The big day is only 5 days away now. I had great hopes of writing a cool optimizer that would seat guests based on their affinity but unfortunately laziness and an over-estimation of my programming skills got in the way. However I have been thinking about the birthday paradox recently and since there will be over 100 people in the room next Friday I thought it was a nice anecdote.

The Birthday paradox arises from the chances of two or more people in a group having the same birthday. Given that there are 365 days (ignoring leap years for simplicitys sake) in a year you would think that the chances that any 2 people might have the same birthday would be extremely low;

however this is not the case.

Wikipedia has a great page on it so I won't reproduce their excellent explanation but it turns out that at 23 people the odds tip over 50%, which is better than a coin toss. In terms of our day we are due to have 106 guests.

The formula is:

1 - (Permutation(365,n)/(365^n)) Where n is the number of people involved.

so 106 guests works out at 99.99999574936430000% or as close to 100% as makes no difference.

We also have tables of 8,10 & 11 which work out respectively at 7.43%, 9.46% & 14.11% respectively. I wonder would it be worth sampling each table to see how many times this actually comes through. with 10 tables we should probably see this at least once!

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