8. TABLE OF PROBABILITIES ----------------------- (i) For break of a suit: -------------------- cards out distribution percentage 2 1 - 1 52 2 - 0 48 3 2 - 1 78 3 - 0 22 4 3 - 1 50 2 - 2 40 4 - 0 10 5 3 - 2 68 4 - 1 28 5 - 0 4 6 4 - 2 48 3 - 3 36 5 - 1 15 6 - 0 0 7 4 - 3 62 5 - 2 31 6 - 1 7 7 - 0 0.4 (a) Generally speaking, odd number of cards out are likely to break more favorably than even number of cards out. (b) To calculate the probability quickly (say 4 - 1), subtract one figure from the other (say 3) and divide 100 by this figure (say 33). Probability will be less than the figure so obtained (i.e. less than 33%). This method cannot be applied for distributions where the difference is only 1 i.e. for 5-4, 4-3, 3-2 and 2-1, as then the result in all these cases will be 100%. (ii) For high cards out, with supporting cards ----------------------------------------- (a) Holding 10 cards: K out ----------------- Singleton K = 26% (13% in either hand) Kx = 52% (26% in either hand) Kxx = 22% (11% in either hand) The chances of finesse succeeding are 26 + 11 = 37% against singleton K (13%) Remaining 50% is immaterial as K, Kx or Kxx in either hand cancel each other. Holding 11 cards and K out i.e. only 2 cards out, 1-1 distribution is 52%, but it is better to watch reaction of opponents and then decide. (b) Holding 9 cards: 4 cards out with K or Q ---------------- Singleton K or Q = 6% ( 3% in each hand) Doubleton K or Q = 40% (20% in each hand) Kxx or Qxx = 38% (19% in each hand) (c) Holding 8 cards: 5 cards are out with K or Q ---------------- Singleton K or Q = 6% ( 3% in each hand) Doubleton K or Q = 28 (14% in each hand) Kxx or Qxx = 40% (20% in each hand) Kxxx or Qxxx = 22% (11% in each hand) (d) Holding 8 cards: 5 cards are out with K and Q ---------------- Singleton K or Q = 12% ( 6% in each hand) Doubleton KQ = 6% ( 3% in each hand) K and Q split in 2 hands = 22% (11% in each hand) (e) Holding 7 cards: 6 cards out with K or Q ---------------- Singleton K or Q = negligible Doubleton Kx or Qx = 18% ( 9% in each hand) Kxx or Qxx = 54% (27% in each hand) (f) Holding 7 cards: 6 cards out with K and Q ---------------- Singleton K or Q = 8% ( 4% in each hand) Doubleton Kx or Qx = 4% ( 2% in each hand) K and Q slpit in 2 hands = 52% (26% in each hand) ??? Kxx or Qxx = 50% (25% in each hand) ??? (g) Putting another way: ------------------- 2 honors out: 52% divided in two hands 48% both in one hand one honor out ----------------------------------------------------------- |cards out | honor | | |-------------------------------------------| | | once guarded | twice guarded | --------------|-------------------|-----------------------| | 3 | 52 | 22 | | 4 | 40 | 38 | | 5 | 28 | 40 | | 6 | 18 | 54 | -----------------------------------------------------------