Note that probabilities smaller than 0.001 are shown as 0.0.

This was originally an applet, but security concerns caused me to remove the applet. I've updated the code and changed it to an application. You can download both the source and an executable jar file below.

When one side has a high probability of being able to destroy ** all
** of the missles of the other side, the situation is said to be unstable.
This is true for two reasons.

- The side with the "first strike capability" might be tempted to strike
first in a tense situation, knowing that they had a high probability of destroying
the forces of the other side.
- More subtle, though, is the thinking of the weaker side. Knowing that the stronger side will be tempted to strike first, and knowing that the weaker side's force will likely be destroyed if that happens, the weaker side has an even stronger incentive to strike first, knowing that they have no way to strike second. This leads to the instability.

Therefore it can be bad for the stronger side to be too strong in some situations. Being too strong can actually decrease your own security.

Henry Kissenger has admitted after the fact that it was probably a mistake to "MIRV" the US misssles during the cold war as it led to such an instability.

- Does increasing your number of missles tend to increase or decrease stability?
- Does putting more warheads on each missle tend to increase or decrease stability?
- Does putting more warheads on each missle, while decreasing the number of missles to keep the number of warheads constant tend to increase or decrease stability?
- Does increasing the accuracy of your warheads tend to increase or decrease stability?
- Historically, what was the situation at the end of the cold war. Determine the number of missles and warheads per missle of the US and Soviet forces. Was the situation stable or unstable? Suppose the same number of missles had only one warhead each?

If the probability that one warhead can kill its target is .90 then the probability that it will not is 1 - .90 = .10.

If we send 3 warheads against the same target and none interfere with the
others, then the probability that they all miss is

(.10 * .10 * .10) = .001.

Therefore the probability that the target will be destroyed is 1-.001 = .999.

If we have 4 such targets, then the probability that all four will be destroyed
if we send 3 warheads against each of them (requiring 12 warheads) is

(.999 * .999 * .999 * .999) = .996

However, if there were 1000 such targets, then the probability that we would
destroy them all with three warheads each would be

(.999 ^ 1000) = .368.

where ^ is the exponentiation operator.

The first strike capability is computed from the formula

( 1 - ( ( 1 - killProbability) ^ warheadsPerTarget) ) ^ numberOfTargets

This work was done jointly by **Detrich Fischer** of Pace
University who developed the model, and **Joseph Bergin** of Pace
University who programmed it. This version was built using Visual Café
for the Macintosh from Symantec. An earlier version was done in Hypercard.

Last Updated: July 29, 2015