Video poker is one of the most popular casino games in the world. It offers a great combination of strategy, skill, and luck.
One of the most exciting hands to hit in video poker is four of a kind. But what are the odds of getting 4 of a kind in video poker? Let’s take a closer look at the math behind this exciting hand.
First, we need to understand what 4 of a kind means in video poker. In this game, 4 of a kind means that you have four cards with the same rank. For example, four jacks or four 7s would be considered 4 of a kind.
There are several different types of video poker games available, and each has its own paytable and odds for hitting different hands. However, we can calculate the odds for hitting 4 of a kind using some basic math.
The first thing we need to know is how many possible combinations there are in a deck of cards. There are 52 cards in a standard deck, so there are 2,598,960 possible five-card hands that can be dealt.
Next, we need to determine how many ways there are to get 4 cards with the same rank out of those possible hands. To do this, we need to use combinations.
There are 13 different ranks in a deck (Ace through King). For each rank, there are four different suits (hearts, diamonds, clubs, and spades). So there are 13 * 4 = 52 possible ways to get a specific card.
To calculate how many ways there are to get 4 cards with the same rank out of five cards dealt, we use combinations. The formula for combinations is:
nCr = n! / r!(n – r)!
Where n is the total number of items (in this case, the number of cards in our hand), r is the number we want to choose (in this case, 4 cards with the same rank), and ! means factorial (which is just multiplying the number by all the numbers below it).
So for our example, we have:
nCr = 5! / 4!
(5 – 4)! nCr = 5
This means that there are five ways to get four cards with the same rank out of a five-card hand.
Now that we know how many ways there are to get 4 of a kind, we can calculate the odds of hitting this hand. The formula for odds is:
odds = number of ways to win / number of ways to lose
In this case, the number of ways to win is five (as we just calculated), and the number of ways to lose is all the other possible combinations that don’t result in 4 of a kind. So:
odds = 5 / (2,598,960 – 5)
odds = 1 in 549,936
So the odds of hitting four of a kind in video poker are approximately 1 in 549,936. This may seem like a long shot, but keep in mind that video poker machines typically deal out hundreds or even thousands of hands per hour. So while it might be rare to hit this hand on any given hand, it’s not uncommon to see it happen fairly often.
In conclusion, understanding the odds of hitting different hands in video poker is an important part of developing a winning strategy. While getting four of a kind may be rare, it’s still an exciting and lucrative hand when it does hit. By understanding the math behind this hand and other hands in video poker, players can make informed decisions about which cards to hold and which ones to discard.
