A thought on probability

I was at my in-laws yesterday and my father-in-law and I were watching some football. As the games were winding down, some channel surfing landed us on the movie, "Once Upon a Crime."

There's a scene where Marilyn Schwary (Cybill Shepherd) is playing roulette. She places her bet on 13 - and wins - on her first spin. On her next spin, she again places her entire bet (including her winnings from the previous spin) on 13.

My father-in-law asked, rhetorically, "what are the chances it will be 13 twice in a row?" I knew what he meant, but it got me thinking... The chances 13 would come up twice in a row is exactly the same as any other two numbers coming in sequence. The probability of that specific sequence occurring may be small, but low-probability events occur frequently.

What lowers the probability in this case is specification. To restate my father-in-law's question including the specification he probably intended, "what are the chances she will bet on 13 - and win - twice in a row?" That dramatically lowers the probability of the event occurring. In fact, if she were to bet on 13 and win 3-4 times in a row, everyone would start to be incredibly suspicious the game was rigged.

She wouldn't even have to bet on 13 each time. The specific sequence of numbers does not matter, since each sequence of 3-4 numbers has equal probability of occurring. What matters is that she correctly chooses the sequence of numbers ex ante.