The Math of Cold Feet

The game Dinosaur Dodger – or rather, the paradox that inspired it, contains some important lessons for life.

The paradox involves an explorer who is trying to get home. He needs to take the second turnoff, or he will be eaten by dinosaurs. Unfortunately, when he gets to a turnoff, he can’t recall which one he’s at. His best strategy is to flip a coin – this gives him a 25% chance of getting home, and this is the best he can do.

However, it also means that when he gets to a turnoff, it’s more likely that he’s at the first one.


What's the best strategy to get home?
What's the best strategy to get home?

After all, he always reaches the first one, every trip – but he only has a 50% chance of reaching the second one. So when he’s at a turnoff, it’s twice as likely to be the first. If he takes this information into account, he will not turn off. But if he never turns off, he never gets home! He would have been better off, on reaching the intersection, sticking to his original plan.

Is that a bit hard to follow? Then imagine Neo, from The Matrix. He, too, is offered a choice – take the red pill, and take up his destiny as the Chosen One, or take the blue pill and forget he ever had the choice. If he really is the Chosen One, and he takes the red pill, he joins the fight against the machines and wins a glorious victory for humanity. If he takes the blue pill, however, presumably his “friends” will try again later, offering him the same choice again. However, if he’s just some ordinary Joe, he’d better take the blue pill. His friends will move on to the next candidate, and he’ll never be any the wiser. Taking the red pill would lead quickly to an untimely demise at the hands of Agent Smith. Should he take the pill?

Logically, the chance of him being the “One” is small, and he should take the blue pill with very high probability. However, faced with the choice, he might reason

“If I am not the One, I only get offered the pill once. If I am, I’ll be offered the choice many many times. It’s therefore more likely that I am the Chosen One, just based on the fact that I have been given the choice”

with that kind of logic, it sounds sensible to take the red pill.


What is Neo's best strategy? Should he change it half way? Image Copyright Warner Bros.
What is Neo's best strategy? Should he change it half way? Image Copyright Warner Bros.

In each of these situations, some character figures out their best strategy from an outsider’s perspective, but then changes their mind when they’re in the thick of things. The logical fallacy they commit on the road is simple. They assume they’re using a birds-eye-view strategy – calculate probabilities based on that – and promptly abandon their original strategy so that all their assumptions are wrong. For if the dinosaur dodger decides to go straight all the time instead of flipping a coin, he can no longer claim he’s more likely to be at the first turn-off. If Neo thinks

“The sensible strategy is for me take the blue pill. If the Chosen One does this, he gets faced with this choice many many more times than an ordinary person. I’m faced with the choice. Therefore, I’m likely to be the Chosen One, so I’ll take the red pill”

then he undermines his own logic. Taking the red pill, he ensures that he only faces the choice once, whether Chosen or not.

The sensible thing to do is simply to resist the temptation to use “on the road” thinking. When dinosaur dodgers or Neos are faced with their critical choices, they don’t actually have any new information. There’s no reason to revise their strategy. In fact, revising it is stupid.

Well, that’s all very well for Neo, but what about us? Well, we face this kind of dilemma all the time – so often we have a name for it : “cold feet”.

For example, we decide to apply for a certain job, but when the offer comes, we get cold feet and turn it down. Why did we change our mind? Has the job really changed?

Or, we decide to express our feelings to the lady or man of our dreams. However, when the conversation starts, we get cold feet and keep silent. Why did we change our mind? Are they really less attractive than before?

It’s not because the job or love interest has changed. We have no new information. Instead, we are like Neo – when the crunch comes, we change our carefully thought-out strategy and do something stupid. No doubt we persuade ourselves we are being sensible. “She might laugh at me,” we say, or “I’d miss my colleagues” or other things we already knew. So we have two lines of reasoning going on. The one we applied to formulate our initial plan, and the one we apply on the run.

I’d like to suggest that if two lines of reasoning – based on the same set of facts – give radically different conclusions, one of them is wrong. My guess is that the more rational thinking was done before the emotional turmoil of Decision Day, and that following ourĀ  cold feet is a less-than-optimal way to live.

This phenomenon cuts the other way, too, making us do things we wish we didn’t do. In the evening, you decide to quit smoking. In the morning, you buy a pack of smokes. On the weekend, you decide to spend more time with the family. Then on Monday evening, you work late. At the start of term, you decide to study enough to keep up with the lectures. The next weekend, you go to a party instead. In all these cases, we make a different decision at the point of decision than the one we earlier decided was best. Like the dinosaur dodger, we go straight and become dinosaur chow, instead of going against our instincts and choosing what we formerly figured was best.

A wise man once lamented “Although I desire to do what’s right, I don’t do it. I don’t do the good I want to do, instead I do the evil I don’t want to do…. It is a war with the standards which my mind sets and tries to take me captive to sin’s standards which still exist throughout my body. What a miserable person I am!”

The lesson of the dinosaur dodger (or Neo’s pills) is not that we should never change our minds – if new information comes to light, we should certainly take this into account and formulate a new plan. For example, if we learn that the girl of our dreams is actually already happily married with 7 kids, or that the new job requires us to be posted to Hargeisa, it may be wise to reconsider our original strategy.

Dinosaur dodger doesn’t teach “Be pigheaded at all times”, rather “Don’t forget, in the rain, what you learned in the sunshine.”

So, next time you’re faced with a temptation to change your well-thought-out plans, remind yourself of the dinosaur dodger’s coin or Neo’s blue pill, and stick to your guns!