How knowing the Birthday Paradox influences business risk


You’re at a party when a stranger approaches you and challenges you to solve a problem. 

How many people have to be at a party before there is a greater than 50% chance a pair of them share the same birthday?

What’s your guess?



This question is referred to as the ‘birthday problem’ or ‘birthday paradox’.

As humans we tend to dramatically overstate or understate the probable chances of an event occurring. 

This inability to accurately estimate the probability of an event occurring also extends predictably to business owners.

The answer to the Birthday Paradox is 23!

Yes that’s right. Just 23 people in the same room. I won’t go through the math but you can check wiki to see the numbers. There are 253 possible pairings of birthdays from the 23 people. 

Interestingly, a 99.9% chance of a shared birthday is reached at just 70 people.

The Birthday Paradox is not a paradox in the sense of leading to a logical contradiction, but it is referred to as a paradox because the mathematical truth contradicts your intuition. An intuitive guess by most people of the probability of how many birthday pairings are shared between 23 people would be much less than 50%.

So what can the Birthday Paradox teach us about business risk?

Next time you are assessing a start-up opportunity, a new division or a new product/service line – conduct the following analysis.

1.    Estimate the percentage chance of the opportunity succeeding. For example, an App might be a 5% chance, a new division might be 20% and a new product/service might be 50%.

2.    Estimate the amount of sales revenue you might generate if it were a success – not blue sky or bust – best guess on balance. This might be say $100,000.

3.    Multiply the estimated percentage chance of the opportunity succeeding by the estimated sales revenue generated. For example, 20% chance of new division succeeding X $100,000 sales revenue = $20,000

What to do with this calculation of $20,000?

Using this example, I suggest that you consider not spending more than $20,000 (make sure you include time and money) on your R&D, due-diligence or cost of production in relation to this business opportunity.

This is a baseline calculation of your risk threshold, expressed in dollars, for that project.

The idea is to try and overcome the notion of blindly spending time and money on an opportunity without assessing risk. In applying a guiding formula you at least objectively assess business risk without regard to the commercial question being ‘what is the comparative likelihood of future sales revenue exceeding time and money spent on the opportunity’.

I accept this calculation is far from perfect (being based on estimates) but it at least forces you to consider the components and the risk/return play on any opportunity beforehand.

The Birthday Paradox reminds us of our failings in stopping to assess risk objectively in comparing costs and returns before we naturally launch ourselves into action as entrepreneurs.

Darren Bourke

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Cheers, Darren K Bourke