May 6, 2021
May 6, 2021

The Billion Dollar Question: Assessing the theory

Would you rather have $1 million guaranteed or a 50% chance of $1 billion?

Where is the risk in this decision?

What would you do?

The Billion Dollar Question: Assessing the theory

Imagine that you are appearing on a TV game show. The presenter puts two boxes in front of you and you have to pick one. In one box is a $1 billion prize and in the other, nothing. Would you pick one of the boxes for a 50% chance of getting $1 billion or walk away to get a guaranteed $1 million? What would you do?

Analysing the decision

For most people, a sum of $1 million would be a significant amount and the cast-iron guarantee that you could walk away from this situation with that cash in your pocket would be very tempting. However, would you be a fool or a reckless gambler if you considered taking the chance on the $1 billion?

Many people would consider it a terrible decision to take $1,000 instead of risking $1 million.

After all, $1 million may be a life-changing amount for you but $1 billion could be a life-changing amount for you, your wider community, and much more. Imagine the good (or evil) that could be done with a fortune that big!

Assuming that most people would take the $1 million guaranteed, what if you were presented with a similar dilemma: Instead of the $1 million, you are now guaranteed $1,000 and one of the boxes contains $1 million. Would you still opt for the $1000 instead of taking a risk on the $1 million?

What’s interesting here, is that most people would take the risk of giving up the $1,000 for a chance at winning the $1 million, yet would do the total opposite in the first example. The ratios are the same, with one amount being worth 1,000x the other, but the psychological effect of losing $1,000 is less painful than losing the $1 million offered in the first example.

What is the psychology involved?

Why is this the case? Theoretically, the two boxes have an expected value of $500 million each ($1 billion divided by two), so there could be a rational reason for taking a chance on one of the two boxes. One could argue that you are no worse off for going home with nothing than you were when you began. Others would consider that you have lost $1 million by your decision.

Kahneman and Tversky’s prospect theory suggests that humans are risk-averse when it comes to gains and we prefer solutions that have a lower expected utility (i.e. less of a financial reward) but with a higher certainty of success. However, if the situation was slightly different - if we are faced with a risky choice that could lead to a loss - we actively seek risk if there is a potential to avoid our losses.

Most people will frame their answer as to how much difference this sum of money will make to their life. $1,000 might be harder to turn into $1 million but $1 million could feasibly be turned into $10 million (or even more) through smart investing and good fortune.

Speaking as a London native, $1 million sounds like a lot (and it certainly is) but it might not be life-changing to the point of securing a financial future. After all, you may be lucky to get a 2-bedroom apartment for $1 million in Central London and the cautionary tales of million-dollar lottery winners who have burned through their winnings with a lavish lifestyle also suggest that this money can only enhance your life to a certain point. $1 billion would be in another category altogether and for some, well worth the risk.

In relation to betting, this is perhaps why people will cash in on an accumulator with only one leg left to run. It might also explain why many bettors dislike betting on short-odds selections as the risk of loss is greater than the risk of reward.

So the question is, with all this in mind: Would you take the $1 million or the chance at $1 billion?

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