Calculating the chance of success for a given SimulGear attack of X units against Y defenders is not a straightforward bit of arithmetic. Say that the chances of an attacker killing a defender are 60% (fairly common). It might seem that if the attacker wants to defeat 6 units, she should attack with 10. But this is not the case! In fact, an attack of 10 units against 6 defenders at 60% has only a 63% chance of success. If the attacker wants a 99% chance of success, she would need to attack with at least 17 units.

The reason for this is that there are many unique scenarios in which the attacker wins and many unique scenarios in which the attacker loses, which makes a straight calculation of probabilities rather complex if you were to attempt to do so with brute force. To calculate SimulGear odds quickly and easily, you need to do math involving cumulative binomial probabilities. Fortunately, there are some handy calculators out there that you can use to make your life easier.

To illustrate, let's use this simple Binomial Calculator.

Again, assume that the attacker has X units, the defender Y units, and the probability of an attacker killing a defender is Z. To calculate the odds of conquering a territory given X, Y, and Z, enter these values into the Binomial Calculator as follows:

1. Enter Z as “Probability of success on a single trial”
2. Enter X as “Number of trials”
3. Enter Y as “Number of successes”

After you hit Calculate, the field “Cumulative probability: P(X > x)” will give you the probability of taking the territory given X attackers, Y defenders, and kill percentage of Z.