# Domination Game

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### V4

#### wy_mentat

Thursday 13th September 2007, 8:27 GMT
still no v4 :-(
WY still retired

#### krang

Wednesday 19th September 2007, 20:50 GMT
I'm sorry MY... been very busy for the past few months.

I would like to say that I will get around to it soon, but I have no idea what I'm doing this weekend, let alone for the next month.

Although tiki is doing a good job at giving me the odd reminder.

Sunday 23rd September 2007, 23:07 GMT
...You know what, Mentat? I now think that some of the equations should be simplified and re-balanced. Especially your quote:
"...in real world attacker unit must be 3 (least 2) times bigger."

Victory probability of two equal armies is 1/3 chance of attack success with a new equation heavily inspired by your past calculations (not exact, but a close mirror).
(a^2) / (a^2 + d^2 + d^2) = attacker's chance out of 1

#### wy_mentat

Tuesday 25th September 2007, 15:57 GMT
I like it, that would make game more balanced and realistic. lets try that!

other thoughts: I considered a bit lower winning chance equation:
(a^2) / (a^2 + 4*d^2) = attacker's chance out of 1

examples:
(1) if a=d, then winnining chance would be 20% - I wouldn't consider to attack, unless situation is so urgent, that I would consider attack as my last chance.
(2) if a=2*d, then winning chance would be 50% - This is a fair 50-50 chance to win. But I wouldn't risk with that, because I, as attacker can choose an attacking place, time and better winning rates, when attacking with more units.
(3) if a=3*d, then winning chance would be 69,23%
- so in this equation I would choose a simple rule form myself: "... attacker unit must be 3 (least 2) times bigger."

So this equation would be realistic, but I think that for dominationgame, your equation is better. Because my last equation suggestion might change game too slow; and that wouldn't be fun at all.

#### j lorenz

Tuesday 25th September 2007, 19:59 GMT
...Heh, you're right, with that ratio I'd imagine nobody would even go to war! :-P

With the equation as-is (2*d^4) the defenders are already twice as likely to win if evenly matched. Making it a landslide may indeed be more realistic but take away from the benefits of violence.

I, too, am interested in testing the new combat eq. out.
cos( arctan( 4 / a ) )^4 = conquered probability out of 1

#### wy_mentat

Wednesday 26th September 2007, 7:29 GMT
btw, Tiki's offered equation
[(a^2) / (a^2 + d^2 + d^2) = attacker's chance out of 1],
winning chances are these:

if 3*a=d, then winning chance would be 5,26%
if 2*a=d, then winning chance would be 11,11%
if a=d, then winning chance would be 33,33%
if a=2*d, then winning chance would be 66,67%
if a=3*d, then winning chance would be 81,82%

#### wy_mentat

Wednesday 26th September 2007, 7:42 GMT
and if U want 50-50 chance with Tiki's equation, then attacking units must be about 1,4142135624 times bigger:

if a=1,4142135624*d, then winning chance would be 50,00%

;-)