Locker Room - Where Probability Theory fails me, repeatedly!

I work out at a 24/7 fitness club where I have the time of my life. However, each time, without fail, I experience a certain situation that got me thinking numbers. Having failed to figure out the math, I write this for two reasons.

1. Others with similar experiences can empathize with me

2. Some one can check my math and make sure I am thinking correct

Each time I get to my (previously chosen) locker after my workout, there is someone currently using the locker either directly above (or below), or to the left (or right) of me. If I reach the locker and find no one there, I can be assured that within seconds, some one wants to access the lockers in the spots mentioned above. To make things more interesting, the above mentioned individual is either (I say this with absolutely no bias in my heart)

a. A senior citizen

b. A super buffed dude ( > 6 pack)

c. A person who shops at a big & tall and not because he is tall

This phenomenon has stood the test of time (2+ years) and is starting to bother me. Apart from the obvious reasons of, someone is invading my bubble, or changing clothes takes much longer, what bothers me is that the math just does not add up!

So I did some recon work and here are the numbers. The club has 12000 members and on any given day 6000 people show up to workout. There are 5 peak hours, 5-7 AM, 12-1 PM and 6-8 PM (my chosen window), during which 5000 workout. Thus on an average, during peak hours, 1000 people are in the club. Lets say 80% avail of the locker room, half of whom are men. This suggests that 400 lockers are in use during the peak hours. There are 420 lockers in the mens room which would suggest that one can always find an empty locker. This has been my experience so far. Assuming the average workout lasts for an hour, out of which 10 minutes is spent at the locker, the random nature of that occurence means that at a given time not all 400 people are in the locker room using their lockers. Once again, I can confirm this. Infact, each time I walk in there are about (0.166*400 = approx 66 people) in the locker room. The probability of two lockers side-by-side in use is even smaller. Furthermore, assuming 1 in 3 is a senior citizen, 1 in 12 is buffed and 1 in 4 is overweight, and these are independent events, the probabilities do not add up to unity.

Then why me?

So I asked my buddies if they have similar experiences and they laughed at me. One by the name of Pee-Ell actually thought I was bluffing, so I asked him to join me in the experience. First, we randomly chose a locker, put my stuff in and then went off to play squash. About an hour later, we finished playing, showered and headed back to my locker. No one was around and I thought the curse was finally broken. I unlocked the locker and barely opened it to hear a polite "excuse me" coming from behind me. It had happened again! Pee-Ell and me exchanged glances, held back our smiles and as the towel automatically fell off the (not so) slender waist of the polite 320 pounder, Pee-Ell said to me with a sigh, "Buddy, you have stacked up some extraordinary odds in your favor, you should buy the lottery"