Hate maths? You’re in luck. Paul Phua reveals the magic formula poker players use to make calculating poker odds simple

On my poker odds page, I explained why knowing the odds is vital to being a money-making poker player. Here I will show you how to calculate those poker odds.
Let’s take the example from my last blog: you have a “gutshot” draw, where there is only one card that will complete your straight – for instance, you have 6-9, and the flop is A-5-8, so you have to hit a 7. I said that would only work 1 in 6 times.
How do I know this? And how can you work out the odds in any poker situation? There’s an easy way, involving a simple “magic” formula; and there’s a harder way, which means relearning some maths you’ve forgotten since school. The easy way is all you need for basic poker; but if you’re more mathematically inclined, read on to the second way.

Step 1. First calculate your “outs”

“Outs” is the term used by poker players for the cards that will help you win. In the above example, only a 7 will help you win. Since there are four 7s in a deck of cards (one of each suit), you have four “outs”.

Step 2. Now apply the magic formula

If you don’t want to be bothered with the detailed mathematics of probability, just follow this simple formula:
* To find the percentage chance of hitting your card on the turn, multiply the number of outs by two
* To find the percentage chance of hitting your card on the turn or the river, multiply the number of outs by four
Is it really that simple? Yes, it is. It’s not absolutely accurate, but it’s very close.
As an example, let’s apply this magic formula to our gutshot draw. We have four outs, so to find out our chances of hitting one of them by the river we multiply 4 x 4, getting 16. So that’s 16% — or to put it another way, 16/100, which some quick mental arithmetic will tell you is roughly 1 in 6. Simple, unless you have no idea what fractions or percentages are, in which case I’m afraid that’s beyond the scope of this blog!
My next blog will explain how you can use these odds in poker to decide whether a bet is worth calling. And that’s it for now. Unless you want to know more about probability, in which case, read on…

Calculating probability the hard way

First, let’s look at probability in general before looking at poker. To find the chance of any particular outcome, you divide the number of desired outcomes into the total number of possible outcomes. Let’s take rolling a die as an example: if you need to roll a 6, your chance of doing so is 1 in 6. That’s one desired outcome divided into the six possible outcomes (since it’s possible to roll any one of six numbers: a 1, 2, 3, 4, 5 or 6). And if what you need to roll is a 5 or a 6, that’s two possible outcomes, so you divide 2 into 6, giving you a 1 in 3 chance.
Now let’s apply this to poker. There are 52 cards, so there are 52 possible outcomes when you turn a card over. On the flop, you know what your two hole cards are, as well as the three cards face-up on the flop, so actually there are only 47 cards left that might contain your outs.
In the gutshot draw example above, there are four 7s that will help, so to get your odds, you divide 4 into 47. We don’t all have a calculator in our heads, so when you’re at the poker table, make sums easier by rounding them up. In this case, 4 into 47 is nearly the same as 4 into 48. So, we now know we have a roughly 1 in 12 chance of hitting a 7 on the turn.
This isn’t too hard, but it gets trickier when calculating several rolls of a die, or turns of a card. When you are dealing with probabilities over multiple attempts, you actually first have to calculate the chance of something not happening, rather than the chance of it happening.
The chance of not hitting a 7 on the turn is 43 out of 47: 43/47. The chance then of not hitting a 7 on the river is very slightly different, since there are now only 46 cards left that might include your hoped-for 7. So the chance of not hitting on the river is 42 out of 46: 42/46.
To find the chance of not getting a 7 by the river, you must multiply these two fractions. (Remember, with fractions you have to multiply the tops and bottoms separately.) From this we get: 43/47 x 42/46 = 1806/2162.
To make this complex figure understandable and useful, we need to express it as a percentage. To do that, we want to turn the number under the fraction bar (mathematicians call this the “denominator”) into 100, and find out what that does to the number above the bar (the “numerator”).
If we divide the denominator of 2162 by 2162, it becomes 1. Multiply it again by 100, and it becomes 100. So now we do the same action to the numerator (we do need a calculator for this). 1806 divided by 2162 is 0.84. Multiply that by 100 and we get 84. So now we can see that 1806/2162 is the same thing as 84/100 – 84%, in other words.
Remember, the figure of 84% we just calculated is the chance of not hitting our hoped-for card. So our chances of hitting our card will be 16% — or to put it another way, 16/100, which is about 1 in 6.
If this all sounds a bit tricky, well, it is! But don’t worry: you always have the magic formula to fall back on.
Read the next article in my mini series on how to play a flush draw.

Paul Phua introduces the latest in a series of “In Conversation With Paul Phua” videos, in which the thrilling young poker pros Rui Cao and Wai Kin Yong discuss how to improve your game

How long would you play poker for in a single session? Eight hours? Twelve? Fifteen?
Try 40 or 50 hours!
As you will see in this three-way video interview between myself and the brilliant young players Rui Cao and Wai Kin Yong, we often used to play for two days and nights without stopping. We don’t do that so much anymore, but a round-the-clock game is still pretty common. As we say in the video, one skill you definitely need to develop as a player is stamina!
As I think comes across in this video, when you play poker together for such long periods, you develop a kind of bond, a friendship. But you also develop an awareness of each other’s strengths and weaknesses – and, if you are a good player, you will become conscious of your own.


Rui Cao admits in this interview that one of his weaknesses is playing too loose, wanting to show the table who is boss. “I think it’s an ego problem,” he says.
Then again, it’s also what makes Rui Cao one of France’s most exciting players. It’s six years since Rui Cao first came out to Macau to test himself in the high-stakes cash game against some of the world’s top poker pros (poker players call it “The Big Game”), and I could tell he was instantly drawn to the thrill of those huge pots of tens or hundreds of thousands of dollars.
As for Wai Kin Yong, he admits his weakness is probably being too “sticky”: “I always find the hands to call,” he says in the video.
Is that a bad thing? Well, on the one hand it’s exciting to make that “hero call”, where you call down a bluff with just Ace high. But on the other hand, if you don’t learn when to lay down a hand, even a hand as good as two pairs, you will lose a lot of money over time. You must ask yourself: are you calling because you’ve thought through the action on every street, and you really think the other person is bluffing? Or is it because your ego won’t let you back down, or you can’t stand not knowing and must see the other person’s cards? It’s something I think you learn as you get older: the patience and humility to fold, and to wait for a better spot further down the line where you are more certain of making money from the hand.
That said, Wai Kin Yong is an exceptional player for one so young. You could say it runs in the family: his father is my friend, the businessman Richard Yong. But Wai Kin Yong also very much has his own style, and has been doing very well in live tournaments. Last September he won the Triton Charity Tournament in Manila, and then just two months later the Triton Super High Roller Series Main Event as well. This February he finished sixth in the Triton Super High Roller Series Main Event. These three pay-outs were together worth more than $3 million!
So it was a pleasure to be able to sit down with these two excellent players, and talk about poker for this video. I hope you enjoy it, and pick up some tips for improving your own playing style.
It’s your decision whether to play loose or tight, aggressively or by trapping other players into making a mistake. Whatever works for you, whatever suits your personality, style and the dynamics of the table you’re on.
But the one thing I think you can definitely take away from this video interview is that good players are always talking about poker with other good players: comparing notes on hands and playing styles, working out what they can learn from each other and how they can play better in future. If you can do this, the next big tournament winner could be you!
Enjoyed this video? Subscribe to the Paul Phua Poker School YouTube channel so you don’t miss the rest in this series. It’s free!

Paul Phua introduces the first in an exciting new series of videos for the Paul Phua Poker School YouTube channel featuring some of the world’s top pros

If you want to improve your poker and become a winning player, there is no better place to start than by watching strategy tips from the top pros. Phil Ivey, Dan Cates and Dan Colman have very generously given up some of their valuable time to film this video for the Paul Phua Poker School – and with these high-stakes cash and tournament players, “valuable time” is not merely a figure of speech!
Phil Ivey is a ten times World Series of Poker bracelet winner, and one of the most fearless and creative players of the game. Dan “Jungleman” Cates passed the $10 million online cash earnings milestone nearly three years ago. And Dan Colman has graduated from internet poker (he rose to fame in 2013 as the first hyper-turbo player to win $1 million on Pokerstars in a year) to take down $28 million in live tournament play.
The Paul Phua Poker School YouTube video team caught up with these players at the Triton High Roller Series in Manila this February, and their tips for beginners are just as insightful as you would expect. And it’s not only beginners who can benefit from their strategy advice.


Phil Ivey tells players that “an important thing is to be able to manage their money”. This is very true: many a player has gone bust by moving too quickly to levels they cannot really afford. For more detailed advice, see my previous Paul Phua Poker School blog on bankroll management.
Dan Colman recommends that you should “get out of your comfort zone”, and “play in difficult games”. This may seem strange: why choose a difficult game if you can find one with poor players instead? But this is something I myself did when starting out in poker. I challenged myself to play with some of the world’s top pros in high-stakes cash games, not because I arrogantly thought I could beat them, but because I humbly felt I could learn from them. If I have any skill at poker (and Phil Ivey has been kind enough to say that “Paul Phua is probably the best non-pro I’ve ever played poker against”), it is thanks to learning from the best.
And if you do find yourself up against more experienced players, Dan Cates’ advice in the video may prove especially valuable. He says, “The first tip for beginners would be to play tighter than they think.” Unless you are sure you can outplay everyone else around the table, you should pick your poker battles with care, going armed with only the best starting hands.
Those are just a few of the useful tips in the video that will improve your poker game. Watch it now to discover more, and subscribe to the Paul Phua Poker School YouTube channel so as not to miss new videos in the series. It’s free!
 

With poker millionaires Charlie Carrel and “Xavi666” making headlines for their big wins, Paul Phua explains why it can take years to become an overnight success.

Two players deserve particular congratulations this week. One is a player from Panama known by his online name of “Xavi666”, who has just won over a million dollars in the PokerStars Guaranteed Sunday Million tournament. He is the 200th poker millionaire created on the online poker site.
The other is the personable young player Charlie Carrel. He proved a good ambassador for the game of poker when he was interviewed on a Channel 4 series in the UK called How’d You Get So Rich? It’s not often poker stories cross over to the mainstream media, but many national papers reported on the TV programme’s featurette on how Charlie Carrel turned his initial online stake of just £10 into £3 million.

The reason these stories have attracted so much attention is that they feed into a common dream about poker: that it’s an easy way to get rich quick.

The most famous example in poker history is when humble accountant Chris Moneymaker turned a $39 investment on PokerStars into $2.5 million in 2003. He entered a $39 satellite tournament, which got him into a $600 satellite, which won him a seat in the Main Event at the World Series of Poker – at which this gifted amateur won the whole thing.
But the truth is, all these players have put in a lot of work behind the scenes that you don’t see. I touched on this subject before in my blog on The Iceberg Illusion. Take young Charlie Carrel. He told the TV presenter Katherine Ryan that he started off at very low stakes, playing for 16 hours a day to improve his game, while living with his grandmother. Having studied Maths, Further Maths and Physics at A-Level, he made a detailed study of all the odds. He applied sensible bankroll management, only moving up to a new blind level when he was sure he had mastered the one he was on.
As to Xavi666, after winning his PokerStars million he said that “finally everything came together”. In other words, he had been working and playing hard to reach this point.
There’s a couple of old sayings that I find very insightful. One is, “It takes years to become an overnight success.” The other is, “The harder I work, the luckier I seem to get.”
What they both mean is that every time you see an actor, musician or poker player suddenly become famous, or seemingly “get lucky”, the chances are they have been perfecting their craft, unnoticed by the general public, for many years before that. When opportunity knocks, they are ready for it.
Certainly when I started at poker, I treated it as a challenge, something to work at. I had fun, of course, as I love the game, but I also had the desire to learn and improve. I regularly sat down to marathon high-stakes cash games with some of the world’s top poker pros, not because I felt I would “get lucky” against them, but so that I could learn from their strategy. That was nearly a decade ago, and I still analyse every big hand at the end of a big poker session to see if I could play it better if faced with a similar situation in the future.
So think about it. Are you going to play poker just for fun, staying in more pots than you should do with poor odds of success, in the hopes of getting lucky? Or are you going to play for fun and for profit, improving your game and learning new strategies over time so that, when you do get your shot at a big tournament, you have the skill and experience to become the next “overnight success”?
If it’s the latter, there is good news: some of the poker pros I often play with have kindly agreed to share their top tips and strategy advice with you, my loyal Paul Phua Poker School followers. There’s quite a line-up to my new video series. We have two big Dans (Cates and Colman), as well as Phil Ivey. Discover the full list of names and watch the trailer here.
So if you do dream of becoming the next Xavi666 or Charlie Carrel, a good first step is to go to the Paul Phua Poker YouTube channel and subscribe, so you don’t miss any Paul Phua Poker School videos. It’s free!
 

Do you want to watch poker tips and poker strategy advice from Phil Ivey, Dan Colman, Dan “Jungleman” Cates and many more top Texas Holdem players? Of course you do!

Hi, it’s Paul Phua here with some very exciting news. My new series of “Tips from the pros” and “In Conversation” videos is almost ready for you to watch! Three months ago I released a series of poker videos on my YouTube channel, and I noticed that the two “Paul Phua In Conversation With Tom Dwan” videos were the most watched, with more than 20,000 views.


So when some of the world’s finest poker players joined me in Manila this February at the Triton High Roller Series, I asked my video team to capture some of their best poker tips and strategy advice. Which poker pros will appear in the video series over the next four months? Watch the trailer video on this page, or read on:

Phil Ivey. That’s right, Phil Ivey! Phil is an incredible player, absolutely fearless, brilliant at reading his opponents. He has ten World Series of Poker bracelets and nearly $24 million in live tournament cashes, even though he primarily plays high-stakes cash games.
Dan Colman. Dan Colman ranks above even Phil Ivey in the list of the ten biggest live tournament earners, having defeated Daniel Negreanu heads-up for a massive payout of $15.3 million in the Big One for One Drop at the 2014 World Series of Poker, only a few days after his 24th birthday. This February he won the 2017 Triton Super High Roller Series Manila HK$ 250,000 6-Max Event, and then, just two weeks later, he won the Aria $25,000 High-Roller as well.
Dan Cates. Also known as Daniel “Jungleman” Cates, after his online poker name, Dan passed the $10 million online cash earnings milestone nearly three years ago. His famously aggressive playing style has made him one of the most formidable heads-up and shorthanded players in the world.
Timofey Kuznetsov. Playing under the name “Trueteller”, Timofey Kuznetsov is another online poker specialist. He hit the headlines in 2015 for a marathon 30-hour high-stakes heads-up session against Phil Ivey on PokerStars during which they played nearly 5,000 hands, and last week he was revealed to be the biggest online winner of the year so far.
Winfred Yu. As President of the Poker King Club, Winfred Yu runs the world’s highest-stakes cash games, in Manila and Macau. He is, of course, a terrific player himself, and has been active on the poker circuit for more than a decade.
Wai Kin Yong. Poker is in Wai Kin Yong’s blood – he is the son of the businessman and high-stakes player Richard Yong. In November 2016 he took down one of the biggest prizes in tournament poker (over $2m) at the Triton Super High Roller Series Main Event in Manila.
Rui Cao. Rui Cao emerged nearly a decade ago as one of France’s strongest players. He built his reputation online as “PepperoniF” before challenging the Macau high-stakes cash games as far back as 2011.
Go subscribe now to the Paul Phua Poker YouTube channel, so as not to miss a thing. It’s free!

I know a lot of my readers are amateur players, practising at home to perfect their game so they can place bigger bets and play bigger tables.

Paul Phua gallery image 9
deck of cards

For that reason, a lot of the stuff on my website is given over to advice on strategy and tactics of play. However, there is one important aspect of poker I haven’t discussed yet – the cards themselves!

The deck you use to play poker won’t necessarily make a huge difference to your success at the game, but I thought it might be interesting for me to tell you a bit about the different types of card deck out there, what brands are being used by pros in casinos, and which might be best for your home play.
A standard deck has 52 cards – a tradition that has been around for more than 500 years. There are more than 80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 different outcomes to the order of shuffle of the 52 cards. The fact that number has 67 zeros means you are extremely unlikely to get the same arrangement twice.
In a casino, it’s pretty standard practice to have more than one deck of cards to hand – this is a good idea in any poker game because if one deck gets damaged or marked, you can switch to the back-up. A marked deck can give an advantage to any player who can spot the marks. In poker rooms, the two decks will usually be two different colours so they are easily distinguished. Most of the cards you buy online will come in sets of two decks and have these contrasting back colours.
For a game at home, I would recommend changing deck every two hours or so. That’s because even an undamaged deck can become marked with fingerprints, or food and drink stains – common for games at home.

However, if a card becomes visibly damaged you should change it immediately.  Players can track the damaged card. If you’re hosting a mini-tournament make sure if that you have a couple of packs per table.

Quite often in professional games, a player might ask for a “new setup”, which is them asking if the decks can be changed. Usually this is because they feel they have had a bad run with the deck of cards currently in use, and want to change their luck with a new pack. I am quite superstitious so I understand – but it can slow the game down quite a bit if you are changing deck every other hand!

When you are thinking about which cards to buy it can be quite overwhelming – there are so many brands and types of deck that you can buy online.

The two basic types of playing cards are 100% plastic cards and paper cards which have then been coated in plastic.
Casinos will always use the 100% plastic ones – and these are the type I prefer to play with. However, coated cards are the more common – they are the sort you will find at a supermarket. However, they are not durable enough for sustained play, and get marked or scuffed much more easily than plastic ones. So if you are going to play quite a bit of poker with your friends, I would go for the more expensive but better value 100% plastic cards.
Professionals use them. Casino dealers like them because they deal nicely and slide smoothly across the table. At a pro-table a dealer will usually use a machine to shuffle the deck, but at home these plastic cards shuffle nicely in your hands and carry a good weight.
It’s not too hard to find plastic cards online, and you can even find the same brands as they use in professional tournaments – which can be useful practice if you are working your way up to your first competition! The brands used most often in casinos are Kem, Copag, Gemaco and Modiano. Kem are probably the most popular because they are used on the World Series of Poker and the World Poker Tour.
One thing a lot of people ask is whether there are different rules for a standard size or design of cards in different countries, but in my experience the international standard is 63.5mm X 88.9mm with regular denomination, suit, and court cards.
But, as I said before – the cards should be your tool to win. It’s useful to have a couple of good decks, but if you are going to invest in something to improve your game, it should be your time.

One of the world’s best poker players, Tom Dwan, met up with Paul recently to play a few hands and talk about the game.

It’s part of our “In Conversation” series where Paul chats to some of the best Texas Holdem players in the world. In this video, Tom and Paul discuss the art of “trapping” in poker.

One of the things you hear discussed most in the poker world is bluffing. When to do it, how often, with how many chips, which player does it the most? All sorts of questions commonly asked on this site by players starting out in poker. But what about its opposite counterpart, trapping? You never really hear it discussed much at all.
With bluffing, you are trying to convince your opponent that you have good cards when in fact you don’t. The means — making big or emphatic bets to give the impression you are confident in your hand. The end game – to scare them away from the hand so you can take the pot for yourself. Trapping an opponent in Texas Holdem poker is the opposite. Here, the aim is to persuade your opponent that they aren’t in fact very good, that you are only barely staying on in the hand more out of hope than expectation. The reality, though, is you have a hand that is very strong. So the aim is to get as many opponents to stay in the poker hand so you can win money from a player who has a habit of betting aggressively. There are lots of ways to do it. Perhaps you might come across as uncertain, or you play slowly and cautiously, perhaps you only play with small bets at the beginning of the hand. Paul Phua doesn’t always recommend this though because keeping lots of players in the hand can sometimes blow up in your face after the flop when your opponents’ bad hands can turn into good ones.

Here Tom Dwan and Paul Phua talk about whether Trapping is a good idea for amateurs or not.

The American poker mega star Tom Dwan met up with Paul Phua in a casino in the Philippines recently to play at a tournament in aid of a cancer charity in the country.

They managed to find some time though to have a chat for the Paul Phua poker website. Watch their conversation on “trapping” here, where Tom Dwan poses the question about whether beginners trap enough, or too much. But in the second video in our “In Conversation” series, Paul and Tom talk about the role of players’ nationalities in Texas Holdem poker. Can you make generalisations about an opponent’s style of poker play based on the country they come from, or on other factors like age and profession? Does a player from Germany for example play in one way, and a player from China navigate their way around the poker table in another? Do old players bluff more or less than young ones? Does a banker have a specific tell? Although generalisations are never the whole truth, even so, Paul and Tom thought, yes, they are often accurate! Watch the video – it’s a lot of fun.

When you are in the casino at the beginning of a poker game, and you have lots of chips, the blinds are something you hardly notice. Towards the end of a poker night, especially if things aren’t going so well and your chip pile is lower than you’d like it to be, or the blind bets are increasing in size, then the blind can really eat into your stack.
The Blinds Poker
Some poker games have antes – forced bets. But Texas Holdem doesn’t, meaning you can fold your cards without betting. Texas Holdem poker does have something called blinds though. They are another type of forced bet, but this time before you have been dealt your cards. Like antes, they exist so that there is a cost to playing, so the poker games don’t go on and on with players just waiting to be dealt a great hand. Paul Phua thinks that the blind keeps the momentum up, and ensures the game of poker finishes within a reasonable time frame – especially since the blinds often increase in value during a game of Texas Holdem to speed things up even further.

There are mainly two blinds in Texas Holdem – the big and small blind, but there can sometimes be three players who have to make them.

The name comes from the fact that players are being asked to bet without seeing their hands. They are betting blind, with no knowledge of the hand’s worth. So in the casino, whether you hold a 2 and a 3 unsuited, or a pair of aces – before you see your hand it’s all the same.
Paul Phua says the blind also marks potential poker strategy. Depending on your position around the poker table in a casino, or a social poker night where the dealer changes as the “button” moves from player to player, you will have to give certain blinds. Being in the small blind spot on a poker table is a disadvantage because you will be the first to act in every round after the flop. But Paul Phua’s poker tip is to remember never feel committed to a pot simply because you have paid your blind, especially in Texas Holdem, and not be afraid to enter a pot if you have a strong enough hand.

Yes, and I’ll tell you why.

For the first few years that I played poker, I often showed my set of cards at the end of the poker hand when I was bluffing (which wasn’t often).

I wanted to get the impression in people’s heads that I was a bit of a repeat bluffer. Maybe I would even throw in a few “tells” to sell the story!

This is a complete poker star strategy – make them think you are a repeat bluffer so that sometimes they would call, when, in reality, you have a good hand.

In another phase of my life in casino games, especially Texas Holdem, I then switched to doing the opposite.

For the last few years, I have begun bluffing a lot more in poker games to get more equity. However, other players around the poker table don’t know that. Because now I show my “real” hands, and not my fake ones at the end. This is to give the impression that I am a solid player, who doesn’t bluff so much.

Perception and reality!