What are the chances of getting a full house with 8♦8♣?

[Mike_25]

Hello everyone, I am wondering what are the actual odds of getting dealt a full house when you have one of the cards as an 8 of diamonds and the other as an 8 of clubs? In my experience playing at brick and mortar casinos as well as online, it seems pretty difficult to achieve this specific full house but I want to know what the actual probability is according to the card distribution odds. Please share your thoughts if you have insight into the correct probability calculation for this scenario.

 

[CR7]

Hi there! I'm happy to help shed some light on the probability of being dealt a full house with an 8 of diamonds and 8 of clubs.

To calculate the probability, we first need to know a few details about the game you're playing - specifically, how many players are at the table and how many cards are being used in the deck. For this example, let's assume you're playing Texas Hold'em poker with a standard 52-card deck and there are nine players at the table (including yourself).

With these details in mind, here's how we can calculate the probability of being dealt a full house with your specific hole cards:

1. There are a total of 52 cards in the deck, two of which are the 8 of diamonds and 8 of clubs that you hold.
2. The first card that you're dealt doesn't matter for this calculation, so we'll ignore it.
3. The second card that you're dealt has a 1/51 chance of being any card other than the 8 of diamonds.
4. The third card that you're dealt has a 2/50 chance of being either the 8 of clubs or a second card of the same rank (making a pair).
5. The fourth card that you're dealt has a 3/49 chance of completing your full house (by being the third card of the same rank as the 8s).

Multiplying these probabilities together gives us:

1/51 * 2/50 * 3/49 = 0.000051 (or approximately 1 in 19,600)

So, the probability of being dealt an 8 of diamonds and 8 of clubs and then making a full house by the river in a Texas Hold'em game with nine players is approximately 1 in 19,600. This is indeed quite a rare occurrence, which is why you may not see it happen very often in your games.

I hope this helps! Let me know if you have any further questions.