crazy pineapple and sets

ok. crazy pineapple.


say you flop a flush and board pairs on river. how much do you have to fear a set?


this is mostly a theoretical question since theres a lot of ways there can be two pair that filled up.


but is it logical to assume that since someone can still have only one pair in there hand that odds of flopping a set are same? (discounting two pair) i think you can put someone on a set *less* often than holdem since there is so much other stuff they can be playing.


just wondering if there is a flaw in my thinking about this somewhere.


brad

Brad - Say the flop is JcTh8h and you have Ah2h in Texas hold 'em. Let's just look at the possibility of an opponent having flopped a set of jacks. There are three ways a particular opponent could have flopped a set of jacks (Js-Jh, Js-Jd, or Jh-Jd). That's out of 47*46/2 or 1081 possible hands that particular opponent could have. Thus the probability of an individual opponent in Texas hold 'em flopping a set of jacks is 3/1081 = 0.002775. (Odds 359 to 1 against).


Now let's say the flop is JcTh8h and you have Ah2h3c in crazy pineapple. There are 3*43 or 129 ways an opponent could have flopped a set of jacks. That's out of 46*45*44/6 or 15180 possible hands that particular opponent could have. Thus the probability of an individual opponent in crazy pineapple flopping a set of jacks is 129/15180 = 0.008498. (Odds 116.7 to 1 against).


We could look at the probability of an individual opponent having any set (not just jacks) - or we could look at the probability of any of your opponents having a set of jacks, or we could look at the probability of any of your opponents having any set - but these problems are obviously more complicated - and we don't need to address them - because you can see from the set of jacks example that the probabilities are different in crazy pineapple than in Texas hold 'em.


In general, hands are more likely in crazy pineapple than in Texas hold 'em. In this example, and I suspect in others, if two cards from someone's hand are needed, particular two card holdings are about (not exactly, but close enough) three times more likely (3.06 in this example).


If you had a jack in your hand already (flop JcTh8h and hand AhJh) in THE, the probability of particular opponent having flopped a set of jacks is 1/1081 = 0.000925. If you had a jack in your hand already (flop JcTh8h and hand AhJh2c) in crazy pineapple, probability of particular opponent having flopped a set of jacks is 1*44/15180 = 0.00290. Probability in this case of an opponent having a set of jacks is 3.13 times as great in crazy pineapple as in THE - again, about, but not exactly, three times as great.


Intuitively, if you have to use two cards from your hand, about three times as great seems reasonable. Just as there are six combinations of two cards from your ABCD hand in Omaha-8 (AB, AC, AD, BC, BD, CD), there are three combinations of two cards from your ABC hand in crazy pineapple (AB, AC, BC), and only one combination two-card combination (AB) in THE.


Just my opinion. And never a guarantee my math is exactly correct - but it's surely at least in the ballpark here.


Buzz

thanks for responding.


in a nutshell, in crazy pineapple its 3 times more likely that an opponent has a pair before the flop, and thats where the increase comes from.


because in both he and cp, theyre only gonna flop a set 1/8 the time about, right?


so the increase must come from the fact that a player is more likely to start with a pair.


does this sound right?


brad

“in a nutshell, in crazy pineapple its 3 times more likely that an opponent has a pair before the flop, and thats where the increase comes from.”


Brad - Not exactly, but that’s an approximate way of looking at it.


“because in both he and cp, theyre only gonna flop a set 1/8 the time about, right?”


I don’t think so. Since pairs are about three times more likely in CP than in THE, I’d expect an opponent to flop a set about three times more often in CP than in THE.


I don’t know where you got the 1/8. What does that represent?


Buzz

flop a set 1/8 the time *when they have a pair*.


this is what messes me up. once the cards are dealt, only 11-12% of the time will a set be flopped, both in he and cp.(assuming a pair)


brad

Brad - O.K. I think I see what you're getting at.


When someone is looking at a hand with a pair in Texas hold 'em, let's say a pair of kings, there are 50 unknown cards, of which three will be revealed on the flop. The chance of a king being one of the three cards flopped is 2*48*47*6/50/49/48/2 = 0.115 = 1/(8.69).


When someone is looking at a hand with a pair in crazy pineapple, let's say a pair of kings with an ace, there are 49 unknown cards, of which three will be revealed on the flop. The chance of a king being one of the three cards flopped is 2*47*46*6/49/48/47/2 = 0.117 = 1/(8.52)


These are both a bit closer to 1/9 than 1/8, but let's not quibble. They are both roughly the same.


However, although an opponent who started with a pair of kings will flop a set roughly just as often in either game, since the chance that an opponent was dealt a pair of kings to begin with is approximately three times as great in crazy pineapple as in Texas hold 'em, the chance that an opponent will end up with a set of kings after a flop with a king is roughly three times as great in crazy pineapple as in Texas hold 'em.


The preceeding sentence is long and hard to read - but that's the explanation. Hope it helps.


Buzz

This is an interesting thread and reminds me of the post Mr. Peterson made below regarding discards. Good hold 'em players can get trapped in pineapple hands because of their high regard for big pairs (AA KK). This is especially true in no limit/pot limit. When you can put your opponent on a big pair, and you have a multiway hand like 99s8s, it can be a real giant killer. The 'three times more likely' figure is a sobering statistic for those playing 'pair poker.'


Buzz, I always appreciate, and marvel at, the work you put into your posts. You might consider collecting them and putting them up on a web site for reference.

Thanks Mack. I really appreciate that coming from you. I always read and learn from your posts.


I don't play crazy pineapple much anymore. I did play it for a few months, but I'm currently mostly sticking to Omaha-8. HPC doesn't offer the game, so that sometimes I play Texas hold 'em or seven stud while waiting for an Omaha-8 seat.


I hadn't intended to get involved in this thread. Giving the first response was easy and just took me a few minutes. Then it seemed worthwhile to try to clear up Brad's question and I got stuck. I mean, if you're going to try to help someone, you might as well go the extra few steps.


Take care, Mack, and thanks again.


Buzz