Question: The birthday problem - probability is actually higher in reality

The birthday problem is a statistical problem where a randomly chosen set of people will have the same birthday. 

The calculated probability is actually lower than reality.  Why?  Most people tend to "celebrate" on special days.  The weekend of Canada day, Valentines Day, Victoria day, etc ... and so you will find higher groupings of people with birthdays 9 months following these celebration days.   Hence probability is actually a little higher that 2 people will have the same birthday. 

Let's say we give a three week window period around each holiday.  So we have 8 separate days of holidays separated by more than 10 days.  (3 weeks)*(7 days)*(8 holidays) = 168 (subject to some argument) but almost half the number of days in a year.  So roughly speaking the birthday probability is almost twice as likely to occur. 

As an example if we take 20 people the calculated probablity of two people having the same birthday is 1- (364/365)*...(345/365) =44% when in reality it is more likely to be 1- (167/168)*...*(148/168) = 73%