" why the t-rex died out and the chicken survived..."

Again , you dont' answer Irish Farmers' question, which is , in my opinion, rather smart.

Where does the spirit of sacrifice come from ?

"i dont have to run any simulation at all. simple math will do the trick"

The only way to study group behaviours is using Montecarlo simulations
Even complex Math can not take into account the complex interactions among thousand entities
You assign a set of attributes to each entity and let the computer run

However also using common sense you can arrive at the same conclusions

A predator attacks a group of preys
He needs to kill just one prey per day to survive

a) The preys defend only the members of their family
b) The preys do not care about their relatives
c) A minority defend every member of the group
d) All the preys defend every member of the group

The "Human like" Behaviour a) can be a disaster for the comunity
The predator can kill more than one prey per day just to defend himself

The "Chicken like" Behaviour b) is acceptable for the comunity
The predator kill only one member per day

Behaviour c) can be the best solution
Just a small group of preys risk their life, togheter they can kill the predator

Behaviour d ) can be also dangerous for the comunity if all the members are willing to risk their life

As a matter of fact b) and c) are the most common behaviours in nature

The explanation is evolution