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 -, 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:

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:

              ♠ -
              ♣ 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
               ♣ T83
       ♠  AJ872
    ♥ QT     
    ♦ K93    
    ♣ AJ4
  ♠ Q53
  ♥ AKJ2
  ♦ A85
  ♣ K65
               ♠ KT9
               ♣ 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 powered store on which I bring you the most important and valuable bridge products out there - bridge books, playing cards, bridge software, bridge apparel.

Sunday, October 3, 2010

The Squeeze Step

I keep thinking that a squeeze is a technical masterpiece that happens most often after at least one of the players made an imperfect action - be it in bidding, leading, defending or playing out a bridge hand. 

Observe the following bridge hand I played on BBO in August 2010 during a friendly "team match".
Sitting South I held, at IMPS, all vulnerable:

♣ AJ

West dealt and passed, North as well, and East opened 1♠. 
The textbook call is 3♠. In red, with a passed partner, you show a strong 1-suiter that requires little from partner in order to make 3NT. Should partner have a balanced collection of points including a spade stopper, he'd bid 3NT. Without the spade stopper you will probably make enough tricks in 4 or 5 diamonds. You can expect partner's hand to contain those 5-8 points that will make these contracts playable.

Having said and thought that, I doubled the 1opening. I fell in love with my controls and hoped to find a magical hand on the other side - something like Kxxx KQJx xx xxx when slam is certain and safe.

So it went : double, 2from East, 4from partner, pass. Passing 4is out of the question - partner can have the above hand when you DO make the diamond slam - so I bid my (now) normal 5 which ended it.

The 2 of spades was lead (3rd - 5th) and I got to play this:




The first trick went 2, J, K, 5.

Next came the 3 and it was time I did some thinking on this board.

It was clear that East had AKxxx in spades. The King showed the Ace as well, at least on this occasion - I knew it was next to impossible that East underlead the A on the bidding, risking to never make it.

It was also impossible that East underlead the K at trick 2 - this would have been  very clumsy play. Surely East deduced from the bidding that I had the missing top heart, diamond and club honors. So playing a heart from the King could not have been a winning move.

Hearts were probably 3-3 (after consulting the opponents and finding out that they give standard count). This left West with the most likely distributions of 3-3-4-3 or 3-3-3-4.

What were my chances against these hands? There were always two spade losers, and no entry to dummy to develop and cash the clubs. There seemed to be a heart loser as well. The way to succeed would be to cash diamonds and find East with the (almost certain) K and the (desired) Q. True, in this case East had a sub-minimal opening, but plausible in 3rd position.

If all my presumptions were correct - and so they were - the board was something like:

All Vul

              ♠ QJ6
              ♣ KT852
       ♠  T32 
    ♥ KT9 
    ♦ T865 
    ♣ Q43 
  ♠ AK874
  ♥ J53
  ♦ 32
  ♣ 976
              ♠ 95
              ♦ AKQJ974
              ♣ AJ

I rose with the A and I played all my diamonds but one. When the last diamond was played the situation became:

              ♠ Q
              ♣ KT8
    ♦ -    
    ♣ Q43 
              ♠ 5
              ♣ AJ

West is now cooked and can only make one more trick.

A spade discard enables me to cash clubs (West cannot cover or dummy wins the T) and exit a heart, taking the last trick with dummy's K.

A heart discard allows me to cash the Q, while a club discard (as happened at the table) simply lets me cash the A and the J. West covers with the stiff Q and I can finally cash that isolated T.

Since all squeezes have beautiful names, allow me to introduce you the Stepping Stone Squeeze. An opponent is under fire in two suits - clubs and hearts. Declarer "almost" has the needed tricks, but cannot develop and cash them (an extra club in South's hand would have solved the blocked suit problem).

The menaced opponent (West) must discard his only communication with his partner to protect these two menaces - otherwise declare duly cashes the established winners. However, declarer then simply unblocks the blocked suit (clubs) and endplays the defender with the other, natural winner (hearts).The endplayed hand now acts as a "Stepping Stone" over troubled waters, permitting declarer to gently hop to his inaccessible winner (T)

Notice that the squeeze would have worked in the same manner when West held the A. In the 5 card ending all discards would have been killers. This version was not possible on the bidding and lead.  

There is an amazing bridge book out there that shows expert bridge technique such as Stepping Stone Squeezes, and I dedicate this board to its authors for describing this position. It's "The Expert Game", by Terence Reese, revised edition by Barry Rigal. I dearly recommend it to everyone dedicated to learn bridge or improve their bridge to an expert level.

You can find it under the link below or by visiting Hef's Bridge Attic, an powered store on which I bring you the most important and valuable bridge products out there - bridge books, playing cards, bridge software, bridge apparel.

What is your opinion? Are squeezes beautiful, useful and common or should we instead try to focus on matters of solid, earthly technique - such as knowing what to bid with the above hand...I would love to discuss this with you, let's comment!.

Kind regards,