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Conditional probability of suit distribution

Known suit: a suit where the distribution is completely known.
Psuedo suit: is a suit where you think you figured out the distribution (based on the bidding).
If the distrubution of a suit between east west is known than this has consequences for the other suits.
The below situation is:
West opened a weak two in hearts (six card).
North-south have nine card spade fit and are in four spades, having six cards in hearts.
The known suit is hearts and the key suit is spades.


Als bekende kaarten tellen:
  • Een kleur waarvan de distributie volledig bekend is.
  • De kaarten in de sleutelkleur.
You are in four spades after east opened a weak two in hearts.
In north-south have six hearts so west has one.
The heart distribution is completely known = the known suit.

North has s KJxx and south has s Axxxx.
You play the spade ace both opponents follow with a small spade.
You play a small spade from south and west follows with a small one.
Spades is the keysuit.

West has 1 heart and 2 spades = 3 known cards → 13 - 3 = 10 vacant places.
East has 6 hearts and 1 spade = 7 bekende kaarten → 13 - 7 = 6 vacant places.
Without the weak two from east you would have played spade ace and king playing for the drop but now taking the finesse is better.
Play for the drop = 49,7% and take the finesse = 62,5%.