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datatec

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Consider two breeding strategies of the fictional Furble. Dominator Furbles can fight for a breeding territory, and if they win, will be able to rear 10 offspring. An alternative is to share territory with another Furble which will allow each to rear 5 offspring. Sharers who attempt to share with dominators will be forced out of the territory, although they will be able to find a new territory. Assume sharers become extra cautious after encountering a dominator and so will always find another territory to share the next time around, but due to lost time will only be able to produce 3 offspring. Dominators are always able to force sharers out of the territory and rear 10 young. Dominators who meet dominators will win 50% of the time. When they lose, they are not able to reproduce that season due to sustained injuries. Individual Furbles cannot switch strategies.

With a total population of 2000 dominator and sharer Furbles, how many would you expect to be dominators?

The extraordinary difficulty of this problem lies in the number of combinations the the dominators and shares can make. One thing is clear, in order to solve this problem we need to maximize the amount of offspring the community can have. I can see a lot of complexity around the bayesian probability of this problem. Can anyone help me solve it?¿