The point is NOT ‘’to go down swinging’’

It’s to not go down at all!

In many situations, there are multiple ways to win.

The first one is the most obvious, to simply win.

But one that’s often forgotten is the opposite, to simply not lose.

In pure mathematics, you learn this early when proving theorems.

Most mathematicians are agnostic as to how you go about proving things (to a degree, there was some debate around the computer proof of the four color theorem). (“ Four color theorem”, 2019) *1

And some theorems are incredibly hard or perhaps impossible to attack one way and much more doable the opposite way.

There’s an excellent saying in the FBI hostage negotiation scene:

‘’Never be so sure of what you want that you wouldn’t take something better.’’

- Chris Voss

(Voss, 2019) *2

An example would be to instead of proving a theorem is true, assuming it is false then creating a logical chain which leads to a contradiction showing that your initial assumption has to be wrong and therefore the theorem is true.

Proof by contradiction.

Another example would be to instead of trying to use a proof by contradiction, you show that something is true in the most base case and assume it’s true in some random case, then you show that it’s true in the first case after that random one, which shows it’s true for all cases.

Proof by induction.

Okay, so there’s more than one way to solve a problem.

Today, we’ll take a journey through some basic game theory.

Before I tie this to something as complex as business, let’s imagine a simple game theoretic situation like a dual:

You and your opponent stand back to back then take 20 steps forward.

After that, you turn around and can decide to shoot once or step forward.

Then your opponent gets to choose between the same two choices, step or shoot.

You have to weigh two probabilities:

The probability of you killing the other person and the probability of the other person killing you.

If you shoot first and miss, the other person can keep stepping forward and make sure to kill you.

If you wait too long, the other person might shoot first and kill you.

Who should shoot first?

The person who’s the better shot? The person who’s most rational? The person who’s willing to bear the most risk? The person who has the highest probability to kill the other person?

What do you think? Don’t cheat.. think about it.

Well, turns out the correct answer is, it depends.

You see, there are 2 ways to win this game.

You can win if you shoot and you kill him.

Or, you can win if he shoots and he misses. Then the two of you keep stepping forward until you’re face to face and you shoot.

So you have to compare the probability that you shoot and kill him this turn

Let’s call that Pa(d), where P = probability, a = player a and d = distance at this step.

with the probability that he shoots and misses.

Let’s call that 1 — Pb(d+1), where P = probability, b = player b and d+1 = distance at the next step.)

If the probability that he shoots and kills you is 0.7, then the probability that he misses is 1–0.7=0.3

So we simple re-wrote ‘missing’ as 1 minus the probability of shooting and killing.

So when should you shoot?

Well if the probability that you shoot and kill him at this distance is bigger or equal compared to the probability that he misses on the next step at that distance.

If the probability that you will kill him is 0.6 and the probability that he will miss the next turn is 0.1 you should shoot because otherwise you’ll likely get killed.

If the probability that you will kill him is 0.2 and the probability that he will miss the next turn is 0.6 you should step because the chances of you winning are higher by him shooting and missing than by you killing him at this distance.

So in game theoretic terms, this means:

Shoot if Pa(d) >= 1- Pb(d+1),

and doing a little algebraic manipulation gets you the following equation:

If (Pa(d) + Pb(d+1) >= 1), then shoot.

Let’s call that exact moment Q.

This means that it would be irrational for anyone to shoot at any distance before Q, the combined probabilities of you shooting and killing him and him shooting and killing you at the next step are bigger or equal to 1.

As I said in the beginning, the point isn’t to go down swinging, it’s not to go down at all.

Your goal is to win the game, not to shoot and lose.

Which brings us back to our original question of who should shoot first?

The answer, the first person to reach Q at Q.

No one should shoot before Q, they should keep stepping forward until the first person who reaches Q shoots.

We’re biased towards action in our culture but sometimes the best course of action is to do nothing and let your opponent act.

Should you really fight hard to have the so-called ‘’first mover advantage’’? (Youngling, 2019) *3

Or should you weigh the probability that you capture the market and win with the probability that your opponent tries to capture the market and fails?

(Assuming that you’re the only two companies and you win if you capture the market first and you win if your opponent tries to but fails to capture it.)

If the probability that you capture the market is near zero (say 0.1) and the probability that your opponent tries and fails is high (say 0.8) does it make more sense to fight for market share or simply wait?

We’re all familiar with the saying: ‘’Don’t just stand there, do something!’’

But occasionally a more helpful heuristic would be: ‘’Don’t just do something, stand there!’’

References

  1. Four color theorem. (2019). Retrieved from https://en.wikipedia.org/wiki/Four_color_theorem
  2. Voss, C. (2019). The Key to Dealing with A Negotiator Who Lies. Retrieved from https://blog.blackswanltd.com/the-edge/2-most-powerful-moves-to-counteract-a-negotiator-who-lies
  3. Youngling, R. (2019). Resisting The Siren’s Song. Retrieved from https://www.younglingfeynman.com/essays/sirensong

*Special thanks to professor Ben Polak. If you’d like to learn more about decision theory and game theory, you can study his lectures here.

Originally published at https://www.younglingfeynman.com on June 5, 2019.

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