Colonel Blotto's Game
Author
The game is simple: Each player has 100 troops to split between 10 territories. Player with the most troops in a territory wins it, and the player with the most territories wins the game.
Is there an ideal strategy? I've created a study, available as a Mathematica Notebook or somewhat less legible but more accessible pdf.
One finding is that it seems the winners allocate less than 20 men to each territory.
(ps: a free Mathematica notebook reader can be downloaded here)
[Edited by - AngleWyrm on December 15, 2008 10:04:28 PM]
do the players take turns putting 1 unit in a territory at a time? or are the unable to see the other players actions and pick all of their actions before seeing what the other play does?
Author
The troop allocation phase was accomplished all at once, deciding on troop deployment in territories with unknown defenses, and without feedback of the outcomes of previous engagements.
It could be entertaining to have the territories fought over one by one. Players would begin to get a feel for enemy reserves toward the end, and could also watch for patterns in deployment.
[Edited by - AngleWyrm on December 16, 2008 5:07:31 PM]
It could be entertaining to have the territories fought over one by one. Players would begin to get a feel for enemy reserves toward the end, and could also watch for patterns in deployment.
[Edited by - AngleWyrm on December 16, 2008 5:07:31 PM]
This is very interesting! But I dont think there can be a "best" approach to it.
If I was to play a game like this, I would do one of these:
a) Distribute all of my troops evenly over all of the territories.
b) Distribute all of my troops over 6 territories (since winning 6 would win me the game).
c) Or some sort of combo of the two above strategies. I would make sure I have at least 1 troop in each territory, so that way I counter if they leave some territories vacant, and then place the rest in 6 territories.
Definately is interesting!
If I was to play a game like this, I would do one of these:
a) Distribute all of my troops evenly over all of the territories.
b) Distribute all of my troops over 6 territories (since winning 6 would win me the game).
c) Or some sort of combo of the two above strategies. I would make sure I have at least 1 troop in each territory, so that way I counter if they leave some territories vacant, and then place the rest in 6 territories.
Definately is interesting!
Author
The study includes one hundred strategies by people competing for a nominal prize ($10). Many people chose strength-17 territories, alternating with strength-0 or 1 territories.
Another thing that showed up in the top ten was that the winners often led with a strong group and trailed with a weak group, alternating through the set.
I produced an effective counter strategy {4, 19, 4, 19, 4, 19, 4, 19, 4, 4} that resulted in a new high score. However it relies on knowing what the enemy did in advance.
The next stage was to compete against completely random opponants. During that phase, the top ten winners did better than the previous human players. (The best humans won about half their games, the best AI won about 3/4 of their games). But the reason for that is that the worst computer-generated losers chose terribly, allocating most of their troops to one or two territories.
The next phase will be to try competing against randomly generated opponants that only produce strategies likely to win 6+ territories. I'm gonna try capping the allocation at 20/territory, on the assumption that 20 is an artifact of the need to win more than 5 territories with 100 troops.
Edit: The random AI vs AI test, where all AI chooses 20 or less troops/territory showed two additional strategies beyond choosing a max of twenty/territory. The winners chose between 5-7 territories loaded with 11 or more troops -- mostly six and seven territories. Additionally, the winners seem to have played at least one 2 or less, usually two or three.
Might be possible to do even better if another reproducible pattern is consistently found in the winners.
[Edited by - AngleWyrm on December 17, 2008 9:28:30 PM]
Another thing that showed up in the top ten was that the winners often led with a strong group and trailed with a weak group, alternating through the set.
I produced an effective counter strategy {4, 19, 4, 19, 4, 19, 4, 19, 4, 4} that resulted in a new high score. However it relies on knowing what the enemy did in advance.
The next stage was to compete against completely random opponants. During that phase, the top ten winners did better than the previous human players. (The best humans won about half their games, the best AI won about 3/4 of their games). But the reason for that is that the worst computer-generated losers chose terribly, allocating most of their troops to one or two territories.
The next phase will be to try competing against randomly generated opponants that only produce strategies likely to win 6+ territories. I'm gonna try capping the allocation at 20/territory, on the assumption that 20 is an artifact of the need to win more than 5 territories with 100 troops.
Edit: The random AI vs AI test, where all AI chooses 20 or less troops/territory showed two additional strategies beyond choosing a max of twenty/territory. The winners chose between 5-7 territories loaded with 11 or more troops -- mostly six and seven territories. Additionally, the winners seem to have played at least one 2 or less, usually two or three.
Might be possible to do even better if another reproducible pattern is consistently found in the winners.
[Edited by - AngleWyrm on December 17, 2008 9:28:30 PM]
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