The Birthday Bet


The prob that a second person has a different birthday from the first is 364 / 365
The prob that a third person is different from these two is 363 / 365

Below are calculated results from Excel - four values per row.

The values are :

Number of people
P(that the last person is different from those already present)
P(everyone's different) : product of all probs above
P(a match somewhere) : 1 - P(everyone's different)

With ten people there's a little above 11% chance of a match
So if the bet is taken 100 times I "expect" around 11 successes each worth £20.
£220 for £100 outlay is worth taking provided I can stand any losses that may occur in the chance of things.

The lowest prize value that is worth taking is £8.55
(1 / 0.116948 )