Whenever a hawk meets a dove, the dove is killed. Whenever two hawks meet, they fight to death, and both are killed. And if two doves meet, nothing bad happens.

There are H hawks and D doves, and you are either a hawk or a dove. Assuming that meetings are random, what are your chances of survival?

(In reply to re(2): not much of a clue here by Matthijs)

The expectation of surviving doves for the 'even case' does not only depend on the ratio D/H but also on the total number of birds. For example the situation of 2 H + 8 D is different than the situation 4H + 16. Oskars solution includes this effect.

Results of additional simulations (M(sim) = averaged number surviving doves of 500000 simulations, M(Oskar) = D/(H+1)):

 H         D        M(Sim)     M(Oskar)

 2          8         2,666        2,666

 4         16        3,204        3,200

 6         24        3,424        3,429

 8         32        3,561        3,555

10        40        3,632        3,636

Looking at these results I am convinced that Oskars solution is really the good solution. The problem is solved.

Matthijs

 

Posted by Matthijs on 2004-09-20 07:29:37