Imagine you’ve been offered the chance to bet on the outcome of a coin toss.
If you call it correctly, you win €100. If you don’t, you lose €10.
Do you take the wager?
For most people, it seems like a no-brainer.
The reward is 10 times larger than the downside, so it makes perfect sense to pursue it.
Although you may not do it consciously, there’s term for the calculation we make in our heads for something like this…
Expected value.
The expected value for our hypotethical coin flip is calculated as follows:
Potential Reward x Percentage Chance of Winning = €100 x 50% = €50
Since our potential loss is €10 x 50% = €5, that’s a 10x difference.
Logically, even a small difference (e.g. 5-10%) should be enough to keep us engaged with the game. Over time, we stand to win more than we lose – we always come out ahead if we stick with it.
Howevever, consider the following scenarios. How do you feel about the following wagers?
- The reward is €100, but your downside is €50 per flip.
- The reward is €10,000, but your downside is €5,000 per flip.
- The reward is €1,000,000, but your downside is €200,000 per flip.
In the first example, the reward is the same… but the cost of being wrong is far larger. We might not be motivated by a 2x return – maybe we need more to take action in the first place. Particularly when the reward is “only” €100. But if we look at things logically, we still see the merits in doubling our money.
In the second example, our reward is much bigger. For most people, €10,000 is a meaningful sum. And the return is the same: we’ll 2x our capital over time. But here, the cost of being wrong is significantly larger as well. How many times could we afford to be wrong – at €5,000 per call – before we need to walk away?
In the third example, the reward is life-changing. But the cost of being wrong is enough to stop most people ever risking it.
The lesson:
Logic can only take us so far.
We might be able see on paper what the mathemathics tells us is the best course of action. But numbers are just one part of the satory.
If we neglect to consider the full picture – our personal tendencies, our tolerance for risk – we’ll always come up short when analysing our behaviour. Or the behaviour of others.
Rather than calling it illogical, it might be worth expanding our definition of the word.