For several years, I've been puzzled by this:

You have 5-3-3-2 distribution with 12 hcp.

What is the distribution of the long suit's hcp?

The computations I have tried are certainly wrong. As the hand's total hcp rises, my computation of the long suit hcp seems chaotic.

I *suspect* that having 0 out of 12 in the long sun is very rare. But I can't prove it.

Does anyone know a reference? (I am not very interested a simulation.)

Carl

> I *suspect* that having 0 out of 12 in the long sun is very rare. But I can't prove it.

I now doubt my suspicion. I've done the computation for a 1-hcp 5-3-3-2. The probability of the jack being in the 5-card suit is only 70 /163 ~ .43

Carl

On Tuesday, September 28, 2021 at 3:08:52 PM UTC-4, judyorcarl@verizon.net wrote:
> I *suspect* that having 0 out of 12 in the long sun is very rare. But I can't prove it.

I have less confidence in this.

I've just done the computation for a 1-hcp hand shaped 5-3-3-2.

The probability that the jack is in the 5-card suit is 28 / 59 ~ .47.

Carl

> You have 5-3-3-2 distribution with 12 hcp.
> What is the distribution of the long suit's hcp?
> I am not very interested a simulation.

Perhaps an actual count, then?

There are 651552408 hands with 12HCP, 5 clubs, 3H, 3D, 2S.

- 22278942
0 22278942 0.034194

J 34145496
1 34145496 0.052406

Q 45532746
2 45532746 0.069883

QJ 38758356
K 58137534
3 96895890 0.148715

KJ 48945708
A 73418562
4 122364270 0.187804

KQ 57861972
AJ 57861972
5 115723944 0.177613

KQJ 24666768
AQ 57555792
6 82222560 0.126195

AQJ 24854688
AK 57994272
7 82848960 0.127156

AKJ 26062560
8 26062560 0.040001

AKQ 20036160
9 20036160 0.030751

AKQJ 3440880
10 3440880 0.005281

--
Don Reble djr@nk.ca

On Wednesday, September 29, 2021 at 1:13:21 PM UTC+7, Don Reble wrote:
> > You have 5-3-3-2 distribution with 12 hcp.
> > What is the distribution of the long suit's hcp?
> > I am not very interested a simulation.
> Perhaps an actual count, then?
>
> There are 651552408 hands with 12HCP, 5 clubs, 3H, 3D, 2S.
>
> - 22278942
> 0 22278942 0.034194
>
> J 34145496
> 1 34145496 0.052406
>
> Q 45532746
> 2 45532746 0.069883
>
> QJ 38758356
> K 58137534
> 3 96895890 0.148715
>
> KJ 48945708
> A 73418562
> 4 122364270 0.187804
>
> KQ 57861972
> AJ 57861972
> 5 115723944 0.177613
>
> KQJ 24666768
> AQ 57555792
> 6 82222560 0.126195
>
> AQJ 24854688
> AK 57994272
> 7 82848960 0.127156
>
> AKJ 26062560
> 8 26062560 0.040001
>
> AKQ 20036160
> 9 20036160 0.030751
>
> AKQJ 3440880
> 10 3440880 0.005281
>
> --
> Don Reble d...@nk.ca

I hope Don Reble won't feel insulted if I tell him what he already knows:
His numbers are correct!
This seemed like a fun little program to add to my fun source distribution;
it was very convenient to have Don's numbers to double-check my code.

Here's a possibly useful result for No Trump bidding:
With 16 HCP and 2-3-3-5, how many HCPs can you expect in your doubleton?
0 - 61235676 22.4%
1 - 23299596 8.5%
2 - 34276284 12.5%
3 - 51778800 18.9%
4 - 66772620 24.4%
5 - 16587972 6.1%
6 - 9555444 3.5%
7 - 10406196 3.8%

Email me at the From: address if you want any of this source.

Cheers,
Jamie

On Thursday, September 30, 2021 at 6:30:55 AM UTC-4, Fabulous Pedigree wrote:
> On Wednesday, September 29, 2021 at 1:13:21 PM UTC+7, Don Reble wrote:
> > > You have 5-3-3-2 distribution with 12 hcp.
> > > What is the distribution of the long suit's hcp?
> > > I am not very interested a simulation.
> > Perhaps an actual count, then?
> >
> > There are 651552408 hands with 12HCP, 5 clubs, 3H, 3D, 2S.
> >
> > - 22278942
> > 0 22278942 0.034194
> >
> > J 34145496
> > 1 34145496 0.052406
> >
> > Q 45532746
> > 2 45532746 0.069883
> >
> > QJ 38758356
> > K 58137534
> > 3 96895890 0.148715
> >
> > KJ 48945708
> > A 73418562
> > 4 122364270 0.187804
> >
> > KQ 57861972
> > AJ 57861972
> > 5 115723944 0.177613
> >
> > KQJ 24666768
> > AQ 57555792
> > 6 82222560 0.126195
> >
> > AQJ 24854688
> > AK 57994272
> > 7 82848960 0.127156
> >
> > AKJ 26062560
> > 8 26062560 0.040001
> >
> > AKQ 20036160
> > 9 20036160 0.030751
> >
> > AKQJ 3440880
> > 10 3440880 0.005281
> >
> > --
> > Don Reble d...@nk.ca
> I hope Don Reble won't feel insulted if I tell him what he already knows:
> His numbers are correct!
> This seemed like a fun little program to add to my fun source distribution;
> it was very convenient to have Don's numbers to double-check my code.
>
> Here's a possibly useful result for No Trump bidding:
> With 16 HCP and 2-3-3-5, how many HCPs can you expect in your doubleton?
> 0 - 61235676 22.4%
> 1 - 23299596 8.5%
> 2 - 34276284 12.5%
> 3 - 51778800 18.9%
> 4 - 66772620 24.4%
> 5 - 16587972 6.1%
> 6 - 9555444 3.5%
> 7 - 10406196 3.8%
>
> Email me at the From: address if you want any of this source.
>
> Cheers,
> Jamie
I was interested in distribution of hcp in *long* suit.

Carl

On Wednesday, September 29, 2021 at 2:13:21 AM UTC-4, Don Reble wrote:
> > You have 5-3-3-2 distribution with 12 hcp.
> > What is the distribution of the long suit's hcp?
> > I am not very interested a simulation.
> Perhaps an actual count, then?
>
> There are 651552408 hands with 12HCP, 5 clubs, 3H, 3D, 2S.
>
> - 22278942
> 0 22278942 0.034194
>
> J 34145496
> 1 34145496 0.052406
>
> Q 45532746
> 2 45532746 0.069883
>
> QJ 38758356
> K 58137534
> 3 96895890 0.148715
>
> KJ 48945708
> A 73418562
> 4 122364270 0.187804
>
> KQ 57861972
> AJ 57861972
> 5 115723944 0.177613
>
> KQJ 24666768
> AQ 57555792
> 6 82222560 0.126195
>
> AQJ 24854688
> AK 57994272
> 7 82848960 0.127156
>
> AKJ 26062560
> 8 26062560 0.040001
>
> AKQ 20036160
> 9 20036160 0.030751
>
> AKQJ 3440880
> 10 3440880 0.005281
>
> --
> Don Reble d...@nk.ca
thank you.