The Complicated Mathematics Behind Poker and Being Successful

Although it’s a gambling game, poker requires skill to play. The thing that separates top players from the others isn’t luck. It’s skill and mathematics. Although luck invariably plays a role in how successful a player is during one game, over hundreds, they need to have probability on their side. The best players are able to develop their strategy based on the probabilities of their hands, making luck work in their favor. 

There are a lot of ways to play poker, but most of the mathematics involves calculating the probability of success as well as the pot odds. Online poker players need to master these techniques if they want to have the best chance of winning consistently, especially when playing at a high level. 

Probability in Poker

Probability, or the likelihood that a specific outcome will occur, is the branch of mathematics that all poker players should know. Probability is best explained by using the example of a coin toss. The coin has two sides, heads and tails. 

Because there are only two sides of the coin and therefore two outcomes, there is a 50% chance that one outcome will result from the coin toss. Probabilities are more difficult to calculate in poker because each game has far more outcomes. A standard 52-card deck is used in poker, with 13 cards in each of the four suits. 

Because there are four versions of each card, you have a 4 in 52 chance of being dealt a specific card. For example, your chance of having an ace in your starting hand would be 4 in 52 or 7.7%. For two of the same cards, you have to work out multiple probabilities together. The calculation would be:

(4/52) x (3/51) = (1/221) = 0.045%. Therefore you can expect to get a pocket pair of aces once in every 221 hands on average. It’s useful to know the probabilities of starting hands, but it’s not the most important. You can also think about the probabilities of certain cards showing up over the next phases of the game.

Aside from knowing the probability of starting hands, you can also calculate the relative probabilities of certain cards showing up on the flop, the turn, and the river. This is particularly important when it comes to knowing whether to fold, call or raise. For example, you may have a suited king queen hand, so you’ll want to think about the probability of the royal flush occurring once the flop has revealed a jack of the same suit. 

Pot Odds

While it’s important to know what your chances are of certain starting hands, being able to work out pot odds is arguably far more important. Pot odds are simply the cost of your probable next move to the size of the pot already in play. Players assess the probability of winning a hand with a future card using pot odds to determine the call’s worth.

Ratios are typically used to indicate pot odds because they are simpler to calculate than percentages. Most players will always work out the pot odds in their head before they make a decision, basing their strategy around the odds. Failing to take favorable odds will see you lose money over time, while only going for value in the odds is the best way to ensure success. 

As an example of what pot odds are, let’s say that there’s $100 in the pot, and your opponent raises by $100 on the turn. At this point, the pot size would be $300 if you choose to call $100. Therefore, the pot odds are the size of the pot divided by the size of the call. So in this case, $300/$100. Or 33.33%.

However, it’s not that helpful to calculate your pot odds on their own. You need to compare them to your chances of winning in order to decide whether or not to call. If your chance of winning is higher than the pot odds, you should take the bet. Let’s take the previous example, where the pot odds were 33.33%. As long as you have a higher than 1 in 3 chance of winning your hand, you should call the raise. 

Counting your outs in Texas Hold’em is the first step in determining your chances of winning. An out is a card that, if dealt, provides you the best hand on a later phase of the game. Something to keep in mind to help you get the most out of your pot odds is that winnings odds are around four times that of your out when on the flop. On the turn, you’re looking for winnings odds 2.2 times higher than your outs. 


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