Saturday, October 30, 2010

Little Deuce Coupe - a challenging card problem

The renowned American bridge player, analyst and teacher Richard Pavlicek has a very interesting challenge running on his website - www.rpbridge.net, which I dearly recommend as a knowledge source for any bridge player (it has helped me develop aspects of my game countless times).

In this post I will present his challenge "Little Deuce Coupe" and my solution. I thank Mr. Pavlicek for his contest and look forward to seeing the best answer to it - be it mine (hopefully :) ) or some other contestant's.

The problem is: construct a complete bridge deal (all 4 hands) in which, ON A GIVEN LEGAL DEFENCE (not necessarily what we call "good" or "practical" defence), SOUTH CAN MAKE 3NT and ALL FOUR DEUCES WIN A TRICK, when the following conditions are also met:

- No revokes, leads out of hand etc. Other than that, you can force all the plays of all four hands to be exactly what you want them to be.
- West has EXACTLY five spades
- No other hand has a suit over four cards

There are probably multiple solutions, therefore Mr. Pavlicek adds that "the fewer high card points (HCP) for North-South, the better. Correct solvers will be ranked by the total N-S HCP, fewest being best."

Until Monday 01.11.2010 you can enter YOUR solution here: http://rpbridge.net/8f17.htm

My solution and reasoning:

- ALL FOUR DEUCES must win a trick. But a deuce can only win a trick when three hands do not possess that suit anymore. So the first deuce that wins a trick is the one that started out in a "lengthy" suit - a four or five card one given the problem's description.
- I chose to attribute the 2 of spades to West, with 4 other spades. I also assume it's the first 2 cashed.
- I then constructed a 4 card ending in which two deuces win a trick for NS. The lead is in North:


              ♠ -
              ♥ -
              ♦ 42
              ♣ T3
       ♠  A
    ♥ - 
    ♦ -    
    ♣ AJ4
  ♠ -
  ♥ K
  ♦ -
  ♣ K65
              ♠ -
              ♥ -
              ♦ -
              ♣ Q972

When North plays the ♦2, both E and W throw high clubs, while S discards the ♣7. Then the ♣T is overtaken with the ♣Q while EW play the ♣6 and the ♣J, the ♣9 wins trick 12 and the ♣2 is won at trick 13.

- Notice that both E and W have the VERY important "spare cards" - the ♠A and the ♥K. Both cards can be kept in when discarding on the diamond, and allow the ♣2 to win the last trick.
- These "spare cards" were protecting the corresponding deuces (otherwise these deuces could not have won a trick). I already assumed the ♠2 to have been with W, and I could now place the ♥2 with E.
- Therefore E had the ♥ length - strictly 4 cards. To promote and cash a deuce when holding 4 cards, one must cash 4 tricks, which would mean at least 5 tricks for EW (the ♠2 plus 4 hearts), incorrect for "3NT". But if everyone else has time to discard hearts, three rounds of hearts can suffice.
- Hearts must then be discarded on spades (the lengthy suit). When cashed, the ♠2 must "squeeze" the same suit of NS, the one protected by E and his deuce, namely hearts. This would be enough so that only 3 rounds of hearts are required to promote the ♥2.
- So 3 tricks in hearts and the dreaded  ♠2 = 4 tricks. EW cannot have any other winners. So spades must bring 3 winners to NS.
- The idea came to me that it would be nice for NS to play hearts voluntarily in order to promote the ♥2. This would make communication simpler (I reasoned this by trial and error mostly).
- For the rest, I kept subtracting honor cards from NS.  

Here is the integrated deal and line of play that came out of it. Please excuse EW for their poor, but legal, defence :).

The full deal:


               ♠ 64
               ♥ 6543
               ♦ T642
               ♣ T83
       ♠  AJ872
    ♥ QT     
    ♦ K93    
    ♣ AJ4
  ♠ Q53
  ♥ AKJ2
  ♦ A85
  ♣ K65
               ♠ KT9
               ♥ 987
               ♦ QJ7
               ♣ Q972

The card play (* = the trick was won by this card; the next trick will be initiated by the same hand)

Trick       W      N      E       S 
  1         ♠J     ♠6    ♠Q    ♠K*         
  2         ♠8    ♠4    ♠5     ♠T*      
  3         ♠7    ♥6    ♠3     ♠9*      
  4         ♥Q*  ♥5    ♥J     ♥9            
  5         ♠2*   ♥4    ♦A     ♥8      
  6         ♥T     ♥3   ♥A*    ♥7     
  7         ♦K     ♣8   ♥2*    ♦Q   
  8         ♦9     ♦6    ♦8      ♦J*  
  9         ♦3     ♦T*  ♦5      ♦7  
  10       ♣A    ♦2*  ♣K      ♣7  
  11       ♣J     ♣T   ♣6      ♣Q* 
  12       ♣4     ♣3   ♣5     ♣9* 
  13       ♠A     ♦4    ♥K     ♣2* 

All four deuces win a trick - at trick 5,7,10,13. EW only gets tricks 4,5,6,7.

Notice that NS needs only 8 points for this to happen. How's that for an inspired card play? :)

I hope my solution proves to be among the best. I spent almost 3 hours dealing with various other paths, but none came out as good as this one.

I dare you to go explore this problem yourself, and to leave your comments on my analysis.

I also recommend you these books to develop your card reading and positioning sense - whether you use them for humor or actual technique development.

Use the links below or explore Hef's Bridge Attic, an Amazon.com powered store on which I bring you the most important and valuable bridge products out there - bridge books, playing cards, bridge software, bridge apparel.

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