Struggling with the basic maths of no-limit hold’em? Don’t worry, we’ve got a simple guide to pot odds to help turn you into a winner
There’s a good chance you don’t play poker because you enjoy maths. You probably play because it’s glamorous and exciting, because it makes your heart beat faster. Well, let us give you something to chew on: all the top players in the world understand the concepts we’re going to talk about here, and they apply them every time they sit at the table. And that’s a good part of the reason why they’re consistently winning players.
So put aside memories of algebra and fractions and embrace the science of poker. Because whether you want to be a world champ or just beat your weekly home game, this article and the concepts covered will bring you a whole lot closer.
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 winner. So, let’s say you’re playing hold’em and you’re on the turn with one card to come. You have four hearts and need the fifth to make a flush. there are 13 hearts in the deck in total and you can see four of them. So there are nine hearts left that will 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 (the nine hearts left that will complete your flush). So the chances of you hitting your flush are 9 in 46, which works out at 19.6% or 4/1.
Does this make sense so far? If you struggle with maths there’s a really simple way to calculate your outs as a percentage probability. If there’s one card to come, double your outs – so, 9×2=18%. You can see this isn’t exact, but it’s good enough.
To work out your probability of hitting with two cards to come, multiply your outs by four. So, if you’re on a flush draw on the op, it’s 9×4=36%. If, say, you have A♣-K♣ on a 9♣-4♣-2♠ op, you might consider your two overcards as outs too, which gives you nine flush outs and six overcard outs. 15×4 gives you a 60% probability of hitting on the turn or river.
It’s worth finding a method that suits you as this is the underlying principle that tells you if a situation represents a good investment or not.
So now you hopefully 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 are one of the key mechanisms in making that judgement. Put simply, they’re the odds of reward offered by the pot in comparison to the cost of a bet.
Pot odds in practice
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 are 10/1. If the chance of making your hand is better than the pot odds then it’s a play you should make. And, of course, the reverse is true as well.
Okay, let’s go back to the example of the flush draw on the turn. The odds of that flush card arriving are 4/1. In other words, four out of five times you won’t make your hand, and the other one in five times you will (on average). Therefore, to make it worthwhile to call the bet you need better pot odds than 4-to-1. So if it costs $10 to call on the turn and there’s $100 in the pot (odds of 10/1), it’s a calling situation.
Let’s 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 pot odds then. Job done – what were you worried about?
There’s a little more to learn. So far we’ve looked at a situation with one card to come. If there’s more than one card to come it becomes harder to calculate your pot odds, unless you’re all-in on the flop.
Let’s say you hold four hearts to a flush on the flop. Now there are two community 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 4/1 – you need both cards to get to your 2/1 shot. If you have to put further money into the pot than the current call, that affects your pot odds and produces implied odds.
Often in poker your reward from the pot may be greater in future betting 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 betting rounds. This means there might be an incentive to call a bet beyond the money currently in the pot, given the money that may be added later. Effectively, the immediate pot odds on offer may be improved when you take into account the money that may be in the pot later.
This concept is known as implied odds, and is an area where you need good judgement about the action in future betting rounds if you want to take advantage of it.
Using pot odds in play
Kudos for coming this far. If everything in this article is new to you you probably 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.
Reread the article and start learning the odds for situations that occur frequently in the game, such as gutshot draws and open-ended straight draws. Pretty soon you’ll have the maths nailed down – and the profits will quickly follow.
Pot odds in action
Had enough theory? Let’s look at a few examples of how pot odds can help you in practise
Example 1: The profitable play
Here we show how knowing the odds of hitting your flush on each street can help you make the right call:
Five people in the hand. Blinds 100/200, two callers (200 each). YOU raise to 600 with A♣-T♣. Both blinds call, as do the two others (600 each). The pot is now 3,000.
You have nine outs to make your nut flush – approx. 19% or 4/1 on the next card. The big blind bets 600, one person calls (pot 4,200), and you call 600 because you’re getting 7/1 on your money, while the odds of you making your hand are 4/1. The small blind folds. The pot is now 4,800.
First person to act bets 1,200, next person calls (pot is now 7,200). You call 1,200, because you’re getting 6/1 on your money, while the odds of making your hand are 4/1.
Example 2: The loser’s call
You’re in a $0.25/$0.50 no-limit cash game. You hold J♦-T♥ in the big blind ($0.50). Three players fold, the button raises to $1.50, the small blind calls and you call too. The pot is now $4.50.
You’ve flopped an open-ended straight draw (you have eight outs – any Eight or king will give you the straight). The small blind checks, you check and the button checks too.
The small blind checks, you check and the button bets $4.50 (the pot is now $9). The small blind folds and you call, getting odds of 2-to-1 on your money. But with only one card to come, your odds of making your straight are now just 17.4% or 4.7-to-1. That’s a bad call.