Shooting the Breeze - making the numbers work

Written by Douglas McLoughlan

Tags: Operations

As you can probably guess I have a penchant for Maths and its application to the work place and indeed as a philosophy for guiding what happens in life... From a mathematical perspective Operations is a complex beast with endless variants, opportunities and threats – but it is apparent that the central tenet is that it is our people who make the numbers work not the other way round. It reminds me of a startling revelation in the 40s where Maths suddenly became the tool of choice for winning wars, using game theory generals could test their tactics and established which would be the best strategy to win the battle. A simple but good example is the story of the ‘truel’.

A truel is similar to a duel, except there are 3 participants rather than 2. So one morning three men ‘The Bullet’ , ‘Moneybags’  and  ‘The Muppet’ decided to resolve a conflict by truelling with pistols until only one of them survives. The Muppet is the worst shot hitting the target on 1 occasion out of 3 whilst Moneybags is better at 2 out of 3 but The Bullet is best shot hitting his target every time. To make the truel fairer The Muppet is allowed to shot first, followed by Moneybags (if still alive) followed by The Bullet (if still alive) and round again until one of them is left alive. So the question is where should The Muppet aim first?

Based on intuition you can quickly come to a conclusion but as you would expect that won’t necessarily be the right one. It is this desire not to take the path of least resistance, not to consider the simplest or obvious answer as the one which gets our job done that we apply day in day out at RESPONSE as we strive to improve our clients’ customers’ lot. So what to do with the first shot in the truel?

The options open to The Muppet are varied. If he successfully shoots Moneybags then the next shot will be from the sharpshooter The Bullet and so the odds are The Muppet is a dead man.

A better option might be to take The Bullet out however if successful Moneybags has the next shot and as he is pretty good but there might be a chance he will miss and so The Muppet may get a chance to fire back and win the truel.

So the second strategy would appear to give The Muppet the best chance to survive the truel. However there is a third and better option - The Muppet deliberate misses by shooting into the air. Moneybags has the next shot and will aim at The Bullet because he is the more dangerous opponent. If The Bullet survives he will shoot at Moneybags because he is the most dangerous opponent. So by aiming in the air The Muppet gets The Bullet to eliminate Moneybags.

This is The Muppet’s best strategy either way Moneybags or The Bullet will die and The Muppet will aim at whoever survives. So The Muppet has manipulated the situation so that instead of having the first shot in a truel he has the first shot in a duel….and that is game theory. And finally…

For those who really need to know the answer from my last blog:

I ate some pie… ...and it was good

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