanding needs some help. Thanks for all of your replies.

Quote: Wino84

Dear Members,

I’m new at No Limit Hold’em and my question is, if someone is playing say a top pair of some kind and the opponent is on a draw either flush or straight, theory says that for the person on the draw, they need “adequate” pot-odds before it’s worthwhile to proceed on the turn or flop or what have you. My questions are, isn’t putting money into that pot as the person on a draw -EV at that point and so isn’t more money bet just putting more money under influence of -EV? Then, when there’s “enough” money in the pot, why would it be a “good” risk to be drawing after a certain point? When the person with the strong pair puts out a large bet to dissuade the person drawing, does it help the person with the pair? does it help the person on the draw or both? And why? My conceptual understanding needs some help. Thanks for all of your replies.

DISCLAIMER: I am not a great Texas Hold 'Em poker player, therefore, my explanation on this should be taken with a grain of salt. If anyone comes along who plays THE more regularly than I do, please feel free to make any corrections to my explanation, offer a better one or simply phrase mine in a better way. /DISCLAIMER

In the simplest terms, "Pot Odds," refer to what you stand to gain, or lose, relative to the draw that you are making, amount you have to bet and the amount in the pot. This is an expected value analysis that has to be done on the fly that many people won't be able to do in their heads.

Let's imagine a 2-5 NLHE game that would have you protecting a big blind with a hand such as 9c7c, so here's the action:

We're going to say that the player before the small blind makes it $15 to see the flop, the small blind calls and you also call. Thus, there is now $45 in the pot.

FLOP: 6c Kc 2h

Okay, so the Small Blind checks post-flop, you throw out a $50 bet to see if you can get folds, the pre-flop raiser shoves all-in for $260 (total), the Small Blind folds...you have enough to cover the pre-flop raiser, so should you call?

For that, you want to look at your expectation.

PreFlop: Pot---$45 Yours: $15

Postflop: Pot---$355 (you bet $50 and the pre-flop raiser made it $260 plus the $45 from before) Yours: $65

If you fold, then you definitely lose $65, so you want your Expected Value for this hand to be better than losing $65 if you were to call.

The nine flush outs are easy and you know that the king on the board is a club. You are pretty sure he has top pair, but at least you don't have to worry about his king eventually giving him a better flush with running clubs. We're going to go ahead and say that we assume getting any flush will cause us to win the hand.*

*(By the way, I've also created a hand with runner-runner straight draw possibilities in it involving at least one eight. I did that so I could conveniently ignore that the player might draw to a better flush if his kicker is a higher club and the board comes running clubs.)

Okay, so we have two cards and there are three on the board. That leaves 47 cards that are unknown, except we are also very confident that the other player has the pair of Kings, especially since he shoved our bet that opened post-flop action...he could have a high inside pair, but probably would have bet more preflop had it been Aces or Kings, so with anything else and us betting, the king on the board should have scared a lower inside pair. The point is, we are acting as if we know he has a king and we know that King cannot be a club...therefore, there are effectively 46 cards that we don't know.

(37/46) * (36/45) = .64347826087 or 64.347826% that neither the turn nor the river will be a club. That means there is a .35652173913 probability that you will catch a club for a flush that will win the hand.

(By the way, one shortcut to approximating outs is to multiply your total number of outs by four on the flop and two on the turn)

Okay, so let's just use that for now. You have to call another $210 into a pot of $355 to make a total pot of $565 of which $275 is your money.

(.35652173913 * 290) - (.64347826087 * 275) = -73.5652173916

Okay, so with that your expectations are probably slightly worse than just folding and losing the $65 guaranteed. Of course, we did take your straights out of account and haven't been accounting for runner-runner hands with your hole cards that are generally going to be winning.

For example, I decided to use the WoO Texas Hold 'Em Calculator:

https://wizardofodds.com/games/texas-hold-em/calculator/

And I gave our opponent KhJs, and KJ offsuit seems like a reasonable hand for this behavior. It gives you a 38.89% probability of winning if that is the case:

(.3889 * 290) - (.6111 * 275) = -55.2715

Okay, so now as you can see you ARE expected to lose either way, but factoring in all of the ways that you could win, this is better than folding given the money that you have in there.

Granted, you would almost definitely fold to a shove here if you didn't have money that you put in after the flop, but that's okay, because the raise was a good play. The Small Blind player checked and, even though we knew the preflop raiser didn't have total garbage, it's more likely than not that he doesn't have a king in his hand and our bet would even give an inside pair pause if he didn't catch something on the board (66 in the hole, for example).

So, you made the right play*** but got stuck in a jam where you have to make one negative expectation decision or the other. In this case, with the hands you do win, you seem to do better by calling his shove.

***Maybe not the absolute, 'Right play,' but you made a defensible play. You should probably bet into this in this situation at least sometimes.

Of course, this is only one example.

K9 and K7 are slightly worse for you, but it's not as bad as you might think. The vast majority of your wins are flushes, anyway. Even though runner-runner clubs becomes less likely with a club in the other player's hand, an over club in his hand is a disaster for your prospects...but it's unlikely and there's no reason in particular to believe that he has a high club...his King can't be a club, for one thing.

Okay, so let's take this example as far as we can with your questions:

Quote:

I’m new at No Limit Hold’em and my question is, if someone is playing say a top pair of some kind and the opponent is on a draw either flush or straight, theory says that for the person on the draw, they need “adequate” pot-odds before it’s worthwhile to proceed on the turn or flop or what have you. My questions are, isn’t putting money into that pot as the person on a draw -EV at that point and so isn’t more money bet just putting more money under influence of -EV?

Yes, but then what matters is whether or not your expected loss is more or less than it would be if you were to fold. In the example above, it is -EV to call, but it loses less than folding in the long run. This is assuming that we are talking about a cash game and I could list about 100 other qualifiers.

Sometimes the best decision is simply the, "Least worst."

(.35652173913 * 305) - (.64347826087 * 275) = -68.2173913046

So, with another pre-flop caller, now it's almost the same thing considering only the flush. Most of these pot odds things will be estimates unless you're a human calculator.

Also, in the long-term poker sense (assuming you'll be playing with these people again) it's good to showdown some draws. You don't want your competition to think that they can bluff you out of every pot just by repping high pair post-flop every time, or you're going to get pushed around a lot.

Quote:

Then, when there’s “enough” money in the pot, why would it be a “good” risk to be drawing after a certain point?

Because you are expected to lose less one way than you are the other way, when it comes to average result. If you fold with $65 in the pot, then you always lose $65.

Let's pretend for a second that the Small Blind checks, but is actually slow-playing K6 (Two Pair) and hoping to get action, you raise the $50 (as before), the preflop raiser shoves (as before) the Small Blind calls.

Okay:

Small Blind: Kd6d6cKc2h

Big Blind (You): 9c7c6cKc2h

PreFlop Raiser: Kh10c6cKc2h (Notice I am giving him an over club here)

You're still 30.9% to win this hand and now:

(.309 * 550) - (.691 * 275) = -20.075

Okay, so you're still losing money on this situation in the long run, but it's now MUCH better than folding for a guaranteed loss of $65. Let's say that neither of the other two players has an over club, so now the calculator says (I changed PFR from 10c to 10s) you are 36.77% to win:

(.3677 * 550) - (.6322 * 275) = 28.38

Hell, look at that! You take the over club out of the preflop raiser's hand and now this is profitable! You're expected to win money in the long run in that situation.

What's the probability that one or the other has an over club? I don't know. If they do, it's probably either a 10 or a Jack because Queens/Aces should bet more with a King. Jacks should probably also bet more. I don't think the small blind is likely to have an over club.

Also, for that player with the pair of Kings and 10c, it probably barely occurs to him that he can catch a running flush.

Quote:

When the person with the strong pair puts out a large bet to dissuade the person drawing, does it help the person with the pair?

It does help him. The thing about this situation is, other than the fact that you don't know if you're going to get outdrawn, it's win-win for top pair.

Either:

1.) You fold and top pair takes the pot down without a fight.

OR:

2.) You call and top pair (at least, presumes he) is at an advantage.

Top pair will either take the guaranteed win or take the value on this one, but generally, top pair not only WANTS you to call, but he's hoping you're calling with some sort of draw rather than a made hand. Imagine he was playing K10 and you were playing 66 on the board in our example, he's DEFINITELY not happy to run into trips here!

If it sounds mutually beneficial that you call the flush draw (in most situations), it's not. The value calculations that we did above are the same as HIS value calculations for that example, except remove the (-) from the right side of (=) as appropriate. In other words, his expected value is better in our example hand if you fold. Your expected value is less bad if you call.

For me, if I'm playing you for a draw in this situation, then I'm happy to see you fold. If you bet into me and want to see your draw, then it's going to cost you as much as I can bet in order for you to get to do that.

Another thing that you have to understand about the draw, from the perspective of the player with the high pair, what's going to happen if you miss all draws? Suppose that I have the high pair and I DON'T bet post-flop...that's silly.

Why is that silly?

It's silly because I am not maximizing the value of my top pair whatsoever. When you look at that board, here are the things that I know:

1.) You absolutely can not have a flush yet.

2.) You absolutely can not have a straight yet.

Therefore, here are the only hands where you're beating me:

1.) Pair of Kings/Aces in the hole. (Almost definitely not based on you not re-raising preflop and I also have a king.)

2.) Pair of sixes or deuces in the hole. (I doubt it. It's unlikely, but I have to take my lumps when this happens.)

3.) Any two pair. (This is mostly unlikely. It's almost definitely not with a king, because I have a king. Two pair with 6-2? I seriously doubt that. You should know better than to call any preflop raise (even if you only have to put 2x more than what you have in there $15 total with $5 already in there) with 6-2 and only one person calling my raise).

4.) King with a better kicker. (This is probably the most likely way you're beating me...but supposing I raised with KJ or K10 off...I would think that you would re-raise me preflop with AK, KQ and maybe even KJ and definitely KJ suited. For that reason, while it's the most likely hand you have where I have the worst of it, I don't think it's terribly likely.)

So, I'm pretty confident that any money I push in there I am getting the best of it. That leads us to if I don't bet (assumes you checked to me):

If you don't bet, then one of two things can happen if I am somehow putting you on a draw and I check:

1.) You can hit the draw and I am screwed.

OR:

2.) You can fail to hit the draw and now I am much less likely to extract any money out of you.

In short, I'm betting my pair here and am betting at least enough to put a lot of pressure on you. That's if I don't shove outright, which I am probably doing.

Quote:

does it help the person on the draw or both? And why?

The pair wants you to either fold or he wants you to bet with the worst of it. In the case of you betting $50 and him shoving in the example, he's mathematically better off (EV) if you fold, but has the best of it either way.

In the case of the example, you generally call your flush draw because it has a lower expected loss in the long run. Keep in mind you bet $50 post flop. If you checked and the other player shoved, then you would want to fold because the guaranteed loss of $15 becomes less bad based on him probably having at least top pair. (Although, if SB checks, you check and he shoves with SB calling the shove...you're probably back to calling unless you are supremely confident that one of those two shoved with a better flush draw than you have...that would be a hell of a read if you could put one of them on that. I sure as hell couldn't.)

I want to add some stuff about the pre-flop decision, since it's such a borderline case in the example hand.

With two callers, and you can verify using the WoO calculator, you're still getting pot odds only having to call for another $10, rather than folding, against most hands. You're getting pot odds against most hands for the other two players that don't have a seven or a nine in them and the situation where you're not getting them (and no other player has a seven or a nine with an overcard) most frequently is another player having suited clubs with something better than a nine.

In fact, with the Raise to only $15, you're even getting pot odds in some instances where one of the other players has your nine covered!

Wired pairs more over nine for one of the other players would frequently result in you not having pot odds, but such a player would probably bet more than the initial raiser did and the small blind probably would not have just called. One of the aspects of the suited 97 situation out of the BB that you're looking at is that it's very likely that the other two players are betting with either one high card, both high cards or a pair lower than nines.

For example, if you have suited 97, another player has QJ (suited or not) and the third player has 66 in the hole, you're actually more likely to take the pot down than the guy holding 66, unless one of his sixes is a club (remember, we haven't seen the flop yet) but even then you still have pot odds that suggest calling.

Obviously, that's for this specific situation. If the first player to bet Raises to $30, then you should always be folding in this situation...especially if the small blind calls. It can be pretty close, though, so if you're an exceptional post-flop player you could maybe mix some calls in here.

Obviously, if either of them shove pre-flop, you're always folding this.

Some people might consider that postflop raise that you did in the example questionable, so I am going to defend that.

1.) The Small Blind has already checked and can be assumed not to have a king. This will sometimes be wrong, but it happens.

2.) If both players missed the King on the flop, from their perspective, you're repping EITHER a king or a flush draw. The nice thing about being the Big Blind in this particular hand pre-flop is that the pre-flop raise was low enough that they can't really put you on a hand when you call. Would you ALWAYS re-raise a King here? Doubtful. But, with a hand like K8, or whatever, you'd definitely at least take a flop at that price.

So, now you've kind of flipped the script on them and they are deciding whether or not they want to call against a king you might have.

3.) If those hands missed the King and don't have any pairs or flush draws, they should usually be folding to your bet. Do you know that they could even have a pair of sixes or deuces with an overcard (to your nine) and as long as they don't have a better flush draw in the process you're still the odds on favorite to win the hand? You'd win it with a seven or a nine if they didn't hit anything else...not to mention your flush draw.

4.) You KNOW you don't have a king or a pair, so if you check, you're putting the original preflop raiser in a position to rep a king (that he might not have) and are in the same situation anyway. Obviously, if he bets or shoves, you're going to assume he has a king. Still, that's why you play these pot odds hands when we get back to the first post...not only do they have value compared to folding, but you don't want other players thinking they can just rep a king here and bluff you off of all of your four flush draws.

5.) If they don't have a king, pair or flush draw, then they are almost certainly not calling. You'll take the guaranteed money from them folding here because, why do you want to risk not hitting your flush and another high card shows up? You know that the other two players either have pairs or high cards, so any high cards that aren't clubs that come on the turn scare you...not to mention the fact that your hand sucks and the probability of you hitting a flush has dropped pretty dramatically.

If the preflop raiser has a pair or overcards, then he should definitely call or raise. Don't worry, you have the best of it against any pair that can be made using a card on the board (except kings), so you're only concerned about Kings, 2P, Trips or better flush draws if you get a call here...all of those hands should raise you anyway, except kings with a poor kicker might just call...but he shouldn't have a very poor kicker with a King since he raised preflop.

Also, trips aren't particularly likely because they would almost have to be sixes. I don't think someone is doing that sort of preflop raise with deuces.

So, with the small blind checking I like betting your four-flush in this situation.***

***Now, there are STILL going to be exceptions to this! I would say that the biggest exception would be if you know your pre-flop raiser won't make a terribly aggressive bet if you do check, or is very unlikely to be very aggressive (maybe likely just to check himself), then maybe you would check if you think you can see the Turn (and maybe catch your flush) cheap or no extra cost. You'd have to know that was a tendency of the other player, of course.

Wow. A big thank you to Missiion146 for exceeding all of my expectations in terms of level of detail in answering my question. Thank you for explaining in a way that gets the concept through. I will need to spend time re-reading for my limited abilities to properly absorb.

Quote: Wino84

Wow. A big thank you to Missiion146 for exceeding all of my expectations in terms of level of detail in answering my question. Thank you for explaining in a way that gets the concept through. I will need to spend time re-reading for my limited abilities to properly absorb.

Welcome to the forum. What if the other player that you think has a high pair you are drawing against to your straight or flush is flat out bluffing? What if he has the same draw as you?

The concept of ‘pot odds’ is of course worth knowing, but it’s not the total picture……

Buy and read Sklansky’s the Theory of Poker. It’s old at this point but well grounded and covers these concepts and many more.

Quote: SOOPOO

Welcome to the forum. What if the other player that you think has a high pair you are drawing against to your straight or flush is flat out bluffing? What if he has the same draw as you?

The concept of ‘pot odds’ is of course worth knowing, but it’s not the total picture……

I agree with what you said, of course, but it really doesn’t matter in my example hand—-which is why I went with 79 suited as an example.

Even if the other player were bluffing, you’re probably not beating him by card rank, which is to say your nine by itself is rarely good here.

For the example hand, that would also be a pretty ballsy bluff in the face of the BB player leading out $50 after SB checks.

Whether or not BB checks, in the example hand, any bluff is probably going to be an ace or something like QJ or Q10 that missed and bluffs are hoping SB and BB missed the king (especially if both check) and maybe are trying to bluff them off a potential flush draw by repping a king.

However, getting back to my first post, that’s why I said it’s good to showdown four-flush once in a while especially when pot odds justify. That tells players that you’re not getting bullied around just because they rep top pair.

If you’re not willing to ever showdown 79 suited, four-flush, like in the example hand…then you are a tight passive nitty player who wants only top pair or nuts/nut draws and should fold 79 suited pre-flop to any raise. Flopping four flushes represents a very substantial portion of your upside seeing flops with this hand.

I am a pretty good Hold'em player.

The reason one might occasionally play 97s (late in the preflop betting) is because you might flop:

- two pair: 97x
- a flush draw (2 suited cards on the board)
- a straight draw (T8x or 86x or (marginally T6x) on the board)
- a 9 on a board that has only one or zero higher cards
- a 7 on a board with backdoor possibilities for a straight or flush (i.e., drawing two cards to a straight or flush)

Those hands might be sufficient for you to continue on to the turn with a call of your opponent's continuation bet. It depends upon the betting.

An advantage of a hand like 97s is that the cards you are looking for are probably not the cards that help your opponent. If the flop comes out 3 cards Ten - Ace, then you know to fold when faced with a bet. However, when the flop comes out with a lot of cards 9 or less then your opponent realizes that this flop is likely to have hit you. Making a bet might actually cause the opponent to fold.

Personally, I would never go to showdown (call a river raise) with a 97s that has not improved. You are throwing chips away. You either raise or fold (and I would almost always fold.) If you must go to showdown with an unimproved hand, do it with an Ace as a bluff catcher.

Quote: gordonm888

I am a pretty good Hold'em player.

The reason one might occasionally play 97s (late in the preflop betting) is because you might flop:

- two pair: 97x
- a flush draw (2 suited cards on the board)
- a straight draw (T8x or 86x or (marginally T6x) on the board)
- a 9 on a board that has only one or zero higher cards
- a 7 on a board with backdoor possibilities for a straight or flush (i.e., drawing two cards to a straight or flush)

Those hands might be sufficient for you to continue on to the turn with a call of your opponent's continuation bet. It depends upon the betting.

An advantage of a hand like 97s is that the cards you are looking for are probably not the cards that help your opponent. If the flop comes out 3 cards Ten - Ace, then you know to fold when faced with a bet. However, when the flop comes out with a lot of cards 9 or less then your opponent realizes that this flop is likely to have hit you. Making a bet might actually cause the opponent to fold.

P

I would say usually fold. When it comes to pot odds, I like my 7c9c even better against a high board with two clubs. The flush is still almost always winning if I hit it and now I have even less to worry about when it comes to my opponents perhaps having suited clubs with one of them being greater than 9, or running clubs on the board and an opponent hitting runner-runner flush with a club greater than 9.

I like to talk about pot odds without using math.

I use the example of a situation where 2 players are all in, or one all in and one call, and it's your decision to stay in or not. In other words, you know you're gonna see all the cards and all the hands and will find out if the decision is correct or not.

In such a situation there are four outcomes:

A - You call and win
B - You call and lose
C - You fold and would have won
D - You fold and would have lost

Outcomes A and D are both good and correct, so we ignore those for now.

You gotta ask yourself: What will hurt more? Outcome B or outcome C? The level of pain of one vs the other is pot odds.

There you have it, ladies and gentlemen. Pot odds without math.

I couldn’t play that way or I wouldn’t call the situation in my example, which I would almost always call unless I had a good read on someone.

And I’ve never had a good read on someone.