[nigulh]

Richard Pavlicek has worked out a very nice formula to evaluate the distribution (or freakness) of a bridge hand.

His method assigns every hand pattern (4333, 4332, ... 13-000) a number in the range [0, 20], which is called freakness of a hand. Obviously, the more freaky your hand is, the stronger it is. Has anyone thought how to add these points to the HCPs?

If we want to estimate the combined value of N and S hands, we may well add their HCPs. The more HCPs, the stronger they are. However, we can't do the same thing with their freaknesses. For example, if N has a very distribution 7=6=0=0 and S has distribution 0=0=6=7, their combined strength is much less, than in case S has 0=6=0=7. Although in both cases the sum of freaknesses of the N and S hands is the same, the combined freakness if different in both cases, because the hands have a fit in the second case but not in the first case.

How could one estimate the fit of two hands given their distributions (with specified suits)? Is their some nice formula that takes into account the distributions of the hands, length of the longest suit, voids & singletons etc?

Thanks in advance
Hendrik

[Chamaco]

You can try this:
the most freakish distribution of a single suit is when N+S hold 0 or 13 cards in a suit.
Therefore, the less freakish hand would be when they hold a combined length of 6.5 (pick 6 or 7 if you like). So, the more a suit length deviates from 6.5, the more it adds to the "hand freakness".

Using "CL" to indicate the Combined Length of NS in a suit, and "abs" to indicate the absolute value of a number (= always itspositive value) then try the follwing index (COMBINED FREAKNESS INDEX):

CFI= abs(CL♣ - 6.5) + abs(CL♦ - 6.5) +abs(CL♥ - 6.5) +abs(CL♠ - 6.5)

The index varies from 1 (e.g. 4333 vs 3433 or 1651 vs 6115) to 26 (eg 13-0-0-0 vs 0-13-0-0)

CFI = 1-4 -----> flat hands
CFI = 5-8 -----> semibalanced to shapely hands
CFI = 9-12 -----> distributional hands
CFI = 13-16 -----> very distributional hands
CFI = 17-20 -----> freaks
CFI = 21+ -----> superfreaks (your friends made you a joke )

You may prefer to adjust these ranges if you want to make the computations easier by using 6 or 7 rather than 6.5.

However, this simple index will not be able to describe the crossruff power.
In fact, say you hold a 5521 vs 5125;
CFI = (5+5-6.5) + (6.5- 5-1) + (5+2-6.5) + (6.5-6) = 3.5+0.5+0.5+0.5 = 5
The same value arises from 5323 vs 5323, since the combined length oif the suits are the same.
So, the CFI is somewhat "conservative", in that it underestimates the freakness of misfit hands, which is often wise, but not really when you have long trumps in both hands and a crossruff is likely, or a long and strong side suit can be developed with ruffs.
Perhaps it is fair to say that this CFI is more a measure of *FIT* rather than of *freakness*.

[Trpltrbl]

nigulh, on Mar 6 2004, 04:15 PM, said:

Richard Pavlicek has worked out a very nice formula to evaluate the distribution (or freakness) of a bridge hand.

His method assigns every hand pattern (4333, 4332, ... 13-000) a number in the range [0, 20], which is called freakness of a hand. Obviously, the more freaky your hand is, the stronger it is. Has anyone thought how to add these points to the HCPs?

Thanks in advance
Hendrik

Yes, it is called Zarpoints. It is based on HCP+ Controls, your 2 longest suit and your shortest suit. All this added up will give you your Zarpoints.
HCP + Controls you count your points a little different ;
A = 6
K = 4
Q = 2
J = 1
I will just give you the link to go there and you can see it for yourself. If you have any quesion, just ask me ZarPoints

Mike