Date: Mon, 22 Feb 1999
From: Jim Geary
To: cgp
Subject: Re: to z or not to z

On Sun, 21 Feb 1999 Spianow@aol.com wrote: 

 Opening Rack:  C H Z L N G ?
(Best Play: ZiLCH) 
 
 Follow up: what if I had no 5-tile Z play?
 Do i keep the z on my exchange?
No. The Z and blank are asynergistic.
The Z usually has to be shed before using the blank, and the blank takes away a letter that might be helpful to shedding the Z.

I compared passing 6 to passing 5, keeping Z? Keeping the Z simulated three points better. Does that mean that I'm wrong about the asynergy? No, any simulated schoolboy will tell you that the Z = +3.0 . Therefor the difference in value is solely attributed to the Z's inherent positiveness. Still, you may argue a zero difference between the aggregate and the sum-of-the-parts hardly speaks of discord. But I counter, the discord measure is biased by the fact that we have a rack with 6 consonants on it. A vowel-heavy bag favors the Z and mitigates the asynergy. To verify this, I ran a similar sim with AEIOUZ? on the opening rack and passed 5 vs passed 6. In that sim, keeping the Z was only one point more favorable than passing 6 despite the Z's innate +3. Therefor one can posit a continuum of asynergy for the Z and ? based on the vowel content of the bag and centered around -1. 

Q: But if keeping the Z is 3 points better than not doing so, why
   shouldn't I do it?
A: Keeping the Z is better than keeping nothing at all, but there are
   better keeps still with this rack.
Quiz question: What two-tile keep with the ? is the best play?

For those of you who answered NG, go back to the fishery!
All the supergeniuses will of course answer CH. 

 
3-move sim; 2000 iterations:

Don't Pass
----------
ZiLCH     56     NG    62.5
GLuNCH    30      Z    35.9

Pass 6
------
-CGHLNZ    0      ?    36.9

Pass 5
------
-LGHNZ     0     C?    40.9
-CGHLN     0     Z?    39.9
-CGHNZ     0     L?    39.8
-CGHLZ     0     N?    39.6
-CGLNZ     0     H?    38.3
-CHLNZ     0     G?    37.0

Pass 4
------
-GLNZ      0    CH?    46.1
-CHLZ      0    NG?    40.0
-CGHL      0    NZ?    38.0

Pass 3
------
-GLZ       0   CHN?    43.4

Absolute Ranking
----------------
ZiLCH     56     NG    62.5
-GLNZ      0    CH?    46.1
-GLZ       0   CHN?    43.4
-LGHNZ     0     C?    40.9
-CHLZ      0    NG?    40.0
-CGHLN     0     Z?    39.9
-CGHNZ     0     L?    39.8
-CGHLZ     0     N?    39.6
-CGLNZ     0     H?    38.2
-CGHL      0    NZ?    38.0
-CHLNZ     0     G?    37.0
-CGHLNZ    0      ?    36.9
GLuNCH    30      Z    35.9

Last Modified 9/26/00

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