If you were to have a gun battle with two other people, would you want to be the most skilled? As it turns out, this is a problem of strategy and probability. And here are the rules:

1 – Each of the three participants get to fire in turn as determined by flipping a coin at the beginning of the match.
2 – Each participant gets to choose who they shoot.
3 – Each participant gets only one shot per turn.

Now here is the tricky part. Let’s assume that the participants have the following skill levels:

Person A hits the target 100% of the time.
Person B hits the target 75% of the time.
Person C hits the target 25% of the time.

Assuming all three choose their best strategy for survival, who has the best chance of being the last person standing?

I won’t take up your time going through the math. The answer is that Person C has the best chance of survival, roughly twice the chance of survival of either of the other two. The math logic that leads to that conclusion is a bit tangled, but the underlying idea is that the person most likely not to be shot at is Person C.

So, what about my first question. Which person would you like to be at the start? The issue is now more than just a math problem. It’s your life. But wait! There’s more! Let’s make the situation even worse. Let’s allow you to choose your skill level in the following way. We will provide three guns, one that fires 100% of the time, one that fires 75% of the time, and one that fires 50% of the time. You then draw straws to see who gets to choose the first gun, who gets to chose the second gun, and who gets the gun that is left. BUT WAIT! THERE’S MORE! Your mother is watching you make your selection. What was a dry problem of mathematics is now a suspenseful novel!

NOTE: This type of duel is indeed called a truel. Various forms and rules have been studied. If you need to look into the matter, I would suggest that you start with the entry about it in Wikipedia.com. For myself, I would rather worry about what my mother would have told me to do.

A statistician once said to me, “Being a statistician means never having to say you’re sure!”  I don’t know if he is the author of that sentence, but it sure sums up the subject.

I, like many of you, never liked the statistics course I took in college.  It’s like chemistry, you never understand it until you actually have to work with it.

Over the years, I have run into a few simple instances where statistical variation was quite important.  So, leaving out words like “normal”, “standard deviation”, “mean”, “mode”, etc., here’s the situation.

You have designed and built something that has to perform within a given tolerance.  However, you can’t sell it to a customer without some reassurance that it meets that standard.  So, you test it.  And right away, you’re in trouble.  The means of measuring the unit’s performance also lacks accuracy.  And, if you were a typical person, you ignore that nagging doubt and proceed.

But wait!  How if you had to show that the temperature drop through a cooling unit was no less than 2 degrees F, and the means of measuring that is only accurate to plus or minus one and one half degrees F?

For now, let’s ignore the nitpicking details and take the simple minded view.

OK, so it looks like this.  If a particular cooler actually only cools the fluid by one half of a degree F, and your measuring instrument reads high by one and one half degrees F, you would think that the cooler was working just fine, and you would sell it to a customer — a customer who would soon be back pounding on your door wanting a full refund plus damages.

Or, it could be that the cooler cools the fluid by more than necessary, say two and one half degrees F, but your test instrument says that it only cooled the fluid one degree F.  So, you throw the cooler into the dumpster, even though it is perfectly good.

Both of these possibilities are going to cost you money, or something much worse.  On the other hand, your temperature measuring device was probably cheap, if that makes you feel better.

Although there are a number of technical issues left out of the story, things like this do happen in practice.  I have been involved in at least two cases like this.  Sad to say, I lost the argument both times.

As someone once said, “We never have the time to do it right, but we always have the time to do it over.”

Well, hold onto your hat, there are more stories on statistics in the queue.  Next time, The Three Way Duel.  (I can’t call it a Truel, can I?)