I've performed an exhausting survey of the probabilities involved in combat in Alpha Centauri. Most important is the chance the attacker will win a single portion of combat, an exchange, where a point of damage is assigned to either the attacker or defender. Prior to these tests, I had believed that the odds the attacker would win an exchange were simply the ratio of the attacker's strength to the defender's strength (after all modifiers). From this, and the number of hit points each unit has, the odds of winning the combat can easily be calculated, and the mean damage to the expected victor is also at hand. My tests have shown that the odds of winning an exchange are definitely not a simple ratio of strengths.

Here is a plot of exchanges won / total exchanges against attacker's strength / (attacker's strength + defender's strength). The error bounds are each two sample standard deviations away from the sample mean.

Here is a plot of exchanges won / total exchanges against attacker's strength / (attacker's strength + defender's strength). The error bounds are each two sample standard deviations away from the sample mean.

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