How to Calculate Poker Odds

Poker odds can appear confusing at first, but once you understand some of the basic fundamentals about how they work, not only will you have a much better understanding of the game itself, but you’ll also stand a higher chance of winning while playing the game.

In this post, we’re going to take a look at all forms of poker odds, from poker hand odds, how to calculate poker odds, the best poker winning hands, and more – and we’ll begin by taking a look at how exactly the odds work in conjunction with the game.

How Poker Odds Work

To look at how poker odds actually work, it can be handy to use an example of a football game. Let’s say the Chargers are playing the Eagles. A bookmaker may give the Eagles 3:1 odds to beat the Chargers. This means that for every $1 you staked, you would win $3, were the Eagles to win.

This, of course, roughly equates to the Eagles having a 1 in 3 chance of beating the Chargers – and this is the general ethos of how odds work, both in sports betting, and poker.

The higher the odds, the less chance you have of winning – and subsequently, the lower the odds, the more chance you have of winning.

Poker Hand Odds

One of the most common scenarios you’ll hear about odds in poker, is when looking at your “outs”. We’ll cover this in the section below – in this part of the guide, we’re going to look at the actual odds of getting some of the most popular and sought-after poker hands.

• Being Dealt Pocket Aces: Pocket aces are the premium starting hand in ALL Texas Hold’em games, and the odds of being dealt two aces is 0.4525% – equating to odds of 1:220. This means that you can expect to be dealt pocket aces once out of every 220 hands you play. (An interesting statistic is the chances of both you AND your opponent being dealt pocket aces. In this situation, the probability is just 0.0816%, equating to odds of 1:1,224!
• Hitting a Set on The Flop: Most players will always try to reach the flop when they hold a pair in their hand, pre-flop, as, if they’re able to make a 3-of-a-kind hand, they stand a very good chance of winning against their opponents. If you hold a pair pre-flop, the chances of hitting a set on the flop are relatively good; the probability is 11.7551%, equating to odds of 1:8.
• Hitting Quads: 4-of-a-kind is one of the strongest hands in Texas Hold’em, and it’s a hand that – despite being very hard to get – probability wise, isn’t actually too hard! The probability of making quads if you have a pair pre-flop, and make it all the way to the river, is 0.8163%, equating to odds of 1:122. Things become a little crazier when you look at the chances of two players hitting quads; in this case, the probability is just 0.0003%, equating to odds of 1:312,663!
• Royal Flush: The unbeatable hand – the hand all players dream of getting – a Royal Flush is the best possible hand in Texas Hold ‘Em poker, and cannot be beaten. Interesting, the board will only allow for a Royal Flush 1 in 59 times – and the odds of just ONE player making a royal flush at a full 9-person ring game is 1:3,628.

That’s just a few of the most common poker odds scenarios. It can be useful to have a rough idea of the odds for various hands and occurrences – but for the most-part, you don’t need to think into it too deeply, as the more important thing to worry about is the odds of you hitting your “outs”.

Outs and How to Use Them to Calculate Probability in Texas Hold’em

In Texas Hold’em poker, if you require an additional card, or more than one card to complete your hand, you’ll be looking to hit what’s known as an ‘out’.

For example, say you hold 5, 6 off-suit pre-flop, and the board comes King, 7, 8. You now have an up-and-down straight draw, meaning you need to hit either a 4 or a 9 to complete a straight – a strong hand that gives you a very good chance of winning over your opponents.

Now, in a 52-card deck, there are four 4’s, and four 9’s, which means you have 8 cards out of the 52 to hit your hand. However, you’ve already been dealt two cards – and there are three showing on the flop – which means the actual probability of hitting one of the cards you need is 8:47.

This means that approximately one in 6 times the turn card is dealt, you’ll hit your hand. Now, you may be thinking “why is this important” – and there are two reasons.

The first, is the simple fact that it’s good to know how likely you are to hit your hand. The second, and far more important reason, is that knowing how many outs you have allows you to make solid mathematical decisions, when faced with a bet. We’ll look at this in the following section.

Should You Call an Opponent’s Bet?

Using the example above, we can safely say that you’ll hit your hand – on average – once in every 6 times when the turn card is dealt.

Now, let’s say there is currently $40 in the pot, and your opponent bets $10. There are no other players in the hand.

In order to see a turn card, you must call $10. With the $40 in the pot, and the $10 your opponent bet, that means you’re required to risk $10, to have the potential to win $50. This means you’re getting 1:5 on your money – which means that over the long run, this would be a losing play, to call.

Now, say that there was $80 in the pot already, instead of $40. Now, when your opponent bets $10, you have to call $10 to have the chance of winning $90 – meaning you’re getting 1:9 on your money. In this scenario, it would almost always be a profitable decision to call, as, while you won’t always hit your hand, you’re getting odds that make it worthwhile, as over the long-run it would be a profitable, winning move.

That’s just one example, and of course, things become more complex when you start involving multiple players, and factoring in the possibility of re-raises. That being said, it should serve as a good starting-point for you to learn more about “outs”, and how they tie in with poker odds.

Tips to Improve Your Knowledge of Poker Odds

Like many things in life, having a firm grasp of poker odds and poker statistics takes time. There is no “quick-fire” way to memorize everything about odds, and how to use them in your game, and much of it comes from practice.

Thankfully, there are many great poker theory books available to purchase today, that you can use to improve your knowledge of the game and determine your odds of hitting your poker outs.
It’s worth pointing out that poker theory can become very complex – and even things like the poker outs example we looked at above can become difficult, when looking at things like reverse-implied odds.

As a general rule of thumb, the best thing to do is to simply stay calm while playing, and figure out how many cards you need to hit your hand. Calculate whether you’re getting the right pot odds to call to try and hit one of your poker outs – and don’t forget to factor in the fact that if there are multiple players to act after you, there’s a chance you may get raised and subsequently forced out of the hand.

Things to Remember

It’s important to note that many times, you’ll probably find that you simply don’t have time – or you forget – to work out the odds, especially when you’re in the middle of a hectic hand. However, try to brush up on your knowledge of poker winning hands from time to time, as you’ll find that this will soon become concreted within your brain, helping you to get a firm grasp on the game.

Frequently Asked Questions

Below, we’re going to finish this guide by answering a few commonly asked questions about poker odds.

How to Work Out Outs In Your Head

Like we just mentioned, there will often be times that it just seems too confusing, or hard to work out the odds in your head. When you find yourself in situations like these, one of the best pieces of advice we can offer, is to just slow down, take a deep breathe, and keep yourself calm and collected.

In most Texas Hold’em games, you’ll have ample time to think about the hand, and the odds – and if you’re looking for a quick way to work them out, it can help to brush up on some of the more common situations you’ll come across. For example, if you hold a pair pre-flop, and find yourself against a player holding two over cards, there is pretty much a 50/50 chance of you winning the hand.

Things like this can help – but above and beyond, it all comes down to practice as we keep mentioning, so spend a few minutes every day reading about poker statistics, and you’ll soon find that it becomes second nature to you!

What Are Outs?

The “outs” are the cards that you can hit to complete your hand. Say, for example, that you hold 2 cards that are suited hearts, and the flop contains another two cards that are hearts, and one spade. You “outs” are the remaining heart cards in the deck that can be drawn on the turn or the river, to help you complete your hand.

How to Count Outs

To determine how many outs you have, you simply need to work out how many cards there are in the deck that help you to complete your hand – and then minus the two hole cards you’ve been dealt, and the community cards currently visible.

Odds of Winning Poker

Some of the most common poker hands that you’d want to know the odds of, include an open-ended straight draw, which has odds of approximately 6/1, four-to-a-flush, which offers odds of around 4/1, an inside straight draw, which is approximately 10/1, and having a pair pre-flop which then turns into a set when the community cards are dealt, which is approximately 8/1.

Odds of Being Dealt Poker Aces

The odds of being dealt pocket aces in a standard Texas Hold’em game is around 220/1. This means that every 220 hands you play, you can expect to see pocket aces once – although, as is the case with ANY type of gambling, it could be 2,000 hands before you see aces… or you may see them back-to-back. It’s all a game of chance at the end of the day.

Chances of Winning with Pocket Aces

Pocket aces are – by far – the strongest starting hand in Texas Hold’em, and the chances of you winning with them largely depends on how many players are also in the hand with you. As a general rule of thumb, if you hold pocket aces on a 9-player table, you have odds of around 25% to win the hand at showdown – but the odds of you winning improve as more players drop out of the hand, so it can often be a good idea to play aces aggressively to avoid too many players joining the hand.