3 -of-a-kind

[Whatsmytotal]

Is there a higher chance of flopping a set when holding a pocket pair, or when holding any card and flopping trips?

E.g., you hold AA and flop is A K 3, VS. You hold AK and flop is A A 6 - Which of these, if any, has a higher chance of occurring?

They are both 3 of a kind...

 

[positiveEV]

(2/50+2/49+2/48) of flopping 3-of-a-kind with a pocket pair, ((6/50)*(2/49)+(6/50)*(2/48)+(6/49)*(2/48)) of flopping 3-of-a-kind with 2 different cards.

So, 12.25% of flopping 3-of-a-kind with a pocket pair against 1.5% when holding 2 different cards.

 

[positiveEV]

They are both 3 of a kind...

But the odds you get a pocket pair are much lower than the odds of not having one! When you get your first card, there is only 3/51 chances you will get the same one again against 48/51 you wont get the same card.

 

[Whatsmytotal]

Should'nt they have the same exact probabilities, being that they both rank the same, namely as 3-of-a-kind?

 

[grandepj]

The odds of having trips after the flop given a random starting hand is the same regardless of that starting hand is a pair or not. But the original post seemed to ask if GIVEN the fact that the starting hand is a pair, is there a better chance for trips, and there is.

AsiaFever's math is correct in determing the odds for trips given a pair in the hole versus the odds for trips given non-paired hole cards, but it is also true that if we don't know the starting hand, we can't say anything about changes in the odds for flops.

 

[grandepj]

The odds of having trips after the flop given a random starting hand is the same regardless of that starting hand is a pair or not. But the original post seemed to ask if GIVEN the fact that the starting hand is a pair, is there a better chance for trips, and there is.

AsiaFever's math is correct in determing the odds for trips given a pair in the hole versus the odds for trips given non-paired hole cards, but it is also true that if we don't know the starting hand, we can't say anything about changes in the odds for flops.

 

[jonas]

playing poker

It is when you get your first card, there is only 3/51 chances you will get the same one again against 48/51 you wont get the same card. In playing, that should be the belief. It's really like that. It's all about luck!