Colonel Blotto game

In an earlier post, we invited you to coordinate presidential campaign within a simple web game. We have also mentioned that the framework of the web game relates to game theory and the Colonel Blotto game. Let us turn our attention for the next few posts to this classic game. As we will see it contains rich strategic landscape, and has numerous practical applications in various fields, including political campaigning (as previously discussed), warfare (as suggested by its original context), marketing, and even sports.

Here, in this post, will start by discussing the original formulation of the game.

The game

Colonel Blotto game involves two warlords who compete to become the next ruler of a country. At the end of the game warlord controlling more castles will be announced to be the next ruler.

Interactive app below allows you to become a warlord commanding 25 troops. Your rival (controlled by a computer) also has an army of 25 troops. Both of you attempt to control as many of the 5 castles built in the country as you can. Controlling 3 castles would be sufficient to ensure your victory, but in some cases 2 will also be just fine.

At the start of the game each warlord secretly allocates their troops to each of the castles. After all troops are allocated, their allocations are compared against each other. Warlord who assigns more troops to a castle gains dominion over it. If both warlords assign same number of troops, the castle remains neutral.

After checking the status of all castles, simply count how many castle each warlord controls. Whoever controls more is the next ruler.

So the question is, how will you allocate your troops?

Interactive app

This app allows you to define your own (fixed) strategy and check how well it fares against a random strategy used by the computer. You may play just a single round, or play lots of consecutive rounds until you pause or reset. Random strategy used by computer is reasonably good, but it is possible to find a way to beat it. Can you do that?

The app below shows you the outcome of the last war. Your castles are colored blue, castles controlled by computer are red, while neutral castles are pale gray. Brief summary of the last round (war) is given along with your overall record in won-drawn-lost format. What you want is for your "won" be greater than your "lost" (my own best strategy gives about 42 percent win rate, against 32 percent win rate by the computer).

To help you in formulating your strategy, last troop assignment used by the computer (CPU) is shown. You might want to compare the numbers in the columns to see why (how) you have won or lost certain castles.