Poker Probabilty Problem for the math people

[Chewbacca]

Hey,

According to this site:
http://en.wikipedia.org/wiki/Poker_probability

The odds of making quads(4 of a kind) in Texas Holdem is 594:1.


What I want to know is the overall odds of making '4 of a kind' 3 hands in a row.

Do I simply multiply by 3 or is it more complex. I am not a math person past the basics, so any serious complexity will go over my head. [img]smile.gif[/img]


BTW- I did indeed get quads 3 times in a row and got paid each time too!

I came in 7th place out of 1200 in the small stakes tournament which this occured.

[ 03-03-2006, 10:32 PM: Message edited by: Chewbacca ]

[shadeoracle]

The answer to your question is (1/594)^3 = 1/209584584 = 0.000000477%. In other words you are extremely lucky! If you think about it you obviously dont multiply it by 3 or else after 594 hands you would have a 100% chance of getting 4 of a kind 594 hands in a row.

[Chewbacca]

Thanks! [img]smile.gif[/img] I doubted simply multiplying by three was the answer.

To make this situation even more improbable the 3 hands were, in order:

4444
5555
6666

starting with a pocket pair each hand.

And yes, I felt very lucky, even more so now that I know the odds!

[Eagle eye]

There is either one very bad dealer in the casino, or it is a message from god...
Go forth, and fufill your destiny fill your pockets!

[ 03-04-2006, 12:37 AM: Message edited by: Eagle eye ]

[shadeoracle]

Getting the first quad is 594:1. To get a quad using the next rank up is (1/13)(1/594)=1/7722. Therefore to get two in a row with sucessive ranks is (1/594)(1/7722)=1/4586868. To do it a third time with the next successive rank has a probability (1/4586868)(1/7722)=1/35419794696. Basically, you just did something that has a 0.00000000282% chance of occuring. In other words it would be 932 times more likely to win first division in the national (New Zealand) lottery than do what you did.

[Chewbacca]

Wow! That's insane improbability! BTW this happened in an on-line game at Pokerstars not at a B&M casino.

I'm a firm believer that skill (understanding poker strategy, grasping game theory, observation skills, ect.) AND luck go hand-in-hand for winning consistently at poker, but being on the recieving end of that kind of extreme luck is still hard for me to fathom.

Well, I'm off to play some poker!

Cheers!

[Sir Goulum]

Hah, poker. I'm only good at it because I bluff on every hand. [img]tongue.gif[/img]

[robertthebard]

Are the odds that high in Texas Hold 'em? I could see them being that high in 5 stud or something similar, but I'd think that 4 of a kind would be easier in a hand with a common hand to draw from. However, like Sir G, my poker skills are based largely on my ability to bluff, more than actually having any real skill or experience.

[Felix The Assassin]

Originally posted by Chewbacca: BTW this happened in an on-line game at Pokerstars not at a B&M casino.

Bah! An M$ franchised software site! [img]graemlins/noevil.gif[/img] Don't worry about buying a lottery ticket then, I thought you were onto something.

[ 03-04-2006, 09:35 AM: Message edited by: Felix The Assassin ]

[Chewbacca]

Originally posted by robertthebard: Are the odds that high in Texas Hold 'em? I could see them being that high in 5 stud or something similar, but I'd think that 4 of a kind would be easier in a hand with a common hand to draw from. However, like Sir G, my poker skills are based largely on my ability to bluff, more than actually having any real skill or experience.

I play NL Holdem I'd say on average 1-3 hours a day, sometimes 2 tables at once. Quads do seem as rare as the odds suggest. I don't see them that often, but when I do they usually hurt.

For example, some one with Quad 2s beat a 3/2 full house of mine just the other night. The only redeeming factor is I still finished in the money.

Omaha is the game where big hands are a little more common.

[ 03-04-2006, 04:49 PM: Message edited by: Chewbacca ]