[Freeciv-Dev] Re: Bombers/Fighters no longer obsolete (PR#1628)

[Gregory Berkolaiko <Gregory.Berkolaiko@xxxxxxxxxxxx>]

On Wed, 26 Jun 2002, Ross W. Wetmore wrote:

> Of course this implies that your attack power formula actually 
> means something rather than being one of many heuristic formulae
> none of which describes reality in any accurate way :-).

I would like to point out that the formula used by Raahul does describe 
reality in a pretty accurate way.  And I can give you a solid 
justification why it is so.  As a matter of fact, I'll give you few hints 
and can fill in the rest.  Since excercise is good for you ;)

We have an attacker A with stats (S_A, HP_A, FP_A) and 
a defender D (S_D, HP_D, FP_D).  We want to decide which one is stronger.  
And of course by "stronger" we mean "which one has larger probability to 
win a fight when A attacks D".

Lets assume FP_A = FP_D = 1.  Otherwise we can substitute 
        HP_A <- HP_A / FP_D
etc.

1. You can compute the win_chance and try to analyse it.  But that is too 
tough :(

2. Alternatively you can say, lets count how many successful hits will A
score, _on_average_, before it dies.  If this _average_ number of hits
will be greater that HP_D, then the defender will die, on _average_,
before the attacker does.  Which implies that the attacker will succeed in
more fights than the defender.

3. So we are running a random process giving us 0s and 1s.  0 means A won 
the round, 1 means D won the round.  The question we have to answer is how 
many (on avergae) zeros will come up before we see HP_A ones. 

4. Probability of having 0 is 
        S_A / (S_A + S_D),
probability of getting 1 is
        S_D / (S_A + S_D).
The rounds are independent.

5. Now, instead of inventing 20 + 20 formulae, you, Ross, should get 
yourself a "probability for kids and gamblers" book and calculate the 
answer. :)
 
> Now my formula of the moment includes defence and in this world 
> one would never want regular fighters ...
>   power formula = defence * hitpoints + attack * firepower

A "power" concept is vague, but "attack power" is quite real.

> 
> And if you don't like this formula, I can dream up 20 others with
> some sort of feeble justification for their efficacy, but basically
> all showing that your choice gives the wrong answer. Tomorrow I can
> join your side and produce 20 in support :-).
> 
> Cheers,
> RossW
> =====