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.

VIRKs by Foxymoron

Bridge conventions are only of use if you are both playing the same one.  It is good to have agreements in slam bidding and a surprisingly large percentage of the field in this week's EBED SIMs missed grand here:

The auction at the table of the Woodberry winners, Mike Bull and John Bernard, was 1D-1S-4C*-4NT-5H-5NT*-6D-7S-All Pass. 4C was a splinter and 4NT RKCB. Mike and John do not show voids in response to RKCB, so 5H was 2 without the queen. 6D showed the king of diamonds, but not the king of hearts. A good method is that 5NT asks for specific kings, and then you bid the one you have or the one you don't have when you have two! It was easy now to bid 7S.

How does one show a void in response to RKCB? Some play that 5NT is two key cards and a void. Others play that it is an odd number of key cards  and a void ... One can see wheels coming off now and the apple cart being upset, and indeed only a quarter of the field bid the grand. Both of these metaphors predate bridge and are from the earliest days of transportation.

A better method, when one side has splintered, is that a raise of the splinter is a VIRK, asking partner to include a void in that suit as a key card, but to respond normally with a singleton. Here, South just bids normally as 5C by North would have been the VIRK, and South knows North does not care if the splinter is a void or not.

The Tyger by Foxymoron

A hand last night at the Woodberry reminded me of a poem by Blake. The following illustration is in the British Museum:

Tyger Tyger, burning bright,
In the forests of the night;

What immortal hand or eye,

Could frame thy fearful symmetry?

It was the symmetry of the two plausible plays on the following hand that caught my eye:

Our auction was (Pass)-1D-(2C)-2D-(3C)-3D-All Pass. West led two top clubs and switched to a spade. Now there are two symmetrical lines as you can only afford one trump loser as you can never avoid a heart loser. The first is to win in dummy, and lead a low diamond to the jack. The second is to win in South and lead the jack of diamonds. The former works when East has a doubleton honour, the latter when West has a doubleton honour. Both are just under 24%, but only one of these is given in the Dictionary of Suit Combinations. My future title Complete Card Combinations remedies that.

My partner unluckily chose the latter line, getting below average. It is the right line at matchpoints as it only goes one off when East has D KQ9x. On this occasion, running the jack was the winning line, which makes the contract whether or not West covers.