I was intrigued following my review of Skyfall when commenter Enkidum said that the implausibilties in this film pale “in comparison to the final poker hand in Casino Royale, which has never occurred in history and likely never would, even if people kept playing poker until the heat death of the universe.”
For those who cannot recall that scene, here it is. In this form of poker, five cards are placed face up and are common to all players, while each player has two cards that are unknown to everyone else. The winner is the one who can make the best combination out of the seven cards.
As other commenters pointed out, any hand in poker (or bridge) is as likely as any other, so why do we think of some hands as being ‘rarer’ than others and are surprised when they occur? The answer is of course because we rank order all the possible hands and assign different values to each based on a purely arbitrary system, and choose just a few (those with easily recognizable patterns) to have high value and many to have low value. So, rather than rare hands being high value we make high value hands be rare. But because the creators of the game have chosen easily recognizable patterns to be the high value ones, we are fooled into thinking that such patterns are rarer than other, less obvious, patterns.
In order to increase the dramatic effect in the film, they made the first player have a high value hand in order to bid high, and he reveals that he has a flush, which is pretty high value and thus quite rare, and also tightly restricts the number of hands that the others must have in order to beat it. The filmmakers wanted the next player to have a hand (full house) that is higher than the first but not as high as the subsequent player, which severely restricts the number of possibilities. The third player’s hand had to be such as to beat the second player but not Bond as the last player, squeezing the range of options even more. They gave him an aces high full house and Bond wins with a straight flush.
So while any one of those hands is rare but not unbelievably so, Enkidum is right that that particular sequence of successively higher value hands is extremely rare because each one has to fit into a very narrow spectrum of hands. I haven’t the heart to calculate the odds of that particular sequence happening to see if dealing it would take longer than the heat death of the universe but I would guess that that is not a bad comparison.