Consider two opposing armies of knights armed only with swords. The sizes of these armies are 500 and 300 knights.

When locked in combat with an enemy each knight has even odds of winning or losing. Knights, being chivalrous, prefer single combat and will not double up on their enemies. The extra knights in the larger army will wait until there is a free enemy to fight.

[Essentially the killing power of the larger army is proportional to the size of the smaller army.]

When the dust settles the smaller army is eliminated. How many knights (are expected to) remain in the larger army?

Generalize for two armies of size A and B where A>B.

I just tried a computer method

The most probable outcome seems to be that 599 jousts occur before the big knights win. This means that 299 died in the larger army, or, in other words, 201 knights are left in the larger army.

(Later calculation gave me P(202)=P(201))

However, most probable is not the same thing as expected :

Edited on August 25, 2005, 10:15 am

Posted by Dimmeh on 2005-08-23 08:20:44