Colonel Blotto
Rules
Colonel Blotto commandeers an army of 100 troops, and is about to fight for 10 different castles. The opposition also has 100 troops and is fighting for the same castles. At each castle, the larger army wins. If both armies send the same number of troops to a given castle, they split it.
Your job is to apportion Blotto's troops in a manner that on average wins as many castles as possible. Your entry consists of an ordered 10-tuple of non-negative integers whose sum is 100.
In a game of CB, each pair of armies plays against each other one-on-one. Your score is the average number of castles you win across all of your battles. So if 50 people are playing, your strategy will do battle against the other 49, one at a time.
Here is a sample game, featuring 3 players:
Player |
#1 |
#2 |
#3 |
#4 |
#5 |
#6 |
#7 |
#8 |
#9 |
#10 |
|---|---|---|---|---|---|---|---|---|---|---|
Groucho |
0 |
5 |
5 |
5 |
10 |
10 |
15 |
15 |
15 |
20 |
Gummo |
11 |
11 |
11 |
11 |
11 |
11 |
11 |
11 |
11 |
1 |
Harpo |
24 |
21 |
13 |
11 |
10 |
3 |
8 |
2 |
1 |
7 |
Groucho wins 9 castles (4 against Gummo, 5 against Harpo) and splits 1 (against Harpo), so his average score is 9.5/2 = 4.75. Gummo's average is 5.75 and Harpo's is 3.50, so Gummo wins!
However, later on Zeppo shows up and plays:
| #1 | #2 | #3 | #4 | #5 | #6 | #7 | #8 | #9 | #10 |
|---|---|---|---|---|---|---|---|---|---|
12 |
12 |
12 |
12 |
2 |
2 |
12 |
12 |
12 |
12 |
All of a sudden, Gummo drops to last place! Zeppo wins (wise guy, eh?), and Groucho and Harpo stay in 2nd and 3rd place.