OT: Game Theory/Statistics

[spoon]

The type of game geo is talking about is called a "blotto" game. Here's a site that talks a bit about it and lists out the results of a game played with a bunch of people...

Colonel Blotto

Space Empires can feel a bit like a blotto game when you are defending multiple wormholes against multiple aggressors.

[Yimboli]

does that mean i can do blotto emergency build and get 150 tokens instead of 100?

[douglas]

Only if you're willing to accept 25 tokens in the rematch.

[geoschmo]

That's the one Spoon. Thank you.

[AngleWyrm]

After reading this, I did a Mathematica notebook on the game. A set of strategies S={ {...}, {...} ...} where each is a list of ten integers, describing a player's troop allotment across ten territories. For a score function, I counted the number of territories that a player has more troops in than the other guy. Comparing each strategy against the set (107 in my set), the result looks like this:



Number of times a player won each amount of territories with their strategy. Some strategies won more territory than others. The total number of territories won, by strategy index number:

[AngleWyrm]

Edit: Much longer analysis notebook

[narf poit chez BOOM]

So, uh, best strategy?

[AngleWyrm]

erm...uh...hehe...uhh...Fire!Fire!...hehe...

There are two levels of victory to this game, the battles and the war. It looks a lot like elections...

If we count the number of games won, Then then the top four strategies won 50, 49, 47 and 46 games out of 107. The next winners were farther behind, with scores of 42 and below.

Winner(50 games won): {7, 18, 18, 2, 9, 3, 18, 5, 2, 18}
Won 35 games by taking 6 territories, 14 by taking 7, and 1 by taking 8.
Some strong pieces, some secondary, and some weak. Nice unit mix.

2nd place(49 games won): {17, 3, 17, 3, 17, 3, 17, 3, 17, 3}
Won 31 games with a 6-territory lead, 17 with 7, and 1 with 8.
Two piece battler, strong units with escourt.

3rd place(47 games won): {2, 10, 1, 18, 19, 3, 20, 2, 8, 17}
Won 39 games by a score of 6 to 4, and 8 games 7 to 3.
Similar to winner, but also invested in a couple expensive super units.

Honorable mention(46 games won): {17, 0, 17, 0, 17, 0, 16, 0, 17, 16}
Won 46 games 6 to 4.
Tank spammer; got what he wanted, but lack of unit mix cost a few games.

Also, some people chose numbers > 20;
Here is the distribution of numbers chosen (unit strengths):



This distribution suggests that unit strengths of 19, 9 and 4 would make a good unit mix against that group of opponants. [EDIT]Yep: {19,19,19,19,4,4,4,4,4,4} did very well. Four battlecruisers with heavy fighters as escourt. It pays to know thy enemy.