How to Calculate a Three-Way Battle

*Special Thanks to Denton Troy and Ah for the explanation* <<Back to Home Page>>

Three-Way Battle Calculator - (3 empire meet, all are at war with one another)

Interesting notes: If all 3 fleets are equal, they will all 3 be destroyed. If not, then the largest will always survive, and the smallest will always be destroyed. If 2 empires are equal, if they are both larger than the third, Both will survive, if they are smaller, both will be destroyed. The smallest the second fleet can be and still survive is 87% of the largest fleet. The third fleet must be at least 44% -58% of the largest fleet for this to happen. (i.e if you have 8 - 7 and 4 ships, all the same br)

Email explanation sent to me by Ah - March 5, 2003

....each empire allocates it's attack strength in proportion to the strengths of the ships it is fighting against. So, in a three way of Emp A, B, and C the amount of damage A gives to B is:

(B's Strength / (B's Strength + C's Strength)) * A's strength

and to C is:

(C's Strength / (B's Strength + C's Strength)) * A's strength

In DT's example:

Emp A has 5 BR3s for 45 BP. Emp B has 5 BR3s for 45 BP. Emp C has 2 BR3s for 18 BP.

Emp A will give45/(45+18) * 45 = 32.14 points (or, 71.43% of 45 as DT states) to Emp B and 18/(48+18) * 45 = 12.857 points (or 28.57%) to Emp C.

Emp B will give45/(45+18) * 45 = 32.14 points (or, 71.43% of 45 as DT states) to Emp A and 18/(48+18) * 45 = 12.857 points (or 28.57%) to Emp C.

Emp C will give 14/(45+45) * 18 = 9 points to both A and B.

A and B both receive 41.14 points and have ships left, while C receives 25.714 points and is eliminated.

If, C had three BR3's A and B would both receive 41.625 damage, and still both have ships left.

In either case, if A was the defender and had a minefield, while B was set to nuke, the system would get nuked while the minefield survived. Cool, eh?

In your example:

A has 64BP (4 BR4s) B has 128BP (8 BR4s) C has 1BP (1 BR1)

A gives B (128/(128+1))*64 = 63.5 BP damage A gives C (1/(129+1))*64 = .5 BP damage B gives A (64/(64+1))*128 = 126.03 BP damage B gives C (1/(64+1))*128 = 1.97 BP damage C gives A (64/(64+128))*1 = .33 BP damage C gives B .67 BP damage A and C are wipes out and B survives, defending the system. B receives 64.17 BP damage. 2 of his ships are destroyed, while the rest are at a BR of (96-32.17)/96 * 4 = 2.659.

Whew! It gets *really* messy when more players are involved and some are at truce!

In a related case...wanna make sure your ally gets a front line base in a hotly contested area? Have him send a BR1 colony! Two allies (A and B) are over a planet and set to nuke it. A has 6 BR3s, B has 1 BR1 colony, and C has 6BR3s. Bs BR1 colony is guaranteed to survive. You do the math.

-Ah

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