Colonel Blotto

From: crb11@cus.cam.ac.uk (Colin Bell)

Date: Mon, 22 Apr 1996 00:00:00 +0000

Colonel Blotto is at war for a third time: the foe is the usual General
Calamity. The two countries they control the armies of are in a
mountainous region and the only routes between the two are ten
passes. In the first war it was thought that whoever controlled the
most passes between the two would have enough of an edge to win, and
so it turned out. However, times have changed, and some of the passes
are now of more strategic importance than others: according to
Blotto's best military advisors, they have Military Values of
10,9,8,...,1, and whichever side controls the passes of greatest
military value will undoubtably win the war.

Each side has 100 companies of soldiers: technology is evenly balanced so
that if one side has even just one more company in a given pass, it will be
able to control it: of course if the same number of companies are sent from
either side, then neither side will have control.

Your mission, should you choose to accept it, is to advise Blotto on how
to distribute his troops...

An example:

Pass: 10 9  8  7  6  5  4  3  2  1
B:    30 15 10 8  5  5  7  5  5  5
C:    25 25 25 7  6  5  4  3  0  0
Wins: B  C  C  B  C  -  B  B  B  B

B controls 10+7+4+3+2+1=27
C controls 9+8+6=23
So B wins.

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I am running two versions of this: in one you just give one distribution
for Blotto to use, and in the other you submit a set of distributions
which Blotto will choose between at random (in the proportions you give).

More details, and the results from an earlier version are available either at
http://www.pmms.cam.ac.uk/~crb11/blotto.html

or by mailing blotto@chiark.chu.cam.ac.uk

To enter, you will need an entry form, also available from the latter address.

The closing date is 10pm BST (GMT+1) on Monday 20th May. I'll post at least
a summary of results and some comments here.

--
Colin Bell, crb11@cam.ac.uk. Dept of Pure Mathematics, University of Cambridge
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I need to go and have a good time with some foam rubber,
assisted by the Queen as soon as possible.