[matmat]

campboy, on 2011-April-02, 06:04, said:

It's not that tedious if you just want a frequency table.

FOR a,k,q,j = 0 TO 4
   p = 4*a + 3*k + 2*q + j
   n = (4 CHOOSE a)*(4 CHOOSE k)*(4 CHOOSE q)*(4 CHOOSE j)*(39 CHOOSE (13-a-k-q-j))
   f[p] = f[p] + n
NEXT j,q,k,a

Add in a function to calculate x choose y (making sure that it returns 0 if y is out of range) and you're good.

Yup. you're right.

[matmat]

fazzzoola, on 2011-April-02, 08:00, said:

I have 3 sources, 2 of which are noted on the web site, and all three differ: 0.05%, 0.00% and 0.36%... since my primary ssource was a 40,000,000 random generated effort, I'd have to stick with it, in that it was an actual set of deals and not mathematical calculations (estimates) of probability. However, having said that, I do recognize that some calculations are more "accurate" than others, and yet, for my general purposes here - since I'm not splitting hairs - it'lll do? (Less than 1% is rather rare... <smiles>)

And the next guy is gonna show up, start running simulations and use your site as a "source" claiming the correctness of their method.

I really have no problem with someone saying, in a bridge context, that 0 HCP happens 0.5% of the time while 10HCP happens 10% of the time so whatever system we're messing around with takes this factor of ~20 into account with its structure, or that 9,10, and 11 HCP are all equally likely. Approximations are fine, and have their place.

I do have a problem with someone putting up a table of (poor) approximate values, without estimating an error, trying to pass them off as exact and backed up by some dubious online "sources," when the actual values can be calculated exactly rather easily(see campboy's succinct pseudocode).

galwood.com said:

"The data are quoted from a published study by (?) in which the author randomly generated 40 million hands. Virtually the same distribution can be found at two other web sites: http://www.bridgehan...istribution.htm,
and http://crystalwebsit...d_patterns.htm. "

a quoted published study?
virtually the same?
since when is a factor of 7 difference in the result considered "virtually the same?"

to be honest, some of your numbers are a few sigma away from the real value, so I'm not even sure I'd say that your quoted values are consistent with the underlying pdf...