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This question is about the card game bridge :

  • How many points can N/S have in a par-zero deal ? (Only consider the high card points)

    In a par-zero deal, no player can make any contract assuming perfect play and full information (all hands are visible).

    In most par-zero deals , N/S have at most 23 high card points.

    What is the limit ?

            S 973
            H K5
            D QJ864
            C KQJ
  S 2                 S AQJ854 
  H T87               H A42
  D T53               D A97
  C 987543            C 6
            S KT6
            H QJ963
            D K2
            C AT2

is an example with 25 HCP for N/S. I found this deal by slightly changing a random deal from pavliceks deal finder which was close to par-zero.

                  S A75
                  H KJ2
                  D AJ63
                  C 762
   S 986                         S JT2
   H 86                          H AQT9
   D T854                        D 972
   C AQ53                        C T98
                  S KQ43
                  H 7543
                  D KQ
                  C KJ4

is an example with 27 HCP-points for N/S

Even with 28 points, there is an example :

                      S 2
                      H QJ73
                      D KQJ
                      C J8743
   S AQT98                          S 73
   H T9542                          H 8
   D -                              D T98765
   C 652                            C AQT9
                      S KJ654
                      H AK6
                      D A432
                      C K

And finally, I found an example with 29 HCP for N/S

                    QJT9
                    942
                    QJ
                    QJ64
      87654                    32
      A3                       T865
      AKT98                    3
      T                        987532
                    AK
                    KQJ7
                    76542
                    AK
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  • 1
    This question tests the limits of what is on-topic for Board and Card Games. While ostensibly about the game of Contract Bridge, it is really about the creation of a puzzle, that by happenstance is about the card game of Contract Bridge. Possibly it is a better fit for Code Golf, as any solution would likely be an exhaustive search of eligible deals. I am interested to see what the community's consensus is about topicality, but am not myself interested in this degree of m-m.
    – Forget I was ever here
    Apr 15, 2015 at 3:20
  • 1
    @pieter my definition of on-topic questions is : 1) They have a clear reference. 2) They are not opinion-based. This question can clearly be answered, it does not matter if it is easy. So, I do not see in which way this question could be off-topic.
    – Peter
    Apr 15, 2015 at 9:13
  • 1
    It seems unlikely that you'll every be able to prove a maximal value of the distribution of points. That's because "points" is not a natural value compared to the question at hand.
    – Thomas Andrews
    Apr 15, 2015 at 21:25
  • 3
    @Peter I would recommend instead of updating your question, you post an answer to your question. Leave the original question as it is, as the original question is solid and good. Your edit appears to invalidate the one answer, which was a reasonable answer to the original question.
    – John
    Jun 10, 2015 at 17:12
  • 1
    I'm voting to close this question as off-topic because the OP keeps changing the question to invalidate answers.
    – Forget I was ever here
    Jun 13, 2015 at 17:31

1 Answer 1

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Here's a deal that my double dummy solver says is parzero with North/South holding 24 points.

          S: KT9
          H: AK942
          D: QT97
          C: A
 S: 72             S: AQ864
 H: J87            H: T653
 D: K84            D: AJ6
 C: JT842          C: 7
          S: J53
          H: Q
          D: 532
          C: KQ9653

I haven't analyzed this deal to see how the sides defeat the contracts.

Note that North/South have their share of the tens, and all of the nines, as well. So this is a good 24.

For north/south declaring. the obvious problem is that north and south's hands have few entries.

I've currently got my dealer search for 25-point examples.

Deal is the dealer than I'm using. I wrote it. It has a double dummy solver built-in. This is the script I'm using for Deal:

main { 
   # Require north/south have exactly 25 points and no fit
   reject unless {[hcp south]+[hcp north]==25}
   foreach suit {spades hearts diamonds clubs} {
       reject if {[$suit south]+[$suit north]>7}
   }

   foreach denom {notrump spades hearts diamonds clubs} {
      reject if {[deal::tricks south $denom]>6}
      reject if {[deal::tricks north $denom]>6}
      reject if {[deal::tricks east $denom]>6}
      reject if {[deal::tricks west $denom]>6}
   }
   accept
}
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  • 1
    Wow, that deal shows the values of aces. The side with 25 points has no major blockages and the spade ace onside.
    – Thomas Andrews
    Apr 17, 2015 at 11:30
  • I have a dealer which can compute double dummy data. It's right there on my web site. I'll post the code that I used with Deal up in my answer.
    – Thomas Andrews
    Apr 17, 2015 at 12:25
  • You can begin your search with 30 HCP (see edit)
    – Peter
    Jun 10, 2015 at 17:09

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