Interesting Deal For Mathematicians

Pages: Page 5 of 10

Dealer: South
Vuln: N-S
Scoring: Pairs
  1. spadeJ 8 2
  2. heartA K
  3. diamondJ 5 4
  4. clubK 9 8 7 6
Green square in centre
  1. spadeA K Q 9 6 5
  2. heart9 8 7 5
  3. diamondA
  4. clubA 2
West North East South
1spade
2spade* etc etc 7spade
End

* Michaels

Answer 1 - Assuming LHO is not kidding about his distribution, it is overwhelmingly likely that he has 5-5 in the red suits. If so, the previous line of play is doomed unless LHO also holds the spade10 as one of his three black cards. Even if East has two hearts he will be able to over-ruff dummy on the third round of hearts. Since there are ten black cards missing, and since LHO could have eleven or more red cards, this reduces the chances of the above line of play to under 30%. Can you do better?
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