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Question on Defender Strength

Virtuoso

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May 27, 2019
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Hi folks

OK - so I don't know what's intuitively correct here. Assuming random dice, which of the following two troop layouts are easier to conquer?

--> 30 total troops

Layout A: 3 terts, 10 troops each
Layout B: 13 terts, with a assortment of 1, 2, and 3 troops each

To answer this question, I've tried comparing A and B at their extremes.
Layout A1: 1 tert, 30 troops on it
Layout B1: 30 terts, each holding 1 troop

Comparing A1 and B1, attacking B1 has the "advantage" that each attack will result in a maximal attack of 3 attackers vs 1 defender. So every attack has optimal odds to succeed. In A1, until and only if the tert has only 1 troop remaining, does it defend with anything other than 2 troops. So almost or sometimes all the attacks are of the less optimal 3v2 (assuming a big stack is attacking). As such, it would seem the B1 layout to be preferable for an attacker.

B1 however, requires the attacker to leave an "occupying" troop for each tert he conquers, so his stack gets reduced as he conquers. Put another way, if you did 32v30 for A1, there are great odds a conquer will occur, but if you did 32v(1x30) (so a stack of 32 attacking 30 terts each with one troop), I don't think anyone would count on a total victory. So in A1 vs B1, an equivalently-sized stack is more likely to defeat A1 compared to B1.

Does this give us any more information on which of A or B is a preferable target? I can't figure it out.

Thoughts?
 

sannheten

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Hi.

Layout A is much easier to conquer. The attacker has to leave 1 troop in every tert, and attacker B will need some 8 troops more to win than attacker A.
 

Virtuoso

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May 27, 2019
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After I wrote the post, it did seem A was easier than B. I guess the reason is the "advantage" of having 3v1 in B1 is not offset by the fact that the attacker in A1 loses an attacking troop for every winning roll of the dice. Extending the idea further, A is therefore easier to defeat than B.

attacker B will need some 8 troops more to win than attacker A.

No understand. Can you explain where you are getting this?

I suppose the next question is, how does one quantify the advantage of A over B? Most choices are seldom apples and apples like that. It'll be deciding whether to attack 41 troops over 12 terts *OR* 36 troops over 17 terts. Any formula to plug the numbers into?
 
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