Card combinations question

SeanC · #1 11-19-2007, 12:31 AM

Hi,

If I wanted to calculate the number of combinations for a range such as AJo-AKo with no card removal, I'm not double-counting or making any weird mistakes by simply counting 12 for AJ, AQ and AK, right? (36 combinations total.)

Dumb questions but just want to make sure.

RustyBrooks · #2 11-19-2007, 12:40 AM

Nope, 12 is right for any 2 offsuit cards. There are obviously 4 versions of the same hand, suited, for a total of 16.

SeanC · #3 11-19-2007, 01:33 AM

[ QUOTE ]
Nope, 12 is right for any 2 offsuit cards. There are obviously 4 versions of the same hand, suited, for a total of 16.

[/ QUOTE ]

Ah yeah, I said AJo-AKo, but practically speaking it would have to include suited too.

Thanks.

RustyBrooks · #4 11-19-2007, 01:49 AM

For future reference it's a very simple combinatorics problem. For AK (suited and off) there are 4 cards for the aces, 4 cards for the kings, so there are 16 combinations.

The number of combos of a pair is actually slightly more complicated because of removal. There are 4 options for the first card and 3 for the second, so that implies 12 combos, but AcAd is the same as AdAc so half of them are duplicates and really there are only 6 combos.

And that's as complex as holdem gets [img]/images/graemlins/wink.gif[/img]

SeanC · #5 11-19-2007, 05:47 PM

[ QUOTE ]
For future reference it's a very simple combinatorics problem. For AK (suited and off) there are 4 cards for the aces, 4 cards for the kings, so there are 16 combinations.

The number of combos of a pair is actually slightly more complicated because of removal. There are 4 options for the first card and 3 for the second, so that implies 12 combos, but AcAd is the same as AdAc so half of them are duplicates and really there are only 6 combos.

And that's as complex as holdem gets [img]/images/graemlins/wink.gif[/img]

[/ QUOTE ]

Makes sense. Thanks. [img]/images/graemlins/smile.gif[/img]

RustyBrooks · #6 11-19-2007, 06:30 PM

Now let's talk about, say... stud. You have JJ8 and there are 2 opponents yet to act, one with a A upcard and one with an 9 upcard. How many card combos can each of them have, that has you beat right now? like AAx KKA QQA JJA AAA 999 KK9 QQJ JJ9? That's some serious yuck right there. In holdem you just have to worry about QQ KK AA and wonder about AK AQ and KQ.

Not to mention in stud, you are not in as good of shape against underpairs, because in holdem an underpair can only improve by making one of his 2 outs and making trips (unless he backs into some weird straight or flush). It's not possible for your opponent to make 2 pair without you also improving to a better 2 pair. In stud, your opponent can make 2 pair and you'll often be guessing as to whether he has 2 pair or not. So with xx9 calls you and his 4th st is, say, a K, you now have to worry, did he have 9K9?

SeanC · #7 11-19-2007, 09:50 PM

[ QUOTE ]
Now let's talk about, say... stud. You have JJ8 and there are 2 opponents yet to act, one with a A upcard and one with an 9 upcard. How many card combos can each of them have, that has you beat right now? like AAx KKA QQA JJA AAA 999 KK9 QQJ JJ9? That's some serious yuck right there. In holdem you just have to worry about QQ KK AA and wonder about AK AQ and KQ.

Not to mention in stud, you are not in as good of shape against underpairs, because in holdem an underpair can only improve by making one of his 2 outs and making trips (unless he backs into some weird straight or flush). It's not possible for your opponent to make 2 pair without you also improving to a better 2 pair. In stud, your opponent can make 2 pair and you'll often be guessing as to whether he has 2 pair or not. So with xx9 calls you and his 4th st is, say, a K, you now have to worry, did he have 9K9?

[/ QUOTE ]

Haha, glad I don't play stud. [img]/images/graemlins/wink.gif[/img] Nah, with enough drilling these things can become pretty automatic, I'm sure.

RustyBrooks · #8 11-19-2007, 10:28 PM

Nah, you just get better at saying "screw it I CALL"

(LOL limit)

SeanC · #9 11-19-2007, 10:56 PM

[ QUOTE ]
Nah, you just get better at saying "screw it I CALL"

(LOL limit)

[/ QUOTE ]

Hahahaha

maverickai · #10 11-23-2007, 12:17 PM

OP, check out this thread, really good stuff about combinations.

http://forumserver.twoplustwo.com/showfl...1#Post10760165z