(Based on a conversation with Nageeb Ali)

When you are selecting seats on a flight and you have an open row should you take the middle seat or the aisle?  Even if you prefer the aisle seat you are tempted to take the middle seat as a strategic move.  People who check in after you will try to find a seat with nobody next to them and if you take the middle seat they will choose a different row.  The risk however is that if the flight is full you are still going to have someone sitting next to you and you will be stuck in the middle seat.

Let’s analyze a simple case to see the tradeoffs.  Suppose that when you are checking in there are two empty rows and the rest of the plane is full.  Let’s see what happens when you take the middle seat.  The next guy who comes is going to pick a seat in the other row.  Your worst fear is that he takes the middle seat just like you did.  Then the next guy who comes along is going to sit next to one of you and the odds are 50-50 its going to be you.  Had you chosen the aisle seat the next guy would take the window seat in your row.

If instead the guy right after you takes a window seat in the other row then your strategy just might pay off.  Because the third guy will also go to the other row, in the aisle seat.  If nobody else checks in you have won the jackpot.  A whole row to yourself.

But this is pretty much the only case in which middle outperforms aisle.  And even in this case the advantage is not so large.  In the same scenario, had you taken the aisle seat, the third guy would be indifferent between the two rows and you’d still have a 50-50 chance of a row to yourself.  Even when he takes your row he’s going to take the window seat and you would still have an empty seat next to you.

Worse, as long as one more person comes you are going to regret taking the middle seat.  Because the other row has only a middle seat left.  The fourth guy to come is going to prefer the window or aisle seat in your row.  Had you been sitting in the aisle seat the first four passengers would go aisle, aisle, window, window and you would be safe.