From: Eric_S_Klien@cup.portal.com
Newsgroups: rec.games.pbm,rec.games.board
Subject: Diplomacy Zine -- Chapter Eight EP #276
Date: Sun, 23 Aug 92 20:53:26 PDT
Organization: The Portal System (TM)
Distribution: world

Issue #276 of ELECTRONIC PROTOCOL:

*************************************************************************
                            Mommy, Mommy...

                   I hate my aunt!  Shut up and eat!
*************************************************************************
 
Chapter One contains:
 
BAGHDAD, BLITZKRIEG II, KING'S GAMBIT, PASSCHENDAELE,
DRAGONS, BLACK OCTOBER, OPERATION DESERT STORM, THE SOMME
 
And is published by uunet!cti1!rlister or rlister@cti.com/Russ Lister

Chapter Two contains:
 
BATAAN, BOADICEA, CONAN, CROATIA, CUBIT, DAGGER, DIEN, DRAM, 
EMU, EYLAU, FONTENOY, GIGGLES, HASTINGS, IONA, KHAFJI, MARENGO, 
OSIJEK, PARIS, PORTNOY, QUEBEC, TIBERIUS, VEGA

And is published by loeb@geocub.greco-prog.fr/Daniel E. Loeb
 
Chapter Three contains:
 
SQUALANE, BRUSILOV OFFENSIVE II, CULLODEN, GANDALF'S REVENGE, 
GOODBYE BLUE SKY, MASTERS OF DECEIT, PANDORA, NOW AND ZEN

And is published by mad-2@kub.nl/Constantijn Wekx

Chapter Four contains:
 
DEADLY DAGGERS, MONTREUIL-SUR-MER, FIRE WHEN READY, THUNDERDOME,

And needs a publisher.

Chapter Five contains:

YALTA

And needs a publisher.

Chapter Six contains:

BERLIN WALL, HIROSHIMA, GENGHIS KHAN, SEA LION

And is published by barry@brahms.udel.edu/Barry Fausnaugh.

Chapter Seven contains:

RIYADH'S RECKONING

And needs a publisher.

Chapter Eight contains:

TIBERIUS, BETELGEUSE, IRON CROSS, GUERNICA, TEUNISGEK, WOLF BLITZER, 
THE COMMANDERS, THE SUTHERLAND CONFLICT, NOW AND ZEN, TRUST ME!

-------------
Chapter Eight
-------------

Table of Contents:

Fleet Quiz answers
Fleet Quiz winner!!!
National zine polls part three: explaining the preference matrix
National zine polls part four: further thoughts on the preference matrix
Variants ideas from Per Westling
----

Here are the Fleet Quiz answers from 
pl436000@brownvm.brown.edu/Jamie Dreier:

1. Which spaces have the fewest "fleet-like" neighbors? A space
has n fleet-like neighbors if it can be occupied by a fleet and
that fleet has a choice of n spaces to (try to) occupy on
its move. (I will count the space it occupies as one of the
spaces to which it can move, since it can hold.)

ANSWER:
StP, Syr, and Por have three fleet-like neighbors each.


2. Define a "second order fleet-like neighbor" as a space
to which a fleet can move in TWO moves. Thus, Mar is a
second order fleet-like neighbor of WestMed.

Which spaces have the fewest second order fleet-like neighbors?
(Again, include HOLD orders in your calculations.)

ANSWER:
Syria has only six (Syr, Eas, Aeg, Con, Smy, Ion)

3. Which spaces share the dubious second place distinction
for fewest second order fleet-like neighbors?

ANSWER:
Many have seven.
Sev, arm, rum have the Black and all its neighbors.
StP(nc) and StP(sc)
Tri and Ven have Adr and its 5 neighbors, plus Nap for
Ven and Gre for Tri.
I think that's it.

                          AIR LIFT

4. Suppose at the start of the game, all players cooperated
to move some given army anywhere it wanted to go. Which
army/destination would take the largest number of
moves? (This looks like an army question, but of course
it's at least as much a fleet question.)

ANSWER:
It takes the Turkish army in Smy 5 moves to get to Munich.
Oddly enough, the German army in Munich could reach Smyrna
in only three moves! Because its trek across land can be
taking place while the fleets are setting up....

                UNANSWERABLE FIRE
5. An army occupies space X, and a fleet occupies Y (count
different coasts as different Y's). The army can attack the
fleet, but for the fleet to attack the army would require
n moves. For which X and Y is n largest?

ANSWER:
Pie and Ven, in either direction, of course.

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c85perwe@und.ida.liu.se/Per Westling is a...

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Here are our Fleet Quiz winner's answers:

A reply to the ***FLEET QUIZ*** of Chapter Eight EP #274

Without looking at the map
1.  Portugal:  Portugal, Spain and Mid Atlantic.  Spain should be
regarded as one space for this purpose even though it has a sc and a
nc as a fleet in Portugal can't swith place with another fleet in
Spain (costal crawl disallowed) as two adjacent provinces can't swith
units.
    Syria:  Syria, Smyrna and Eastern Med.
    StP nc:  StP nc, Barents and Norway.
    No more.

((He is exactly right here.))

2.  Syria:  Syria, Eastern Med, Ionian Sea, Aegan Sea, Smyrna,
Constaninople giving 6 spaces.
    No more.

((He is exactly right here.))

3. Sevastopol:  Sevastopol, Armenia, Ankara, Constantinople, Bulgaria
ec, Black Sea, Rumania;  7 spaces.
   Rumania:  See Sevastopol.
   Armenia:  See Sevastopol.
   Ankara:  See Sevastopol.
   StP nc:  StP nc, Barents, Norway, Skagerak, Sweden, North Sea,
Norwegain Sea;  7 spaces as well.
   No more.

((Jamie agrees with him on Sev, Arm, Rum, and Stp.  They disagree
over Ank.  I think Jamie is right here.))

4. I would guess that it would be to move Army Liverpool to Syria.
This is done by the following:
  SPRING 01  England F Lon->ENG, A Lpl->Wal, F Edi->NTH
             France F Bre->MID
             Italy F Nap->TYRS
     Austria F Tri->Alb/ADR
     Turkey F Ank->Con, A Con->Bul
     Russia F Sev->BLA
  FALL 01    England F ENG->MID, F NTH->ENG
             France F MID->WES
             Austria F ADR/Alb->ION
             Turkey F Con->AEG, A Smy->Con
  SPRING 02  England A Wal->Smy Convoyed by lots of fleets
  FALL 02    England A Smy->Syria
So it isn't hard for English armies to reach coastal spaces (from Smy
you can reach Armenia, so Sev is 5 steps away).  How about an area in
the inner part of Europe?  Budapest?  Well, convoy to Albania instead
of Smyrna and Budapest is reachable by land (Alb->Serbia->Budapest).
Other inner parts may be reached by A Lpl->Yor->Den (C Nth)->Lva (C
BAL)->War->Ukr or Lva->Mos->Sev or Den->Pru->Sil->Gal.  So the
farthest is A Lpl->Sevastopol, 5 steps.

((Both Jamie and Per have given 5 step answers.  Perhaps they're both
right?))

5. X = Livonia, Y = StP nc, n = 4

If I win I wouldn't mind a subscription to Diplomacy World.

((Both Jamie and Per have given 5 step answers.  Perhaps they're both
right?))

Per Westling should confirm that his address is "c/o Lindh, Drabantg 11
S-583 46 LINKOPING, SWEDEN" and let me know if the one year subscription
to Diplomacy World will be a renewal or a new subscription.  
Congratulations, Per!

I received the following from pl436000@brownvm.brown.edu/Jamie Dreier,
the winner will get a one year free subscription to the Diplomacy
magazine of their choice:

                     DEEPLY TROUBLING QUIZ

******
Call a given space with a given type of unit (on a given coast, if
relevant) "Potentially Deadly" to a unit in some other space IFF
there is some configuration of pieces on the board and some
set of orders such that the dislodgement of the second unit
depends on the orders given to the first.

E.g., a fleet on the north coast of Spain is Potentially
Deadly to an army in Gascony, because there is a configuration
and set of orders (namely, f MAO - Gascony) in which Gascony
will be dislodged if and only if Spain orders support for MAO-Gas.

Ok? Now, call a given unit in a given region (and coast)
"Deeply Troubling" IFF it is Potentially Deadly to EVERY
space on the board.

That's the set up. Here's the question.
How many unit/space pairs are Deeply Troubling?
(You needn't give the actual number if you can describe
in some other illuminating way which unit/space pairs
are Deeply Troubling. Or for that matter, if you can
describe in some illuminating way which one's are NOT.)

And, more difficult, can you prove it??
*****

I received the following from amt5man@sun.leeds.ac.uk/Mark Nelson:

    NATIONAL ZINE POLLS PART THREE: EXPLAINING THE PREFERENCE MATRIX
    BY MARK NELSON

SECTION ONE: What is A Preference Matrix?

   In Part One of this series we presented a history of the UK Zine 
Poll and examined how the idea of a National Zine Poll had spread 
into other diplomacy hobbys.  In Part Two we surveyed some of the 
different methodologys that have been used over the years.  In this 
part we explain in more detail the hows and whys of using the 
Preference Matrix.  

   As we showed in Part Two the earlist Zine Polls were run using an 
average votes system.  Before we can show why the Preference Matrix 
is a *Good Idea* we first show some of the problems that a Poll based 
solely on Average Votes has.  

   Almost all of the faults with the Average Vote system stem from 
its subjectiveness.  How good does a zine have to be to receive the 
top mark (normally 10), how bad does it have to be to receive the 
bottom mark (1 in the UK, 0 in North America). Does a vote of 5 
represent an average zine, and if so what is an average zine?  

   And what does it mean if I give one zine 2/10 and another 4/10?  
Does it imply that I consider the higher ranking zine to be two-times 
better than the lower ranking one?  Does the differential I use 
between zines indicate anything?  

  How should you vote? If 5 represents an average zine should you try 
and make sure that the average of all the votes that you cast is 5?  
If you see only one or two zines then it's likely that you think that 
these are going to be great zines and vote them high marks.  What 
happens if you see more zines?  

   In fact several Zine Poll Custodians have released figures which 
show two interesting things:The more zines you vote for the lower the 
average of the votes that you cast and that zine-editors cast lower 
votes than non-zine editors.  

  These phenomena are relatively easy to explain.  The more zines you 
see the more likely it is that you see zines which do not 
particularly enjoy/which you do not rate as being outstanding.  Hence 
you will cast low votes for these zines.  Traditionally zine-editors 
undertake wide-spread trading and see more zines than non-publishing 
voters.  Additionally zine-editors are more critical of rival 
publishers and pay more attention to content/lay-out and the such 
like and mark zines down.  

  One think that was discussed in the First Part of this article was 
"what is the purpose of a Zine Poll?"  If the purpose is to find 
which zines the hobby prefers then one serious problem with a 
methodology based upon average voting is that a zine with a small 
number of enthusiastic subscribers could easily win the Poll.  Hence 
the average voting method is not method to guarantee that that the 
ranking of zines in the Poll corresponds to how the hobby as a whole 
views them.  

   Combining all this information we see that whilst the Average Vote 
method has some merit, it is not perfect.  Can we get another angle 
onto which zines people prefer?  

   Earlier I asked if I voted twice as much for zine A as for zine B 
does it imply that I consider it to be twice as worthy as the lower 
ranking one?  One thing which it does show is that I prefer zine A to 
zine B.  And because there is so much flucturation in what voters 
mean by the numbers which they attach to the zines that they vote for 
perhaps we can gain something useful by just considering their 
*preferences*.  

   The preference matrix does this.

   When a voter lists 5 zines on their ballot paper they are telling 
you their preferences.  They are saying that the they prefer the zine 
at the top of their ballot to all other zines, that they prefer all 
other zines to the one at the bottom.  It doesn't matter that the 
votes may be 10-9-8-7-6 or 10-7-5-3-1 or 10-7-7-6-6-2, whatever the 
value of the vote the voter is given us a indication of whether he 
prefers Zine A or Zine B.  

   How do we calculate a Preference Matrix?

   Suppose there are N zines in the Poll. Let us chose two particular 
zines, A and B.  Then on every ballot paper that contains zines A and 
B there are three different outcomes: Either Zine A will appear 
before Zine B, Zine B will appear before Zine A or the two zines will 
appear at the same place on the ballot in which case they draw.  

   So by going through all ballots which contain both zines we can 
arrive at a Win-Draw-Loss table which will tell us how many times 
Zine A beat Zine B, how many times Zine A and Zine B drew and how 
many times Zine B beat Zine A.  

   At it's simplist level we can say that if Zine A has more `wins' 
against Zine B then it has `loses' then Zine A has beaten Zine B, in 
the sense that more people Prefer Zine A to Zine B.  

  We can do these comparisons for each zine in the Poll, that is to 
say that we can compare every zine in the Poll to every other zine in 
the Poll and to see if voters express a preference for one zine 
against another. If there are N zines in the Poll then there are (N-
1) + (N-2) + (N-3) .... + 1 distinct preferences that can exist.  

   If there are N zines in the Zine Poll then the Preference Matrix 
is an nxn matrix.  Along each column or row, there will be (N-1) 
entries (obviously you can't compare zine A to zine A!). We may label 
each entry in the matrix with the unique reference (i-j) where for 
entry (i-j) we are comparing zine i to zine j.  Each entry (i-j) will 
contain three numbers (k-l-m) as described above.  We refer to the 
label (i-j) as an Index Pair.  

   At it's most simplest implementation the Preference Matrix will 
tell us that for any of these N zines it won A Index-Pairs in the 
Preference Matrix, lost B Index Pairs in the Preference Matrix and 
drew (N-A-B) Index Pairs in the preference matrix.  

   What now?  We can award a simple mark scheme.  Perhaps for every 
Index Pair thata zine wins it scores 3 points and for every Index 
Pair that it draws it scores 1 point.  Then we can total up all the 
points that a zine has scored and arrive at a listing of zines which 
is independent of the actual numbers voters accorded each zine.  

SECTION TWO: The Preference Matrix and The Zine Poll

   There are obviously many different ways in which you score a 
Preference Matrix.  For instance you could score 2 pts for winning an 
Index Pair and 1 for drawing.  Or even 2 pts for winning and 0 for 
drawing.  

  One disadvantage of a Zine Poll run purely on a Preference Matrix 
is that no indication is taken whatsoever of the actual value of the 
votes cast, although this is also one of its strengths.  Although in 
the past there have been instances when the Zine Poll has been scored 
purely on the preference matrix nowdays the scoring of the Zine Poll 
(both in the UK and North America) uses a mixture of average votes 
and prefence matrix.  

   But before explaining how to splice the average vote and the 
preference matrix together there is another question to answer:  
Under what circumstances should you use a Preference Matrix in a Zine 
Poll?  

   The essence of the Preference Matrix is that there are 
"sufficient" voters who can make a comparison between zines on the 
list.  That is to say that given any index pair (i-j) there are are 
"sufficient" voters who see both of these zines.  To take one 
extreme, if there are six zines in the Poll and twenty voters but all 
ballots contain the name of one zine then it would be absurd to use 
the Preference Matrix because no-one was casting any preferences.  At 
the other extreme, suppose all twenty voters saw all six zines, then 
for each of the 15 distinct comparisons there are twenty voters and 
so meaningful results are being extracted.  

   The question is, how many votes are required before a comparison 
can be construed as being meaningful?  For instance comparisons which 
are either 1-0-0, 0-1-0 or 0-0-1 are not particularly useful (this is 
to say that only one voter sees the two zines in question).  How many 
votes are required before a comparison is meaningful?  How long is a 
piece of string?  

   To some extent this depends on how many votes the zines in the 
Poll are attracting.  For instance if each zine attracts 100 votes 
then an Index Pair containing only 5 votes is not meaningful as it is 
based on only 5% of the voters.  On the other hand if each zine 
receives only 10 votes then an Index Pair with 5 votes is not so bad 
(although not good).  Obviously there are no hard and fast rules 
here.  

   We have discussed above how many ballots are required before an 
index pair can be meaningful.  There is the related question of how 
many index pairs have to be meaningful before the Preference Matrix 
is telling us useful information.  

   For instance.  Suppose that there are 6 zines in the Zine Poll.  
Then there are 15 distinct index pairs.  If 14 of these contain zero 
or one preferences (so are telling us either nothing or not very 
much) and the 15th contains 10 preferences then it isn't worth 
running a Preference Matrix.  For a decent Preference Matrix you 
require to have 80%+ of Index Pairs being meaningful.  (This 80% 
value has been plucked from thin air, the true value is almost 
certainly higher but not lower.) 

   This boils down to resolving an important question about your 
national hobby: Do people see a number of different zines or do they 
tend just to see one or two zines?  

   So we have seen that a preference matrix is only reasonable if a 
large enough number of people are expressing a preference for most of 
the zines in the Poll.  

 PART THREE:  Splicing The Preference Matrix and The Average Vote 
 Together 

   Before covering this, we should explain in more detail why most 
people are not in favour of vasing their Zine Poll solely on the 
Preference Matrix.  There are two reasons.  Firstly it takes no 
account of the actual numbers cast, it doesn't matter if you score 
two zines as 10-9 or 10-3; in the end they both score up as a 
preference for one zine over another.  

   Secondly people who vote for a large number of zines have a 
greater influence than those vote for a small number.  In fact a 
person who only votes for one zine has *no* influence on the Zine 
Poll because he casts no preferences.  When John Piggott ran the UK 
Zine Poll one of the rules was that you had to vote for a minimum of 
*two* zines.  This means that people who are more active in the Hobby 
have a grater influence than those are not.  The feeling is that the 
Zine Poll should try and include the votes of everyone who votes, and 
the best way to do this is to combine together scores from an Average 
Vote and from a Preference Matrix.  Now, how do we do this?  

   Let us suppose that that there are N zines in the Preference 
Matrix, and that you score A points for winning each index pair and B 
points for drawing an index pair.  Then the maximum score that any 
zine can obtain is (N-1)*A.  

  Now the maximum score that you can score in an Average vote is ten.  
The maximum score in the Preference Matrix is likely to be not only 
higher than this, but much higher than this.  In the UK a typical 
preference matrix will contain on the order of 50 zines, with 3pts 
for a win.  Hence the maximum score on a preference matrix will be 
(50-1)*3=147.  Adding the average vote onto these scores is unlikely 
to change the result of the Poll.  

   So the first thing to do is renormalize all scores from the 
Preference Matrix so that the highest score is ten.  If a Zine Scores 
C then it's new score is C/((N-1)*A).  

   In the past there have been different ways of combining the 
Average Vote (AV) and Renormalised Preference Matrix Score (RNPMS).  
It's perfectly possible to weight them equally, but at present this 
is not done.  

   In the UK the present Custodian uses 2*(RNPMS) + AV which gives 
zines a total of 30.  Zines are then ranked in order of their final 
score.  In North America the current custodian (Eric Brosius) uses 
the formula: Final Score = ( 2*Modified Mean + Preference Score)/3.  

   It is interesting to note that in the UK we emphasise the 
Preference Matrix over the Average Score whilst in North America they 
emphasise the Modified Mean over the Preference Matrix. We shall not 
attempt to explain the reasons for these fundamental differences 
here, a commentary on this appeared in (1).  

Part Four: Some Advanced Features of and Comments on The Preference Matrix

   Running a Poll using Average votes is straight-forward and not 
particularly time-consuming.  Calculating a Preference Matrix for a 
small number of voters and a small number of zines is slightly more 
time consuming.  Calculating a Preference Matrix for a large number 
of voters and a large number of zines is *very* time-consuming!  

   If you vote for N zines how many do preferences are you making?  
(N-1) + (N-2) + (N-3) + ... 1 = quite a lot!  You can see that if 
people start voting for more than 20 zines then it can take some time 
to store that information.  

   In the UK Iain Bowen has recently introduced two new innovations 
to the Preference Matrix.  Firstly he scores all indices which 
contain only one preference as a draw for both zines regardless of 
preference.  

   The reason for this is two-fold.  Firstly he does not consider 
such pair-indices to contain meaningful information.  Secondly an 
obscure fanzine which a low number of voters could do very well in 
the Poll by winning  a large number of 1-0 preferences.  A 
methodology which could allow a fringe zine to either win or do 
particularly well is not considered to be sound.  

   The other innovation re-defines the concept of winning an Index 
Pair.  Traditionally to win an Index Pair you simply had to score 
more wins than loses to the other zine in the Index Pair.  You only 
drew the Index Pair if both zines had the same number of preferences.  

  This can lead to strange results.  Suppose the Index Pair contains 
the following preferences 1-20-0.  Twenty one voters, twenty say the 
zines are equal but one says that he prefers zine A.  Should this 
really count as a win for Zine A?  Iain's innovation is to say that 
to win the Index Pair you have to have greater than 50% of the voters 
giving you their preference.  So a 1-20-0 is a draw, as is a 10-4-6.  

   Obviously this idea can be developed further.  Is it "fair" that a 
10-4-6 scores as a draw but a 11-4-6 (one extra voter!) scores as a 
win for one zine and a lose for the other?  Using the (k-l-m) 
notation defined earlier we could instead do away with the concept of 
winning and drawing index-pairs and instead define a score for each 
index pair as follows.  Let A be the number of points for "winning" 
an index-pair.  

   Then a zine scores A*(k/(k+l+m)).  This means that one vote does 
not dramatically swing your score from a draw to a win.  
Unfortunately this system means that fringe zines with fewer 
preferences may score better than zines with large circulations.  

   Perhaps there is material on this topic for another article...  

(1) Northern Flame 34 (March 1992)

NATIONAL ZINE POLLS PART FOUR: FURTHER THOUGHTS ON THE PREFERENCE MATRIX
                    BY ERIC BROSIUS

Here is how I would do preference scores if I were going to be a 
TurboPhreak about it: 

My feeling is that the Pref Score should measure how certain we are 
about the fact that one zine is preferred to another.  This can be 
computed using probability theory if we make some basic assumptions.  
I'd start by breaking down all individual comparisons into wins, 
losses, and ties.  For example, let's suppose we have 40% wins, 40% 
losses, and 20% ties.  (I do not mean we break down the *matchups* 
into these categories, but the *comparisons*.  I.e., if we pick a 
random pair of votes on the same ballot, there is a 20% chance they 
will be the same.) 

I'd then compute a function  P(n,m)  for each pair of integers  (n,m)  
with - n <= m <= n.  Loosely speaking, this would represent the 
chance that, given n  comparisons taken from the hypothetical 
distribution,  wins - losses  would be less than (or no greater than)  
n .  The larger  P(n,m)  is, the less likely it is that a zine could 
achieve a  wins - losses  score of  m  by pure chance alone.  Thus, 
the more certain we are that the result of the matchup is due to more 
than just chance.  Note that I waffled above between "less than" and 
"no greater than".  This was deliberate.  For symmetry purposes, I 
don't want to prefer one to the other.  So in actual practice I would 
compute  P(n,m)  on a "less than" basis and *also* on a "greater 
than" basis, and I would add the two values.  

Let's do a few small examples.  For larger ones, you'd need a 
computer or a lot of patience.  

If  n = 1,  we need to compute  P(1,1), P(1,0), and P(1,-1).  First 

P(1,1)  =  [P(wins - losses < 1) + P(wins - losses <= 1)].  

Let's do the easy one first.  P(wins - losses <= 1) = 100%, since you 
can't do better than  1-0  on a single comparison.  The harder one is 

P(wins - losses < 1)  =  P(a 0-0 matchup) + P(a 0-1 matchup)

                      =  20% + 40%  =  60%.

This means P(1,1)  =  60% + 100%  =  1.6 .


Now let's do P(1,0)  =  [P(wins - losses < 0) + P(wins - losses <= 0)]

                     =  [P(wins - losses < 0) + P(wins - losses < 1)]

                     =  40% + 60%  =  1.0 .

And similarly, P(1,-1)  =  0.4 .

How would this be used in the preference score?  Simple.  I'd add  
P(n,m)  to a zine's pref score for a matchup composed of  n  
comparisons if we had wins - losses = m.  

For example, on a 1-comparison matchup I'd add  1.6  for a 1-0 win, 
1.0 for a 0-0 tie, and  0.4  for a 0-1 loss.  These values are on the 
same scale as the current Runestone raw preference score (i.e., 
before normalizing.) 

I'll give further values of these numbers in the chart below.  These 
numbers are rounded to the nearest hundredth.  

P(n,m)

n | m = -3    -2    -1     0     1     2     3  
------------------------------------------------
1 |                0.40  1.00  1.60
2 |          0.16  0.48  1.00  1.52  1.84
3 |    0.06  0.22  0.56  1.00  1.44  1.78  1.94

You can generate more of these if you want by writing a program.  
Note the zero-sum nature of this process:  the two zines involved in 
a matchup always split 2 points.  

Would this be an improvement?  Yes, if you are interested in 
accuracy.  But I don't think it would be an improvement if you are 
interested in being able to explain the scoring system to those who 
are interested.  It's just too complicated for most people to have 
the patience for (remember, the values of  P(n,m)  would have to be 
recomputed each year depending on the number of tied comparisons.)  
And furthermore, the difference is not that great.  For a 1-0 matchup 
on on ballot, we'd award  1.60  points instead of the  2.00  I award 
now.  The bigger effect would be on a close matchup with a lot of 
votes on either side---for instance, an 8-7 matchup on 19 ballots.  
In these cases, the result would be very close to 1.00 for each zine.  

Variant Ideas from Per Westling <c85perwe@und.ida.liu.se>

As of this moment all variants implemented for Judge is available on 
all judges.  But this might not be the case in the future as there 
are some attempts to implement other variants at other cites.  

I think that is a good idea, but would like to see more of it.  I 
suggest that some kind of variants should only be available at some 
cites, and not all, so that the people interested to play in that 
variant would be attracted to just that judge.  

The central judge could either have all variants implemented 
available or maybe have them archieved and include a pointer to there 
that variant could be played.  

Here are some variants I would like to see implemented:

* Captalist Dippy  [buy and sell currencies, the one with most
currenices after a season controls that power the next season]
* Fleet Rome  [like regular Dip but Italy starts with Fleet
instead of Army in Rome]
* Baseball Diplomacy  [you collect points for each inning, the
highest sum wins, an inning is a year controlling on power, the game
consist of 7 years so that each player get to control one power one
year]
* Intimate Diplomacy  [two player variant]
* Stab  [a blind variant, the only thing one sees (except what
ones units sees) is the failed orders]

All the above use the normal map.  There are some other with special
maps that could be implemented:

* Hardbop Downfall  [play Diplomacy in Middle Earth setting]
* Aberation  [maybe the best variant?]
* India 1501  [easy variant for 5 players, no fleets]
* 1885[a 9-player variant with Sweden and Spain as extra
powers, uses the Army/Fleets rules]
* Song of the Night  [the most known of all fantasy variants
(except maybe Downfall) in no special fantasy settings, uses Wizards,
Kings, Heroes, Magic Items, ...]
* Gilgamesh  [The German extended version of "Song of the
Night"]


As you can see, a lot of good variants.

Stay tuned for the rules of Capitalist Dippy.

------------------------------------------------------------------------

                          CAPITALIST-DIPPY

                      by Lukas Kautzsch (1985)
 
Capitalist-Dippy (CD) contains two games, Dippy Stock Exchange (DSE) 
and Diplomacy. The owner of the most shares leades units of this 
country in the next season.  

Now to the details:
At the beginning each players owns of each of the 7 currencies 
(Kronen, Pound, Francs, Mark, Lira, Rubel, Piaster) 1000 shares and 
no Swiss Franks (SFr, this is the base currency). The price of all 
currencies is 1.00 SFr.  

As usual in Dippy, a year is divided in 3 seasons (Spring, Autumn and 
Winter), which are played in 3 or 2 rounds (Autumn and Winter 
together).  

In the first round of the game (Winter 1900) there is only action at 
the DSE, in each further round there are military movements and 
following orders at the DSE.  

At the DSE the players can buy and sell currencies based of the 
prices of the last round. Selling shares is limited up to 500 shares 
of each currencies. You can buy up to your cash. The cash you got by 
selling shares is converted to SFr and added to your cash. You can 
save it for the next turn, or reinvest in other currencies. I.e.: You 
own 1000 Shares of French Francs at 2.50 SFr, you sell 500 shares. 
You get 1250 SFr. If you buy 735 Lira at 1.70 SFr, you have to pay 
1249.50 SFr.  

At the end of the turn the price of the currencies changes. For every 
100 Shares of a currency which were more bought than sold, the price 
raises by 0.01 SFr. Vice versa it falls by 0.01 SFr for every 100 
shares, which were more sold than bought. The value of currencies can 
never fall below 0.01 SFr (but see below). There is also no upper 
limit of the price.  

When a country runs out of supply-centers, this currency is in the 
next turn without value and can no longer be traded with at the DSE.  

The player with the most shares of a currency at the end of a turn 
leads the units of this country in the next season. (When two players 
are equal, the one who had the most in the last turn). The game is 
finished at the end of the dippy-game which will be after Winter 1910 
unless a power owns more than 17 centers before that.  

The decision about victory and the places is not based on the leader 
of the winning country, nor the value of the currencies in SFr. Only 
the point value (victory points) of the existing countries, computed 
as follow: 

The number of supply centers is multiplied with every 100 shares of a 
country. The amount for all exisiting countries is added to the plaer 
amount. The player with the highes score win this game.  

NMR-arrangment: If a player fails to give orders for the DSE, he 
sells of each currency as many as possible up to 500. In the 
diplomacy-part all units will hold.  

-----------------------------------------------------------------------

                         CAPITALIST-DIPPY II

                      by Per Westling (Dec 91)

This is a revised version of Lukas Kautzsch's _Capitalist-Dippy_ 
influenced by other similar variants like for example Douglas 
Huskins' _Speculation_.  
                                  Per Westling -- constructor (Dec 91)

1. Any number of players may participate in this game, but 10--15
is recommended. It's up to the GM if the players should be anonymous
or not.

2. Capitalist-Dippy (CD) contains two games, the Stock Exchange (SE) 
and the normal Diplomacy orders. The owner of the most shares (of the 
power's currency) leades units of this power in the next season. At 
the beginning each players owns of each of the 7 currencies (Kronen, 
Pound, Francs, Mark, Lira, Rubel, Piaster) 1000 shares and no ECUs 
(European Currency Units, this is the base currency). The price of 
all currencies is 1.00 ECU. ECU is used as this is just an abstract 
measure of worth.  

3. As usual in Diplomacy, a year is divided in 3 seasons (Spring, 
Fall and Winter), which are played in 3 or 2 rounds (Autumn and 
Winter together).  

In the first round of the game (Winter 1900) there is only action at
the SE, in each further round there are military movements and
the following orders at the SE.

4. A round consist of the following actions:
 i ] Orders in the Diplomacy game
ii ] Financial Orders are executed at the SE
iii] Resignations and adding of new players
iv ] Determination of new prices for the currencies
v  ] Determination of Leaders of each Power

During Winter 1900 step *i* is skipped, and during the last round 
(Winter 1910 or when a power exceeds 17 centers) only step *i* and 
*ii* take place.  

5. At the SE the players can buy and sell currencies based of the 
prices of the last round. Selling shares is limited up to 500 shares 
of each currency. You can buy up to your cash. The cash you got by 
selling shares is converted to ECUs and added to your cash, but you 
can use it the same round if you like. I.e.: You own 1000 Shares of 
French Francs at 2.50 ECUs, of which you sell 500 shares. You get 
1250 ECUs. If you buy 735 Lira at 1.70 ECUs, you have to pay 1249.50 
ECUs. The 0.50 ECUs extra you won by this transaction is lost as the 
fractions are dropped after transactions are finished.  

6. The Financial Orders (FO) are transactions for the SE, and they 
should be given in a format similar to this: 

    Crowns   +500
    Pounds   +200 
    Francs  -1000
    Marks     N/T
    Lira     +100
    Rubles   +750
    Piastres -500

Pluses (*+*) mean buy, and minuses (*-*) sell. "N/T" mean No
Transaction.

As usual a player can't sell more than 500 shares, or more than 
(s)he's got.  If a player tries to buy more than (s)he can afford the 
biggest buy order in the number of shares (randomly determined if 
several) will be lowered until the FO is legal.  

7. If a player resign all his shares and ECUs will be returned to the 
bank without affecting the prices.  

8. The GM may allow new players to enter the game, for example to 
always have the prearranged number of players in the game. They will 
be given shares of each _remaining_ currency to the value of 1000 
ECUs. Fractions will be dropped and if possible ECUs will be given 
instead. E.g.: A new player enters the game when the prices are 0.95 
ECUs for 1 Pound, 1.10 ECUs for 1 Francs and 1.00 for the rest. This 
players will get 1052 Pounds (cost 999 ECUs), 909 Francs (cost 999 
ECUs), 1000 of each of the remaining currencies and 2 ECUs in "cash".  

9. After the Winter adjudications (either separate or togehter with 
the Fall orders depending on the House Rules) the GM will determine 
which power that have changed their numbers of supply centers since 
the previous adjudiaction. If a power has lost center(s) the GM will 
place a sell order under the title "World Events" for 1,000 shares 
(in that powers currency) for each center lost, and vice verse for 
gains and buy orders.  

10. All the amounts sold in each currency are added, giving the 
(total) demand. All the amounts bought in each currency are added, 
giving the (total) supply. If the demand or supply is less than 100, 
it is raised to 100.  

The new price (used for sales and buys in the next SE) is computed by
the following formula:
       newprice = oldprice * cube-root(demand/supply)

The price are rounded to two decimals, towards 1.00, i.e.: 1.323 is 
rounded down to 1.32 and 0.973 is rounded up to 0.98.  

A price may not fall below 0.01 as long as the power remains in the 
game.  

When a power runs out of supply-center, the currency of that power is
worthless and may not be traded with for the rest of the game, 
starting the round the Fall/Winter season the elimination takes 
place.  

11. If there are two or more players with the most amount of shares 
in one currency, the one of them who had the most amount in the 
previous round will be the Leader of that power. If this is still 
undecidable, the round before that will be determine among them, and 
so on. If still undecidable, the most recent Leader will remain 
Leader, or if the first round, random choice will be used.  

12. The first time a player fails to send in any transactions for the 
SE (N/T suffices to avoid this) the GM will sell 500 (or all if less 
reamins) shares of each currecny the player posses. The player will 
keep the ECUs from this sale. The player failing to enter any FO wont 
be chosen as the leader of any power, regardless of the amounts of 
shares held.  

If a players fails to make any transactions for the SE a two seasons 
in a row, the player will be regarded as resigning, so the GM wont 
sell any of the players shares, but instead treat him as a resigner.  

If a Leader of a power NMRs during the Diplomacy part, all the units 
will hold (unless the House Rules dictates any other NMR arrangement) 
and (s)he wont be chosen as the Leader for that power during the next 
round. The player may be chosen as Leader for another power though, 
if (s)he makes FOs during the same round as the NMR.  

13. The game ends after Fall/Winter 1910 (or the year some power 
reach 18+ centers). Draws are not allowed.  

Victory is decided by the number of Victory Points (VP) each player 
have. VPs are computed by the multiplying the number of supply 
centers held by a power by the number of shares held in that currency 
and divide this by 100. ECUs give no VPs.  

E.g.: England finishes a game with 11 centers, Russia with 18 centers  
and Italy with 7 centers. A player has 2523 Pounds, 1002 Rubles, 302 
Francs and 3201 Liras. The Francs are worthless (France has been 
eliminated) but the other currencies are computed into VPs in the 
following way: 
           2523*11 + 1002*18 + 3201*7
           --------------------------      =681.96
                      100

-----------------------------------------------------------------------

--
Per Westling              |
c/o Lindh, Drabantg 11    |  c85perwe@und.ida.liu.se
S-583 46 LINKOPING        |  In praise of Idleness -- Bertrand Russel
SWEDEN                    |
Fax: 105235, Home: 273054, Work: 104890  --  Add 013 or +4613 before.
Stuff regarding DPP may be sent to x90perwe@ida.liu.se instead.

Publisher comments:

I need scribes to type in articles.  I am also interested in people's
experiences with scanners.  I would like to know what brands of scanners 
and OCR software are the best.  I am also very interested in finding two 
players for a new 1914 game.

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