The critical difference between spending BTC on a pizza and the Monty Hall problem is that you only receive additional information once you no longer have any option to change your mind.
If Monty Hall asked you if you wanted to change doors before opening one the problem would not be much of a problem.
Except the OP was (almost certainly) in possession of $20 USD in 2012. The opportunity cost of buying that Pizza with Bitcoin rather fiat totals ~$34k at the time of comment.
If Monty Hall asked you if you wanted to change doors before opening one the problem would not be much of a problem.