Have you noticed that the numerator and the denominator of hitting the second card changed? When we got the first card, there were only 51 of 52 cards left.

And the probability that you are dealt another 9, regardless of its suit, would be 3/51.

We’ve already known that the probability of being dealt a 9 is 4/52, which is the one you are holding now.

Now you are wondering what is the probability that you are dealt a 9 again. Suppose you are holding a 9♦, and you want to be dealt a pair. To sum up, the probability of dealing any random card is 1/52, the probability of hitting any specific card such as Ace or King, Queen is 4/52, and the probability of dealing any suit is 13/52. Then the probability of dealing any ♦ would be 13/52, because there are 13 cards of the same suit.

The same logic also applies to the situation where we only need one card from a certain playing card suit, diamond♦ for example.

On the other hand, if we want to be dealt an Ace, regardless of its suit, the probability would be 4/52, because there are four Aces among the 52 cards.

If we want to be dealt a 9♦，the probability would be 1/52, because there is one 9♦ in the whole deck.

Remember there are 52 cards in total in a deck: For example, when we want to be dealt one specific card: The two numbers we use most often in calculating hand probability are how many cards are in a deck and how many cards we want to be dealt in the game. Everything we cover in this article can be easily understood, allowing you to better understand how to calculate a hand’s probability before the flop.

In this article, we will discuss some common probability principles in Texas Hold'em poker games and how they are used.ĭon't worry about the poker math. Have you every felt overwhelmed by the numbers in odds charts? When seeing the winning percentages, probabilities, and various other mathematical probabilities in poker games, have you ever wondered where they come from?

Calculating probability of poker hands