Poker odds

1 May 2006 PokerPlayer Cash Games Strategy

Nick Wealthall explains how pot odds can make you famous, win you millions of dollars and get you laid

Did I get your attention? Okay, I admit it, I may have used a touch of hyperbole to sucker you in, but if we’re going to stand any chance of getting through this together I thought you’d need something a bit more inspiring than ‘correct use of pot odds can improve your play’.

You see, I know for a fact that I might well have lost you just by using the phrase ‘pot odds’. Suddenly, the grey fog is descending and you’re clicking the back button.

Well, I hear you. I know the way your brain works – ‘Odds… sounds like maths… maths = pain’ – because mine works the same way, too! After all, this is being written by a man who – many years ago I hasten to add – thought a right angle was one that was pointing to the right.

The fact is you don’t play poker to do maths homework. You play because it’s glamorous and exciting, because it makes your heart beat faster; in short, because you want to be the next Phil Ivey or Daniel Negreanu.

Well let me give you something to chew on – all of the top players in the world know the concepts we’re going to talk about and apply them every time they hit the table. And that’s a good part of the reason why they’re consistently winning players.

So put aside memories of algebra, fractions and the cold sweats of a maths exam and embrace the science of poker. Because whether you want to be a world champion or just beat your home game every week, this article and the concepts covered, will bring you a whole lot closer.

The purity

Poker is played with 52 cards – always the same 52 cards. This means that its parameters are defined. You will always know the chance of a particular card or group of cards appearing. This is why no matter how many lucky rabbits feet, oranges or fossils appear in front of players, poker is a game of skill not luck. And given that you know the chances of any sequence of cards or events occurring in the game, you have the potential to make precise calculations of your chances in any given hand.

This means that, on occasion, you don’t have to make your decision according to ‘judgment’ or ‘feel’ but according to immutable truths – and that makes poker a whole lot easier to play.

Outs and basic probability

You may have heard the phrase ‘outs’ in relation to poker. An ‘out’ is a card that will improve your hand and, hopefully, make it a winning one.

So, let’s say you’re playing Hold’em and have reached the river. You have four hearts and need the fifth to make a flush and win the hand. There are 13 hearts in the deck in total and you can see four of them. So there are nine hearts left that will help you complete your flush.

You can see six cards (two in your hand and four on the board). Therefore there are 46 possible outcomes for the next card and nine are winning cards – or ‘outs’ for you (i.e. the nine hearts left that will complete your flush). So the chances (or probability) of you hitting your flush are nine out of 46 – or 19.57%.

I hope this makes sense to you – if not it’s worth re-reading the above paragraph and making sure it does as this is the underlying principle that tells you if a situation represents a good investment or not.

Yes, but what are pot odds?

Okay, so now you understand the basic probability that underpins poker – but how does that get you closer to slipping on a WSOP bracelet or two?

Well, poker is about finding favourable situations for your money, then investing in them. And making sure you get away from the unfavourable situations as cheaply as possible. Pot odds is one of the key mechanisms in making that judgement; put simply, the odds of reward offered by the pot in comparison to your bet.

So let’s say you’re in a hand with just the river card to come and there’s $100 in the pot. Someone has bet and it will cost you $10 to call. The odds offered by the pot in this instance – or your pot odds – are 10/1. Right, pay attention, this is the important bit. If the chance of making your hand is better than the pot odds (i.e. if it’s more likely) then it’s a play you should make – it’s a good investment for your money. And the reverse is, of course, true. If the pot odds are worse than the chances of hitting your hand it’s a poor investment for the money you’d have to put in.

Okay, let’s go back to the example of the flush draw on the river. The odds of that flush card arriving are 4/1. These are always the chances by the way – you can squeeze your rabbit’s foot, cross your fingers or cover the screen. That flush card will come up one time in five. Therefore, to make it worthwhile calling the bet you need better pot odds than 4/1. So if it costs $10 to call on the river and there’s $80 in the pot – odds of 8/1 – it’s a calling situation.

With the same example – still looking for that fifth heart – imagine there was $20 in the pot and it costs you that same $10 to call. Now you’re only being offered pot odds of 2/1 – far worse than the 4/1 chance of making your flush. It’s a bad investment and you should muck your cards.

I need to be clear here – this is not a matter of ‘feel’, ‘instinct’ or ‘luck’ – these are the immutable laws of the game and you must know them or your ability to win money at poker is very limited. So that’s it… pot odds job done – what were you worried about?

Effective odds

Okay, I confess, there’s a little more to learn. So far we’ve only looked at situations with one card to come, which is a problem involving a lot of certainty. If there’s more than one card to come it becomes harder to calculate your pot odds.

Let’s say you hold four hearts to a flush on the flop, not the turn. Now there are two cards still to come. In terms of the chances of making your flush there are two chances of catching that elusive heart, which is effectively nine out of 47 unseen cards on the turn then nine out of 46 unseen cards on the river. This works out at about 35%.

Now, if your opponent was to bet all their chips on the flop you could make a straightforward pot odds calculation. However, if there’s further betting to come on the turn the calculation is complicated. That’s because the odds of making the flush on the turn are 4.2/1 – you need both cards to get to your 1.9/1 shot.

If you’re going to have to put further money into the pot than the current call, that affects your pot odds and produces your effective odds. If you’re playing limit poker it’s possible to work this out exactly. For example, let’s say you have four cards to the flush on the flop and you’re in a $10-$20 limit game with $60 in the pot. It’s going to cost $10 on the flop to call and then $20 on the turn, if your opponent bets twice. Therefore, the total in the pot will be $90 plus your calls of $30 – effective odds of 3/1 – good enough to call.

In no-limit poker it’s a lot harder to judge as you don’t know what your opponent will bet in a future betting round making calculating effective odds something that involves strong powers of judgement.

Often in poker your reward from the pot may be greater in future rounds. For instance, if your opponent holds a good hand – let’s say three of a kind – but you make a better hand to beat him, like a straight, then he may end up giving you a lot of chips in later rounds. This means there might be an incentive to calling a bet beyond the money currently in the pot, given the money that may be added in future rounds. Effectively the immediate pot odds on offer may be improved upon when you take into account the money that may be in the pot later in the hand.

This concept is known as implied odds and is something where you need good judgement about the action in future betting rounds to take advantage of. It’s a huge topic in itself and to do it justice we’re going to look at the complexities of implied odds next month.

Force the mistake

Poker is a game of mistakes – you’re looking to eliminate your own and force your opponents to make them. You could try getting them to order the casino’s sandwiches but a more profitable way is to use your awareness of pot odds.

A no-limit game provides a great chance to do this because of the opportunity to manipulate the size of the bet. For example, let’s say you have top pair, top kicker, in a game of no-limit Hold’em and the hand has reached the river. Your opponent has been calling all the way and you’re sure he’s on a flush draw. His chances of success are roughly 4/1, so you need to offer him a poorer proposition than this.

Let’s say there’s $60 in the pot; that means you need to make a bet that offers poorer pot odds than 4/1 – in other words you must make a bet of more than $20. If you bet $10, you’d be offering your opponent odds of 7/1 (the initial $60 in the pot plus your $10) on his $10 call. Whereas if you bet the pot – $60 – it will give your opponent odds of 2/1 (the initial $60 in the pot plus your $60, making a $120 pot) on their $60, to call. This is poorer pot odds than the chances of making their hand, and therefore a bad bet and one where they should fold.

Whether they do or not, you have to remember that playing to favourable pot odds will make you money over time. Don’t worry about inividual instances where you end up losing the hand – it’s going to happen. But if your opponents continually make bad calls you’re guaranteed to make money in the long-term.

Using pot odds in play

Kudos for coming this far. If everything in this article is new to you I’m sure you won’t have taken it all in first time. It’s going to be difficult to use this new knowledge instantly at the table, and cardrooms – or your opponents – won’t appreciate you pulling out a calculator in the middle of a hand!

However, like a lot of concepts in poker it’s about learning it, mastering it and then letting it pass into your subconscious so that you can make judgements instantly when combining the odds in a hand with the other factors you have to consider.

Re-read the article and start by learning the odds from the ‘outs’ table and applying them to situations that frequently occur in the game. Pretty soon you’ll have the maths nailed down and the profits will follow. Who would have thought it? Maths does have its uses after all!