hchollenbeck
Joined: Feb 6, 2014
• Posts: 5
February 6th, 2014 at 4:06:05 AM permalink
What is the probabilty of getting Aces Full of Jacks, or better, using both hole cards, in Texas Hold Em? I've been all over searching for the answer.....please help.
endermike
Joined: Dec 10, 2013
• Posts: 584
February 6th, 2014 at 4:30:47 AM permalink
for one player, or a whole table of hands?
hchollenbeck
Joined: Feb 6, 2014
• Posts: 5
February 6th, 2014 at 5:05:59 AM permalink
For one player to get at least AAAJJ. I dont think it matters how full the table is....
endermike
Joined: Dec 10, 2013
• Posts: 584
February 6th, 2014 at 5:08:34 AM permalink
What range of hands is the player playing?
mickeycrimm
Joined: Jul 13, 2013
• Posts: 2299
February 6th, 2014 at 5:44:17 AM permalink
Quote: hchollenbeck

What is the probabilty of getting Aces Full of Jacks, or better, using both hole cards, in Texas Hold Em? I've been all over searching for the answer.....please help.

Are you trying to figure out bad beat odds?
endermike
Joined: Dec 10, 2013
• Posts: 584
February 6th, 2014 at 6:18:38 AM permalink
Quote: mickeycrimm

Are you trying to figure out bad beat odds?

This is my assumption as well
DJTeddyBear
Joined: Nov 2, 2009
• Posts: 10059
February 6th, 2014 at 7:05:23 AM permalink
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁 Note that the same could be said for Religion. I.E. Religion is nothing more than organized superstition. 🤗
hchollenbeck
Joined: Feb 6, 2014
• Posts: 5
February 6th, 2014 at 2:12:14 PM permalink
Here is the complete problem that Im facing: I need to figure out the probability for any random player to get Aces full of jacks or better, using both his hole cards, with a random number of opponents (we can say a seven handed table on average), to qualify for a high hand jackpot that I'm trying to incorporate into a poker promotion. (I work for a casino.) The player only needs to get this hand, he doesn't need it beaten etc. Basically it should be a number around 1/700 I'm thinking because the odds of getting ANY full house or better is 1/560.
paisiello
Joined: Oct 30, 2011
• Posts: 546
February 6th, 2014 at 9:20:31 PM permalink
The odds will be greater than 1/700 for sure.

First the probability of getting any full house is approximately:
C(13,1)*C(4,3)*C(12,1)*C(4,2)*C(11,2)*C(4,1)*C(4,1) / C(52,7) = (13)(4)(12)(6)(55)(4)(4)/ (133,784,560)
= (3,294,720)/(133,784,560)
= 2.46% or about 1 in 40

The probability of getting quads or a straight flush are comparatively negligible so the probability of getting any full house or better can be said to be about 1 in 40.

Now the probability of getting Aces full of Jacks is approximately:
C(1,1)*C(4,3)*C(3,1)*C(4,2)*C(11,2)*C(4,1)*C(4,1) / C(52,7) = (1)(4)(3)(6)(55)(4)(4)/ (133,784,560)
= ( 63,360 )/(133,784,560)
= 0.0474% or about 1 in 2,000

Again the probability of getting quads or a straight flush are comparatively negligible so the probability of getting Aces full of Jacks or better can be said to be about 1 in 2,000.

Now if the requirement is to use both of your hole cards then this will exclude (2/7)+(5/7)(2/6)= approx. 1/2 of the results. Therefore, the probability reduces to (0.0474%)(1 - 1/2) = 0.0226% or about 1 in 4,000.
tringlomane
Joined: Aug 25, 2012