Quincunx by Foxymoron

Quincunx is not just a high-scoring word in Scrabble or similar word games. It is also another name for the Galton Board, which illustrates both the binomial distribution and the normal distribution and allows one to understand the distribution of cards in bridge as they "fall from the sky". The illustration below is from the science museum in Oregon:

Balls drop from the top of the machine and, at each peg that they hit, they randomly go right or left and settle at the bottom in a bell-shaped curve. This is similar (but not the same) as the dealer from above in bridge, who has to allocate each of the 26 missing cards to one of the two opponents. The difference is that there is a constraint that each person should get 13. I say "should" in that 12 or 14 sometimes occur at the Woodberry!

 "What are the chances of 7NT making on the hand below?" asked my partner this week. My first guess was much lower than it should have been:

We bid sensibly, uncontested, 1H-2NT (Jacoby)-3H (extras)-4NT (RKCB)-5S (2+Q)-5NT (please cue kings)-6C (king of clubs or both pointed kings)-7H. Only half the field bid the grand, so bidding 7NT would have been both wrong and greedy. There are slim chances of ♦JT9 or ♣QJ but essentially it needs the queen and jack of clubs to be with the diamond guard, or one opponent to be 4-5 in the minors or longer. Once you give one of the opponents 4 or more diamonds, the Galton pegs will tend to send the queen or jack of clubs to his partner more often than not, so the chances of success will be less than 25%, although the extra chance of any five clubs will make it close to that. 

Some software I have, called Bridge Analyser, quickly played 1000 hands with the NS cards and found that 7NT made 25.5% of the time, so the chances that the same player is 4-5 or longer in the minors compensates for the fact that the person with four or more diamonds is less likely to have both the queen and jack of clubs.