Frequency of Set-Over-Set Confrontations?

> I don't understand why you don't just ask the question, why you always put
> it in the parlance of "I sent this message to my friend..."

Alan seems genuine enough and I like the guy, but I wonder the same thing
here also.

TIGERS World Series- 35, 45, 68, 84
RED WINGS Stanley Cups- 36, 37, 43, 50, 52, 54, 55, 97, 98, 02, 08
PISTONS Championships- 44, 45, 89, 90, 05
LIONS Superbowls- lol

BOOM byae
John

_____________________________________________________________________ 
: the next generation of web-newsreaders : http://www.recgroups.com
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

> Is everyone you know in the witness protection program?

lol

GC actually made another funny. He must be off his meds.

TIGERS World Series- 35, 45, 68, 84
RED WINGS Stanley Cups- 36, 37, 43, 50, 52, 54, 55, 97, 98, 02, 08
PISTONS Championships- 44, 45, 89, 90, 05
LIONS Superbowls- lol

BOOM byae
John

----- 
RecGroups : the community-oriented newsreader : www.recgroups.com
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Wed, 01 Oct 2008 17:33:34 -0700, "brewmaster"
<a163b RemoveThis @webnntp.invalid> wrote:

>
>You could have asked the question in 1/20th of the space you used, like
>"what is the percentage that on any given hand two players will flop sets?
>I'm not sure how to figure it out..."

A more interesting question to me would be, "Given the I've flopped a
set, what is the likelihood that one of my opponents has also flopped
a set?
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Oct 2, 5:21 pm, Pepe Papon <hitmeis... RemoveThis @mindspring.dot.com.invalid>
wrote:
> On Wed, 01 Oct 2008 17:33:34 -0700, "brewmaster"
>
> <a1... RemoveThis @webnntp.invalid> wrote:
>
> >You could have asked the question in 1/20th of the space you used, like
> >"what is the percentage that on any given hand two players will flop sets?
> >I'm not sure how to figure it out..."
>
> A more interesting question to me would be, "Given the I've flopped a
> set, what is the likelihood that one of my opponents has also flopped
> a set?

This shouldn't be an interesting question to any poker player. You
flopped a set. Math can go fuck itself. End of story.

You let elements of weak/tight play creep into your game just by
anaylzing sceanrios like set over set or KK vs AA. It's like worrying
about if your wife or girlfriend is faking her orgasm. Who cares? Is
it gonna make one bit of difference or slow the Stallion down? Not for
second. You just block the thought out and keep pounding/raising away.
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

garycarson wrote:
>> Les (not his real name):
>>
>
> Is everyone you know in the witness protection program?
>
> ----
> RecGroups : the community-oriented newsreader : www.recgroups.com
>
>

All his friends are really named "Bubba".


--
Kenneth Sloan KennethRSloan DeleteThis @gmail.com
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://KennethRSloan.com/
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Oct 1, 7:40 am, "K9way" <ad14... DeleteThis @webnntp.invalid> wrote:
> On Oct 1 2008 3:22 AM, lawho... DeleteThis @HiWAAY.net wrote:
>
>
>
> > Dear Math Experts:
>
> > Here's a change (for me) - a poker-related post!! ))
>
> > I sent a message to a friend of mine concerning set-over-set
> > confrontations. I have been involved in two such confrontations in
> > practice versus the Wilson software - one which I won and one which I
> > lost. At first I thought such confrontations are infrequent,
> > occurring maybe once in every [close to] 500 hands. After putting pen
> > to paper and trying to do a probability calculation, I concluded that
> > the actual odds may be closer to 203:1 against flopping a set and
> > being up against another set; but I'm not even sure about that. (I'm
> > not that good at math.) I'm wondering if the actual odds may be
> > closer to something like 100:1 against? Here is my message to my
> > friend.
>
> > Alan C. Lawhon
> > Huntsville, Alabama
>
> > Les (not his real name):
>
> > An interesting hand came up last night versus the Wilson Software that
> > makes me think set-over-set confrontations may not be that rare. I
> > was UTG with pocket Jacks versus a nearly full table. I decided to
> > limp and see how many players entered the pot. If there was a strong
> > open-raise, a call, (and/or a re-raise indicating that I might be beat
> > pre-flop), I intended to fold as it was early in the game and I was
> > out of position. If there was only one caller or an open-raise from
> > the button, then I would call and hope for a Jack on the flop.
>
> > That’s exactly what happened: It folded around to the dealer button
> > who came in for a standard 4x BB open raise. Both blinds folded and I
> > called. The flop came down J-9-x. I immediately led out with a pot-
> > sized bet. I was re-raised twice the pot so I re-re-raised (all-in)
> > for my remaining 530 chips. I was called. We had both flopped sets:
> > I flopped a set of Jacks and the dealer had a pair of pocket 9’s. My
> > three Jacks held up and I stacked the dealer to take the chip lead. I
> > went on to finish in second place.
>
> > So this is twice (in two games) where I have been involved in set-over-
> > set confrontations. Given all this, I’m beginning to think that set-
> > over-set is not that rare. Rather than occurring maybe once in every
> > 203 hands, (which is more often than being dealt pocket Aces), maybe
> > set-over-set occurs closer to once every 100 hands?
>
> > Alan
>
> prolly closer to 1000:1
>
> Thank you Lord for the TV Scooter Morons we are about to deceive
>
> -----
> RecGroups : the community-oriented newsreader :www.recgroups.com

Assume a 10-handed table where anyone with a pocket pair sees the flop
- typical for the games I have played.

The total number of deals + flops possible is a = 52!/(32! * 2^10)*32!/
(29!*3!) = 1.48 x 10^23

Exactly 3 sets will occur in b = 13!/(10!*3!)*6^3*(10*9**2^3*43!/(29!
*2^7) = 1.90 x 10^29

So set over set over set occurs with probability 0.0000128, or about 1
hand in 78166

Exactly 2 sets will occur in c = 13!/(11!*2!)*6^2*(10*9)*2^2*44*45!/
(29!*2^ -3*b = 2.29 x 10^30

So set over set occurs with probability 0.00154, or about 1 in 647
hands
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Oct 2, 6:12 pm, FaceDownAcesUp <superbee....TakeThisOut@yahoo.com> wrote:
> On Oct 2, 5:21 pm, Pepe Papon <hitmeis....TakeThisOut@mindspring.dot.com.invalid>
> wrote:
>
> > On Wed, 01 Oct 2008 17:33:34 -0700, "brewmaster"
>
> > <a1....TakeThisOut@webnntp.invalid> wrote:
>
> > >You could have asked the question in 1/20th of the space you used, like
> > >"what is the percentage that on any given hand two players will flop sets?
> > >I'm not sure how to figure it out..."
>
> > A more interesting question to me would be, "Given the I've flopped a
> > set, what is the likelihood that one of my opponents has also flopped
> > a set?
>
> This shouldn't be an interesting question to any poker player. You
> flopped a set. Math can go fuck itself. End of story.
>
> You let elements of weak/tight play creep into your game just by
> anaylzing sceanrios like set over set or KK vs AA.  It's like worrying
> about if your wife or girlfriend is faking her orgasm. Who cares? Is
> it gonna make one bit of difference or slow the Stallion down? Not for
> second. You just block the thought out and keep pounding/raising away.

That is a pretty good post. Howeve, I think it is impolite to mention
that you are fucking his wife or girlfriend, whether she is faking
those orgasms or not.

--
Will in New Haven
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Oct 1, 3:22 am, "lawho...@HiWAAY.net" <lawho....TakeThisOut@hiwaay.net> wrote:
> Dear Math Experts:
>
> Here's a change (for me) - a poker-related post!!   ))
>
> I sent a message to a friend of mine concerning set-over-set
> confrontations.  I have been involved in two such confrontations in
> practice versus the Wilson software - one which I won and one which I
> lost.  At first I thought such confrontations are infrequent,
> occurring maybe once in every [close to] 500 hands.  After putting pen
> to paper and trying to do a probability calculation, I concluded that
> the actual odds may be closer to 203:1 against flopping a set and
> being up against another set; but I'm not even sure about that.  (I'm
> not that good at math.)  I'm wondering if the actual odds may be
> closer to something like 100:1 against?  Here is my message to my
> friend.
>
> Alan C. Lawhon
> Huntsville, Alabama
>
> Les (not his real name):
>
> An interesting hand came up last night versus the Wilson Software that
> makes me think set-over-set confrontations may not be that rare.  I
> was UTG with pocket Jacks versus a nearly full table.  I decided to
> limp and see how many players entered the pot.  If there was a strong
> open-raise, a call, (and/or a re-raise indicating that I might be beat
> pre-flop), I intended to fold as it was early in the game and I was
> out of position.  If there was only one caller or an open-raise from
> the button, then I would call and hope for a Jack on the flop.
>
> That’s exactly what happened: It folded around to the dealer button
> who came in for a standard 4x BB open raise.  Both blinds folded and I
> called.  The flop came down J-9-x.  I immediately led out with a pot-
> sized bet.  I was re-raised twice the pot so I re-re-raised (all-in)
> for my remaining 530 chips.  I was called.  We had both flopped sets:
> I flopped a set of Jacks and the dealer had a pair of pocket 9’s.  My
> three Jacks held up and I stacked the dealer to take the chip lead.  I
> went on to finish in second place.
>
> So this is twice (in two games) where I have been involved in set-over-
> set confrontations.  Given all this, I’m beginning to think that set-
> over-set is not that rare.  Rather than occurring maybe once in every
> 203 hands, (which is more often than being dealt pocket Aces), maybe
> set-over-set occurs closer to once every 100 hands?

What you have to remember is that a couple of hands that you run into
are certainly a big enough sample to generalize from like this.

--
Will in New Haven
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

"Tim Norfolk" <timsn274 DeleteThis @aol.com> wrote in message
news:ed22be3c-c9b9-495f-b726-f8373760bc7d@p59g2000hsd.googlegroups.com...
On Oct 1, 7:40 am, "K9way" <ad14... DeleteThis @webnntp.invalid> wrote:
> On Oct 1 2008 3:22 AM, lawho... DeleteThis @HiWAAY.net wrote:
>
>
>
> > Dear Math Experts:
>
> > Here's a change (for me) - a poker-related post!! ))
>
> > I sent a message to a friend of mine concerning set-over-set
> > confrontations. I have been involved in two such confrontations in
> > practice versus the Wilson software - one which I won and one which I
> > lost. At first I thought such confrontations are infrequent,
> > occurring maybe once in every [close to] 500 hands. After putting pen
> > to paper and trying to do a probability calculation, I concluded that
> > the actual odds may be closer to 203:1 against flopping a set and
> > being up against another set; but I'm not even sure about that. (I'm
> > not that good at math.) I'm wondering if the actual odds may be
> > closer to something like 100:1 against? Here is my message to my
> > friend.
>
> > Alan C. Lawhon
> > Huntsville, Alabama
>
> > Les (not his real name):
>
> > An interesting hand came up last night versus the Wilson Software that
> > makes me think set-over-set confrontations may not be that rare. I
> > was UTG with pocket Jacks versus a nearly full table. I decided to
> > limp and see how many players entered the pot. If there was a strong
> > open-raise, a call, (and/or a re-raise indicating that I might be beat
> > pre-flop), I intended to fold as it was early in the game and I was
> > out of position. If there was only one caller or an open-raise from
> > the button, then I would call and hope for a Jack on the flop.
>
> > That’s exactly what happened: It folded around to the dealer button
> > who came in for a standard 4x BB open raise. Both blinds folded and I
> > called. The flop came down J-9-x. I immediately led out with a pot-
> > sized bet. I was re-raised twice the pot so I re-re-raised (all-in)
> > for my remaining 530 chips. I was called. We had both flopped sets:
> > I flopped a set of Jacks and the dealer had a pair of pocket 9’s. My
> > three Jacks held up and I stacked the dealer to take the chip lead. I
> > went on to finish in second place.
>
> > So this is twice (in two games) where I have been involved in set-over-
> > set confrontations. Given all this, I’m beginning to think that set-
> > over-set is not that rare. Rather than occurring maybe once in every
> > 203 hands, (which is more often than being dealt pocket Aces), maybe
> > set-over-set occurs closer to once every 100 hands?
>
> > Alan
>
> prolly closer to 1000:1
>
> Thank you Lord for the TV Scooter Morons we are about to deceive
>
> -----
> RecGroups : the community-oriented newsreader :www.recgroups.com

Assume a 10-handed table where anyone with a pocket pair sees the flop
- typical for the games I have played.

The total number of deals + flops possible is a = 52!/(32! * 2^10)*32!/
(29!*3!) = 1.48 x 10^23

Exactly 3 sets will occur in b = 13!/(10!*3!)*6^3*(10*9**2^3*43!/(29!
*2^7) = 1.90 x 10^29

So set over set over set occurs with probability 0.0000128, or about 1
hand in 78166

Exactly 2 sets will occur in c = 13!/(11!*2!)*6^2*(10*9)*2^2*44*45!/
(29!*2^ -3*b = 2.29 x 10^30

So set over set occurs with probability 0.00154, or about 1 in 647
hands


-------

Stop calculating the odds of the 1st set... it's a given!
I *already have* a set... just watched the door card
drop that matched my hole cards!

What is the probability that someone else also flopped
a set just now? I've read 1:100 or 1% and I'm sticking
to it unless you work your magic and show me otherwise

Mark
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Oct 3, 1:54 pm, "Mark B [Diputsur]" <diput... DeleteThis @gmail.com> wrote:
> "Tim Norfolk" <timsn... DeleteThis @aol.com> wrote in message
>
> news:ed22be3c-c9b9-495f-b726-f8373760bc7d@p59g2000hsd.googlegroups.com...
> On Oct 1, 7:40 am, "K9way" <ad14... DeleteThis @webnntp.invalid> wrote:
>
>
>
>
>
> > On Oct 1 2008 3:22 AM, lawho... DeleteThis @HiWAAY.net wrote:
>
> > > Dear Math Experts:
>
> > > Here's a change (for me) - a poker-related post!!   ))
>
> > > I sent a message to a friend of mine concerning set-over-set
> > > confrontations.  I have been involved in two such confrontations in
> > > practice versus the Wilson software - one which I won and one which I
> > > lost.  At first I thought such confrontations are infrequent,
> > > occurring maybe once in every [close to] 500 hands.  After putting pen
> > > to paper and trying to do a probability calculation, I concluded that
> > > the actual odds may be closer to 203:1 against flopping a set and
> > > being up against another set; but I'm not even sure about that.  (I'm
> > > not that good at math.)  I'm wondering if the actual odds may be
> > > closer to something like 100:1 against?  Here is my message to my
> > > friend.
>
> > > Alan C. Lawhon
> > > Huntsville, Alabama
>
> > > Les (not his real name):
>
> > > An interesting hand came up last night versus the Wilson Software that
> > > makes me think set-over-set confrontations may not be that rare.  I
> > > was UTG with pocket Jacks versus a nearly full table.  I decided to
> > > limp and see how many players entered the pot.  If there was a strong
> > > open-raise, a call, (and/or a re-raise indicating that I might be beat
> > > pre-flop), I intended to fold as it was early in the game and I was
> > > out of position.  If there was only one caller or an open-raise from
> > > the button, then I would call and hope for a Jack on the flop.
>
> > > That’s exactly what happened: It folded around to the dealer button
> > > who came in for a standard 4x BB open raise.  Both blinds folded and I
> > > called.  The flop came down J-9-x.  I immediately led out with a pot-
> > > sized bet.  I was re-raised twice the pot so I re-re-raised (all-in)
> > > for my remaining 530 chips.  I was called.  We had both flopped sets:
> > > I flopped a set of Jacks and the dealer had a pair of pocket 9’s.  My
> > > three Jacks held up and I stacked the dealer to take the chip lead.  I
> > > went on to finish in second place.
>
> > > So this is twice (in two games) where I have been involved in set-over-
> > > set confrontations.  Given all this, I’m beginning to think that set-
> > > over-set is not that rare.  Rather than occurring maybe once in every
> > > 203 hands, (which is more often than being dealt pocket Aces), maybe
> > > set-over-set occurs closer to once every 100 hands?
>
> > > Alan
>
> > prolly closer to 1000:1
>
> > Thank you Lord for the TV Scooter Morons we are about to deceive
>
> > -----
> > RecGroups : the community-oriented newsreader :www.recgroups.com
>
> Assume a 10-handed table where anyone with a pocket pair sees the flop
> - typical for the games I have played.
>
> The total number of deals + flops possible is a = 52!/(32! * 2^10)*32!/
> (29!*3!) = 1.48 x 10^23
>
> Exactly 3 sets will occur in b = 13!/(10!*3!)*6^3*(10*9**2^3*43!/(29!
> *2^7) = 1.90 x 10^29
>
> So set over set over set occurs with probability 0.0000128, or about 1
> hand in 78166
>
> Exactly 2 sets will occur in c = 13!/(11!*2!)*6^2*(10*9)*2^2*44*45!/
> (29!*2^ -3*b = 2.29 x 10^30
>
> So set over set occurs with probability 0.00154, or about 1 in 647
> hands
>
> -------
>
> Stop calculating the odds of the 1st set... it's a given!
> I *already have* a set... just watched the door card
> drop that matched my hole cards!
>
> What is the probability that someone else also flopped
> a set just now?  I've read 1:100 or 1% and I'm sticking
> to it unless you work your magic and show me otherwise
>
> Mark- Hide quoted text -
>
> - Show quoted text -

I also made the assumption that the flop had no pair, say the flop is
xyz, where you have xx.

Any given player can be dealt their hole cards in 47!/(45!*2!) = 47*46
ways, of which 6 ways give them a set.

There are 9 other players, so the approximate (ignoring two other
sets) probability is 9*6/(47*46), which is about once in 43 hands.

Hope that helps.
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Fri, 3 Oct 2008 13:31:01 -0700 (PDT), Will in New Haven
<bill.reich.TakeThisOut@taylorandfrancis.com> wrote:

>On Oct 2, 6:12 pm, FaceDownAcesUp <superbee....TakeThisOut@yahoo.com> wrote:
>> On Oct 2, 5:21 pm, Pepe Papon <hitmeis....TakeThisOut@mindspring.dot.com.invalid>
>> wrote:
>>
>> > On Wed, 01 Oct 2008 17:33:34 -0700, "brewmaster"
>>
>> > <a1....TakeThisOut@webnntp.invalid> wrote:
>>
>> > >You could have asked the question in 1/20th of the space you used, like
>> > >"what is the percentage that on any given hand two players will flop sets?
>> > >I'm not sure how to figure it out..."
>>
>> > A more interesting question to me would be, "Given the I've flopped a
>> > set, what is the likelihood that one of my opponents has also flopped
>> > a set?
>>
>> This shouldn't be an interesting question to any poker player. You
>> flopped a set. Math can go fuck itself. End of story.
>>
>> You let elements of weak/tight play creep into your game just by
>> anaylzing sceanrios like set over set or KK vs AA.  It's like worrying
>> about if your wife or girlfriend is faking her orgasm. Who cares? Is
>> it gonna make one bit of difference or slow the Stallion down? Not for
>> second. You just block the thought out and keep pounding/raising away.
>
>That is a pretty good post. Howeve, I think it is impolite to mention
>that you are fucking his wife or girlfriend, whether she is faking
>those orgasms or not.

My wife wouldn't give him the time of day.
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

On Oct 3, 1:54�pm, "Mark B [Diputsur]" <diput....TakeThisOut@gmail.com> wrote:
> "Tim Norfolk" <timsn....TakeThisOut@aol.com> wrote in message
>
> news:ed22be3c-c9b9-495f-b726-f8373760bc7d@p59g2000hsd.googlegroups.com...
> On Oct 1, 7:40 am, "K9way" <ad14....TakeThisOut@webnntp.invalid> wrote:
>
>
>
>
>
> > On Oct 1 2008 3:22 AM, lawho....TakeThisOut@HiWAAY.net wrote:
>
> > > Dear Math Experts:
>
> > > Here's a change (for me) - a poker-related post!! � ))
>
> > > I sent a message to a friend of mine concerning set-over-set
> > > confrontations. �I have been involved in two such confrontations in
> > > practice versus the Wilson software - one which I won and one which I
> > > lost. �At first I thought such confrontations are infrequent,
> > > occurring maybe once in every [close to] 500 hands. �After putting pen
> > > to paper and trying to do a probability calculation, I concluded that
> > > the actual odds may be closer to 203:1 against flopping a set and
> > > being up against another set; but I'm not even sure about that. �(I'm
> > > not that good at math.) �I'm wondering if the actual odds may be
> > > closer to something like 100:1 against? �Here is my message to my
> > > friend.
>
> > > Alan C. Lawhon
> > > Huntsville, Alabama
>
> > > Les (not his real name):
>
> > > An interesting hand came up last night versus the Wilson Software that
> > > makes me think set-over-set confrontations may not be that rare. �I
> > > was UTG with pocket Jacks versus a nearly full table. �I decided to
> > > limp and see how many players entered the pot. �If there was a strong
> > > open-raise, a call, (and/or a re-raise indicating that I might be beat
> > > pre-flop), I intended to fold as it was early in the game and I was
> > > out of position. �If there was only one caller or an open-raise from
> > > the button, then I would call and hope for a Jack on the flop.
>
> > > That s exactly what happened: It folded around to the dealer button
> > > who came in for a standard 4x BB open raise. �Both blinds folded and I
> > > called. �The flop came down J-9-x. �I immediately led out with a pot-
> > > sized bet. �I was re-raised twice the pot so I re-re-raised (all-in)
> > > for my remaining 530 chips. �I was called. �We had both flopped sets:
> > > I flopped a set of Jacks and the dealer had a pair of pocket 9 s. �My
> > > three Jacks held up and I stacked the dealer to take the chip lead. �I
> > > went on to finish in second place.
>
> > > So this is twice (in two games) where I have been involved in set-over-
> > > set confrontations. �Given all this, I m beginning to think that set-
> > > over-set is not that rare. �Rather than occurring maybe once in every
> > > 203 hands, (which is more often than being dealt pocket Aces), maybe
> > > set-over-set occurs closer to once every 100 hands?
>
> > > Alan
>
> > prolly closer to 1000:1
>
> > Thank you Lord for the TV Scooter Morons we are about to deceive
>
> > -----
> > RecGroups : the community-oriented newsreader :www.recgroups.com
>
> Assume a 10-handed table where anyone with a pocket pair sees the flop
> - typical for the games I have played.
>
> The total number of deals + flops possible is a = 52!/(32! * 2^10)*32!/
> (29!*3!) = 1.48 x 10^23
>
> Exactly 3 sets will occur in b = 13!/(10!*3!)*6^3*(10*9**2^3*43!/(29!
> *2^7) = 1.90 x 10^29
>
> So set over set over set occurs with probability 0.0000128, or about 1
> hand in 78166
>
> Exactly 2 sets will occur in c = 13!/(11!*2!)*6^2*(10*9)*2^2*44*45!/
> (29!*2^ -3*b = 2.29 x 10^30
>
> So set over set occurs with probability 0.00154, or about 1 in 647
> hands
>
> -------
>
> Stop calculating the odds of the 1st set... it's a given!
> I *already have* a set... just watched the door card
> drop that matched my hole cards!
>
> What is the probability that someone else also flopped
> a set just now? �I've read 1:100 or 1% and I'm sticking
> to it unless you work your magic and show me otherwise
>
> Mark- Hide quoted text -
>
> - Show quoted text -

This is actually easier, but my reply from last night appears to have
not posted. If it does post, I forgot a factor of 2 before.

Given that you hold xx, and the flop is xyz, the number of possible
hole card combinations for any given player is 47*46/2. Of these,
exactly 6 give them a set too. With 9 other players, the approximate
(ignoring two other sets against you) probability is thus 9*6/(47*23),
or about 1 in 21.
 >> Stay informed about: Frequency of Set-Over-Set Confrontations? 

First off, face down aces up is pretty much right. Who cares. The
only way you're folding a set is if the person you're up against went
all in and then flipped his cards over before you act. I mean, maybe,
just maybe, I could be enticed to fold a set against a super-tight,
super passive player if it goes bet, raise, reraise. But I doubt it.
You just don't flop enough sets in any situation to be cutting them
loose. I suppose there are other situations, given the prize ladder
of a specific tournament, where it might be smarter to lay it down,
just because your EV for the tournament goes up simply by folding and
surviving the hand...

But for math fun, here's how I see it:

The original question did not assume that I had already made a set.
It asked how often a set over set confrontation happens. And
truthfully, it cannot be answered without more information being
provided. It happens alot less often heads up than 4 handed, and alot
less often 4 handed than 10 handed. Furthermore, it depends on
whether you're playing against players that will play any pocket pair
in any situation, or some combination of tighter players who won't.
You can only calculate an exact probability if you assume that
everyone plays all pocket pairs in any situation.

A pocket pair will be dealt to someone 1 in 17 times. If there are 10
players in the hand, then the odds that SOMEONE got a pocket pair is
10 in 17.

However, the given that one pocket pair is already out there, the odds
are slightly different that a second person will also get one, because
there are now two cards left in the deck that are more difficult to
pair up than the other 48. 48 cards are still giving the other 9
players a 1 in 17 chance, for a 9 in 17 total, but 2 other cards are
still in the deck that can't make a set. This actually makes the odds
of the second pair being dealt to one of the other 9 players very
close to 1 in 2. (49%, by my calculations)

Thusly, the odds that two players at a ten handed table will get
pocket pairs is something very close to 5 in 17. The odds of one of
them flopping a set is about 6 in 47 (2 in 48 plus 2 in 47 plus 2 in
46). The odds that the second person will also flop theirs is about 4
in 46.5 (2 in 47 plus 2 in 46). The odds that both will happen is
about 24 in 2186, or 1 in 91. Thus, if playing 10 handed and all the
players see the flop with any pocket pair, the odds of exactly two
players making sets on the flop is 5 in 17 times 1 in 91. The answer
is 5 in 1548, or 1 in about 300. Some of my calculations are
approximate, so I could be off a little, but I don't think I'm off by
much.

However, that doesn't account for the times when three players get
pocket pairs, or even four, or the unlikely event that all 10 players
got pocket pairs. Each scenario is less likely than the previous to
occur, but more likely to result in a set over set when it actually
happens. I'm not going to bother with calculating them all, but I
suspect that the likely result is about a 10 percent decrease in the
odds. So I think it's probably closer to 270 to 1. However, that
number should be adjusted up, considering not all players play all
pocket pairs in every situation. The amount of that adjustment
depends on the number of pocket pairs that a given player won't play
in a specific situation, and how often that situation should occur.
That can't be calculated, without knowing who you're playing against.
It also varies signifcantly depending on whether you're playing limit,
no limit, tournament, or a ring game.

Mark B, on the other hand, wants to know what the odds are that
someone else has one when you've got one. As I calculated above, the
odds of one of the other nine players having a pocket pair when you
have one is very close to 1 in 2. The odds that their pocket pair
also trips is about 1 in 12. So the odds that you're also up against
a set is about 1 in 25 or so. Again, this goes up depending on who
you're playing and what type of game.

It seems that the odds should be much higher than 1 in 25, But I can't
find a flaw in my math. If someone else does, that'd be great. I
think 1% idea comes from the fact that your odds of making a pocket
pair set on any given hand is about 1%. So people theorize that if
their odds of making a pocket paired set are 1%, then the odds of
someone else doing it too are about 1%. But this idea forgets that
you're playing against 9 other people, not just one other person. 1%
is probably about right for a heads up game, but not against 9 other
players.
 >> Stay informed about: Frequency of Set-Over-Set Confrontations?