The Odds Of A Full House

The Odds Of A Full House

Table of content:

The full house is one of the strongest poker hands that a player can create in any game of poker. It consists of 5 cards and includes three-of-a-kind and a pair. But here the question arises what are the odds of getting a full house in poker? To answer the same - we have made this in this in-depth guide for you, covering the meaning, mathematical calculation, the odds of getting a full house at the flop stage and the odds of getting a full house at the later streets.

What is a full house in poker?

A full house is characterized by any three cards that are of the same face value or number combined with any two cards that are of the same number or face value. To put it simply, a full house consists of 3 cards that are of the same rank and 2 cards that belong to another rank. For instance – a hand consisting of king of hearts, king of spades, king of diamonds, queen of clubs and queen of hearts is regarded as a full house in poker.

When it comes to determining the winner amongst two hands of full houses, the rank or denomination usually holds the utmost importance. Vital to this, a hand consisting of Aces of hearts, Aces of spades, Aces of diamonds, King of hearts and King of clubs is often regarded as the best full house hand in the world of poker. So much so, that this hand holds the potential of beating any another full house in any game of poker.

What are the odds of getting a full house in poker? – A mathematical calculation

So, you have got a fair idea of the basic concept behind a full house in poker. Now, let us understand what are the odds of getting a full house in poker using a mathematical calculation.

1)      To begin with, you should know the number of 5-card hands that can be dealt from a standard deck of 52 cards. The figure stands at 2,598,960.

2)      Thereafter, calculate the number of ways in which 5 cards can be dealt to produce a full house. To calculate the same follow the 4 below-mentioned steps.

·          A playing card can have a rank of 2,3,4,5,6,7,8,9,10, Jack, Queen, King, Ace. Since we are talking about a full house, just choose any 2 ranks from the 13 ranks. The number of ways to calculate this is 13C2

·          Since a full house contains a three-of-a-kind of one rank and a pair of another rank, just choose 1 rank from the 2 ranks chosen above. The number of ways to do this is 2C1.

·          Furthermore, choose a suit for the three-card combination. There are 4 suits in a                   standard deck. From there choose any 3, the number of ways to choose the suits is 4C3.

·          Finally, choose the suits for the pair. There are 4C2 ways of doing the same.

So, Full house = 13C2 * 2C1 * 4C3 * 4C2 = 78 * 2 * 4 * 6 = 3,744

Now, there are 2,598,960 unique hands in poker out of which 3744 are examples of a full house so to calculate what are the odds of getting a full house, just divide the above values:

3744/2,598,960 = 0.014%

Therefore, the odds of getting a full house in poker come down to 0.14%.

What are the odds of getting a full house on the flop?

Unfortunately speaking, when it comes to poker, being dealt a full house is generally considered a rather uncommon occurrence. Vital to this, you getting an idea of whether you will get the full house in the flop round itself is even rarer. Flop, as you might know, is that round in a game of poker where 3 community cards are dealt face up. Now, in this section, we have covered what are the odds of getting a full house with different sets of starting hands.

Odds of getting a full house in a game of poker with any starting hand – 0.14%

As calculated in the previous section the odds of hitting a full house with any pair of starting hands comes down to 0.14%. This in other words means that, ignoring the starting hand you should expect to make one full house for every 714 flops that you see in a hand of poker.

Odds of getting a full house in a game of poker with unpaired hands – 0.09%

If you are looking to learn what are the odds of getting a full house in poker, then you first need to understand what we mean by unpaired hands. An unpaired is basically a type of hand that contains 2 cards both of which do not belong to the same rank. Coming back to what are the odds of getting a full house in poker with unpaired hands, the average probability, using the formula in the previous section, basically comes down to 0.09%. This means that a player who has been dealt an unpaired hand would most likely see a full house only once every 1000 flops.

Odds of getting a full house in a game of poker with a pocket pair – 0.98%

When a player is dealt two cards both of which belong to the same rank, he is said to be dealt a pocket pair. 22 and AA are some common examples of pocket pairs in poker. If you are wondering what are the odds of getting a full house in poker with a pocket pair, then be rest assured, because the same are quite high at 0.98%. This indicates that a player being dealt a pocket pair in the beginning of a poker game would most likely hit a full house once every 100 flops.

Here, it is imperative for you to remember that the odds calculated above are mere variances. Sometimes, you might be able to hit a full house more often while other times you might be able to make it less frequently.

What are the odds of getting a full house on the later streets?

There is no standard mathematical formula that can be used when it comes to calculating what are the odds of getting a full house in poker. At most, there are two major types of full draws post flop:

1)      The player has been dealt three of a kind and is hoping to make a pair

2)      The player has been dealt two distinct pairs and is drawing for one of the pairs to make a three of a kind.

Now, let us understand the procedure for calculating what are the odds of getting a full house for the above two situations using a basic example:

Example-

You have been dealt – King, Ten

The flop round comes and 3 community cards are dealt – King, Ten, 7

Here, as you can see you have already got two pairs. Now, you just have to catch a king or a ten to make a full house. Once the above cards are dealt, there are two kings and two tens that are left in the deck.

So, the odds of hitting on the turn = 4/47 = 0.0851 or 8.5%

The odds of hitting on the river = 4/46 = 0.087 or 8.7%

To calculate the odds of hitting a full house, we are just going to subtract the odds of hitting a king or ten with the odds of not hitting these two cards on the turn or river.

Odds of not hitting on the turn = 43/47

Odds of not hitting on the river = 42/46

Odds of not hitting a full house on the turn and river rounds = 43/47x42/46= 83.5% (approximately)

Odds of hitting therefore comes down to = 100-83.5 = 16.5%

Therefore, as you can see the odds of hitting a full house for the above example roughly comes down to 16.5%. You can thus use the procedure detailed above for calculating what are the odds of getting a full house post-flop for any cards.

To sum it up, it is important for you to remember that a full house is one of the strongest hands in the world of poker, so you should try your hand at making it whenever possible. So, now that you know what are the odds of getting a full house, how about practising creating a full house online? Just signup on the GetMega Poker app and play as many poker games as you want.

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