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Poker is one of the most common and popular card games, both online and offline. From large online casino tournaments to small neighborhood basement games, poker has been attracting players for generations. For instance, when analysing what online poker sites in New Zealand offer, it has been reported by online-casinos.com that when playing any kind of casino game, it’s always crucial to pay attention to the theoretical payout, and this is particularly true when you are paying poker. But how can you calculate that payment? How do you easily assess the terms and probabilities when playing poker? And how has Bill Chen changed the way that many players look at the game all together? Here’s everything you need to know! 

Understanding How Poker Works

In order to understand poker game theory and how maths can impact the game, it’s important to understand the basics of how poker works. Typically, the winner of each hand of poker is the player that holds the highest ranked hand when it is time to show their cards – this is known as the ‘showdown’. The strongest hand you can play is a ‘Royal Flush’ (a ten, Jack, Queen, King and Ace all from the same suit) followed by a ‘straight flush’ ( 5 cards in a row from the same suit) or ‘four of a kind’ (4 of the same cards: one from each suit). However, if you aren’t blessed with a strong hand then that doesn’t mean that you can’t still win the game: it is here that poker strategy comes in. 

If you want to win consistently then you will need to invest both time and effort. Your goal should be to make the best possible play that you can every time, and if you’re making consistently good decisions then the quality of your game will improve. But it’s not enough to simply make wise decisions, have a good poker face, and make the most of the cards your dealt: you also need to try to make an educated guess about what hands the other players at the table might have. 

The Changing Face of Poker

The face of poker is changing, and this is largely due to the impact of mathematician-come-poker champion Bill Chen. Traditional gamblers who rely on their instincts are slowly being replaced by a new generation with a new approach: One of the most important features of this new approach is that these poker experts rely on quantitative analysis and go to great lengths to apply mathematics to the game. Put simply, the world’s new poker experts are geeks, and Chen exemplifies this perfectly! Chen still works as a quantative analyst and software designer, using his poker skills as a lucrative hobby.  

One of the most notable books on the subject, and the one that really brought maths-based poker play to the fore, is The Mathematics of Poker by Bill Chen. This book revolutionized the game of poker and introduced game theory to a broader audience, and if you can comprehend this fairly complicated approach to the game, then it could well fast track you to great success in your own game. When you apply maths to poker, you can calculate the expected value for your hand, evaluate your odds, and even work out what the likelihood is that you’ll come out of the game on top. 

The best way to think about it is that poker is a game of incomplete information. You know what hand you have been dealt, but you don’t know any of the other variables in the game. This is a poker strategy puzzle and maths, and game theory, can help you to solve it. One of the things that makes poker such a fascinating game is the sheer variety of different approaches, styles and ways to play.

Calculating Poker Terms and Probabilities

A full evaluation of game theory would be much too long and complex to cover in this article, but perhaps the easiest way to apply mathematics to poker is to look at probability. This includes probability of being dealt certain hands and how often they’re likely to win. 

For those not already in the know, probability is the branch of mathematics that deals with the likelihood that one outcome or another will occur. (for example, if you toss a coin you will either get a result of heads or tails, and the probability is 50% that it will lend on either option). Obviously, the number of options are much greater when dealing with a deck of cards: you have a 1 in 52 chance of getting any single card. But once one card has been dealt (an ace for example) you changes of getting another Ace drop, because one of the aces is already out of play. The odds of getting any Ace as your first card are 1 in 13 (7.7%), whilst the odds of receiving another Ace are 3 in 51 (5.9%). This figure will get lower and lower as each subsequent Ace is drawn, and you can use this information to help you calculate the odds that you will receive the hand you need. This same rule can be applied to every other card, and you can use the same principles (albeit with more complicated calculations) to ascertain the likelihood that you will get a pair, or a flush, and so on. These figures will change constantly, with each new card that you are dealt. 

A strong knowledge of how maths and probabilities can be applied to poker will help you adjust your strategies and tactics during the game, as well as giving you reasonable expectations of potential outcomes. This is a very simplistic look at how probabilities can be applied to poker, because you will be playing with at least five cards, and therefore the odds and the calculations will become more complex with each hand that is drawn, but the fundemental principle remains the same. 

Wondering if applying maths to poker really works? When we look to Bill Chen, we see that the answer is certainly yes! As of 2017, Chen’s total live tournament winnings exceed $1,900,000 and $1,725,000 of this has come from his 38 cash prizes from the World Series of Poker. has been a longtime participant in the recreational gambling poker newsgroup and its offshoot, and he has also been a member of Team PokerStars. Despite it not being his full time career, Chen has certainly made poker a very lucrative side hustle! His book is extensive (and very difficult to read) because  it certainly isn’t a simple process, but it is one that anyone with the will to learn, and a mathematical mind, could replicate. 

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