Resolution of the Game of Blotto Problems Discussion

The answer requires an explanation of the solution as well as the actual numeric answer. Thank you for any help.

One game (technically, class of games) we like to play is called Blotto.
Here are 10 castles, numbered 1,2,3,…, 10, and worth 1, 2, 3, …, 10 points respectively. You
have 100 soldiers, which you can allocate between the castles however you wish. Your
opponent also (independently) does the same. The number of soldiers on each castle is then
compared, and for each castle, whoever has the most soldiers on that castle wins its points.
Additionally, you lose 0.2 points for each “extra” soldier that you have, in excess of your
opponent’s army size, at each castle that you win. You still need to deploy all 100 soldiers.
In the case of a tie, no one gets points for that castle.
See example below:
C2
C3
C4
C5
C6
C7
C8
C9
Castle C1
Alice 10
Carol
20
C10
10
10
10
10
10
10
10
10
10
0
10
5
10
5
10
20
0
20
In this match, Alice wins castles 2, 4, 6, 9 and takes a 6-point penalty, for a total of 15 points,
and Carol wins castles 1, 8, 10 and takes a 6-point penalty, for a total of 13 points (no one
wins castles 3,5,7).
We’re going to play a tournament. You get one entry and your final score is the average
(mean) of your scores against all the other entries from applicants.
What’s your entry? How did you go about coming up with it? An entry should be
submitted as a list of 10 non-negative integers, adding up to 100, where the nth element
is the number of soldiers being sent to castle n.