Poker probability involves math as its crucial factor. In all honesty, psychology also plays a part in the game, besides the overall excitement, entertainment, and profitability. Regardless, improving your poker skill is impossible without understanding the underlying importance of mathematics in this game.
There are numerous definitions of probability. It’s easiest to think of this concept as mathematics, which explains a particular event’s likelihood (outcome). The simplest example of probability is a coin flip. In any case, the result of a coin flip will either be heads or tails. Because there are only two outcomes, each probability is 50% (one outcome of two).
How Does Probability Apply To Cards?
The standard playing deck contains 52 cards, meaning that the number of possible outcomes is much higher. Every deck also has thirteen ranks (Ace, King, Queen, Jack, and numbers between two and ten) and four suits (spades, hearts, diamonds, and clubs).
As a result, you have a 25% (1 in 4) chance of getting a spade as your first card and a 7.7% chance (1 in 13) chance of your first card being an Ace. But, there’s more: cards are different than coins because they have “memory.” The deck’s makeup changes after each card that’s dealt.
For instance, let’s imagine you get your first card that’s an Ace. After your first card, only 51 cards remain in the deck, including only three Aces. Consequently, you will now only have a 5.9% (3 in 51) chance of getting another Ace. Compared to the previously mentioned 7.7% chance of the first Ace, the odds are now significantly lower.
Poker Probability: Practical Examples
While it’s significant to understand the theory of probabilities in poker, there’s no substitute for practical demonstrations. To that end, we’ll cover several pre-flop and post-flop possibilities as numerical examples:
- Pocket Pairs
- Hand vs. Hand
- Strategy Improvements using poker probability.
Let’s imagine you’re interested in finding the odds of receiving a pair of Aces. The steps you need to take are straightforward: you must multiply the probabilities of getting each of the two cards. In other words, you need to multiply 4/52 with 3/51, and the approximate likelihood will amount to 0.45%.
What does this probability mean practically? If you’re playing at an online casino, let’s assume you’re playing an average of 30 hands each hour. Following this assumption, a simple calculation reveals that you can receive pocket aces once every 7.5 hours, on average.
Simultaneously, you have a 5.9% chance of getting any of the thirteen possible pocket pairs (twos through Aces). The calculation is similarly straightforward: 13/221 = 1/17 = 5.9%. In other words, you should get your hands on any pocket pair approximately every 35 minutes.
Hand Vs. Hand
Now that we’ve gotten the basic poker probability theory out of the way let’s observe some more pre-flop situations. While understanding poker math is crucial, it is equally essential to be aware of your opponents. You must note all of your opponents’ hands as well, particularly if some of them are going all-in prior to the flop.
Here are some common examples. If you’re holding two high cards, and your opponent has a low pair, there’s a 55% chance you’ll win. In a situation where you’ve also got two high cards, but your opponent has two low cards, the winning probability goes up to 63%.
When you have a middle pair, and your opponent has one high card and one low card, you’re looking at a 71% chance of winning. Additionally, if you have a high pair and your opponent sports a low pair, there’s an 82% chance you’ll win. However, if your opponent has two low cards instead, your odds go up to 83%.
As Hold’em is one of the most popular poker variants available, let’s also observe some valuable math for this game with particular starting hands. For instance, there’s a 0.25% chance that a pair will flop four of a kind. Conversely, there’s a 12% probability that a pair will flop a set.
The chances that two suited cards will flop a flush are 0.85%, but the odds of the same cards flopping a four flush is 10.9%. You’re looking at a 6.5% poker probability of two suited cards making a flush and a 32% probability that non-pairs will pair at least one card.