Back in my previous existence as an artillery officer, I participated in the war for a little while.  Our main job---my Marines and I---was to provide counter-fire support for units in and around the city of Fallujah, Iraq.  Basically, whenever our guys started taking rocket and/or mortar fire, radar would track the source of those rounds and send us their point of origin as a target.  Then we would shoot at it.  Simple.  Kind of.

By the time I got to Fallujah, all the dumb bad guys had been selected out of the gene pool; the ones who were left knew that what they were doing was extremely risky, and they took steps to minimize that risk.  They tried their best to make every opportunity count, and our goal was to make it just as costly as possible for them to shoot at us.  It was a deadly serious game-theoretical problem for both sides.  A game measured in seconds.

The typical rocket/mortar team would consist of only a few bad guys who would move into position, aim, fire, and withdraw as quickly as possible.  But, because an attack was both physically dangerous and materially costly, they went to great lengths to make the most of each strike.  If a team escaped our retaliatory volleys, they would often return for a second, hasty attack after our counter-fires had ended before retreating in earnest.  Since we were already pointing at their position, this second strike had to be much quicker and less deliberate, but the bad guys were still essentially getting two-for-one opportunities to try and kill us.  From our standpoint, this was not an ideal situation.

Part of our difficulty was bureaucratic.  When we first took over the battle space, our parent regiment handed down an order saying that all artillery counter-fire missions were to consist of eight rounds.  All of them.  So, in order to roughly double their chances of success, all the bad guys had to do was count to eight.  Immediately after the last round impacted, the rocket/mortar team could move back into place, with relative peace of mind, for a second attack.

Now as I said before, these teams were only a few guys deep, with very little in the way of physical protection, so the particular decision to mandate eight rounds was somewhat arbitrary.  In fact, for a target of that size and disposition, anywhere between five and eight rounds would be both effective and proportionally appropriate.  So our available pure strategies in this game would be of the form Shoot x rounds, where x is in the set {5, 6, 7, 8}.  Which x should we choose?

Any of them, with equal probability.  Assuming the bad guys liked their shoot-withdraw-shoot strategy (which, empirically, they did), it had just become a lot more costly.  If we ended up shooting eight rounds, then they could do what they'd always done and be exposed to the same level of risk as before.  But now, if we shot fewer than eight rounds, they'd have to hang around longer in the withdrawal position, waiting to see whether the last round of a mission really was the last round.  And if there's one thing that bad guys in the middle of doing something bad universally hate, it's hanging out in the open and waiting.  Lots of bad things can happen.  Simply by mixing it up, we immediately made them more hesitant and vulnerable 75% of the time.  And thus, less likely to get a second attack in.

The bad guys, being smart, certainly figured out what we were doing pretty quickly, but the beauty of the random mixed strategy is that it doesn't matter.  We could have held a meeting to explain to every bad guy in Fallujah what we were planning to do, and it wouldn't have helped them a bit.  They still couldn't have deduced how many rounds I would tell my Marines to fire, because I couldn't have deduced how many rounds I would tell my Marines to fire.  You can't out-think randomness.

It's interesting to think of the incredible premium that war puts on quality decisions, and how I found myself in a situation where I was able to make better decisions by sharing some of the responsibility with a mindless, spinning wheel.

Special thanks to Capt Greg Ostrin for the photo and associated nostalgia.