I’d like to introduce you to Jack, a bridge playing friend of mine. Jack is substantially better than your average club bridge player and can play any number of different systems but he is exceptionally good at playing a hand, particularly in teams play where he often manages to play for that particular layout that lets him make his contract. As an example, look at this hand:
North South
S J932 T764
H AJT KQ9854
D A62 K
C Q64 C K3
Both sides bid to 4 hearts when this hand came up in a Venice Cup final in China, despite having AKQ of spades and A of clubs to lose. Both sides, however, had a reprieve when West led the jack of diamonds. I couldn’t decide what the best line of play was at this point so I asked Jack. Before reading on, however, consider what you would do now.
After a little thought Jack decided to draw trumps ending in the South hand and lead the small club towards the Queen. If West has the Ace and doesn’t play it you can discard the King of clubs on the Ace of diamonds. If West does play the Ace, there’s still the chance that the spades are blocked after one or two tricks and you can then discard a spade on the Ace of diamonds and another on the Queen of clubs.
The spades were indeed blocked, with East having the singleton King and this is exactly the play that Cecilia Rimstedt of Sweden and Wen Fei Wang of China found to make their contract!
Despite being up there with the best when playing a hand, however, Jack can’t play in any local club since there isn’t a section for computer programs! He has, however, won the World Computer Bridge Championship ten times since 2001.
Jack found the solution to the above problem by dealing 1000 pairs of E/W hands consistent with the actual bidding and play so far. He then tries playing each card from the hand currently on lead and performs a double dummy analysis on every deal to find the best card to play on average. His plays are based on the actual statistics for the hands he has generated rather than rules of play like ‘eight ever nine never’ for whether to take the finesse when missing a queen. For example, looking at what card to play after taking the Jack of diamonds with the King he finds that on average he will score about 93 points by leading a heart (he is non-vulnerable hence making 4H would score 420) but by leading a spade he would score -59 on average. He would also score -35 by leading the 3 of clubs or -54 by leading the King of clubs hence he leads a heart. He sees what West plays (I have to put in an actual full deal) and repeats the dealing of 1000 hand pairs since now he knows another card that must be in West’s hand and determines the best card to play from North’s hand and so on. Strictly, therefore, Jack doesn’t have a strategy as I presented the answer above. He merely determines the best card to play at any time based on everything he knows up to that point, bidding and play. I put in the actual E/W hands, Jack drew trumps in two rounds and led the small club to the queen. As West I played the Ace and then ran the simulation a second time when I played small. Having seen the resulting play I produced the strategy description,
Note that Jack has found a solution based on the best possible play by the opponents and hence he plays for the possibility that the spades are blocked. He cannot look for plays which might induce an opponent to make a mistake. This is beyond his capabilities.
Jack can be found at http://www.jackbridge.com/eindex.htm It's worth downloading the free demo to see Jack's capabilities. It's a Windows only program though so Mac users would have to use Boot Camp, Parallels or something similar.
This hand came to my attention when I saw it in ‘A New Bridge Magazine’ which is a free on-line publication. See https://www.newbridgemag.com/