A Posteriori Probabilities  A posteriori refers to knowledge derived
from experience. Relating to playing a hand of Bridge, after players
view one hand and dummy (26 cards), players can make an initial probability
assessment (a priori) for suit breakage. Thus, as the cards are played
and information about suit breakage was observed, players use the "a
posteriori" concept to revise their probability assessment.
As an example, let's assume your opponents hold 4 cards in your trump suit.
Using "a priori" calculations, we know the normal suit split. But
let's say we know some more about the opponent's hand. For instance,
if one opponent made a preempt showing a large number of cards in another
suit, that opponent has less remaining "vacant spaces" to hold cards in your
trump suit. Here's the mathematical formula, based on "a posteriori"
data:
Trumps
Suit 

Second Suit 
a priori 
54 
63 
72 
81 
90 
40 
4.78% 
2.94% 
1.47% 
0.63% 
0.21% 
0.04% 
31 
24.87% 
21.17% 
14.71% 
9.24% 
5.04% 
2.19% 
22 
40.70% 
42.35% 
39.71% 
34.66% 
27.73% 
19.66% 
13 
24.87% 
28.24% 
35.29% 
41.60% 
46.22% 
48.07% 
04 
4.78% 
5.29% 
8.82% 
13.87% 
20.80% 
30.04% 
Thus, if one opponent preempted at the 4 level (likely showing an 8 card suit),
notice the likelihood of a 22 trump split is reduced from 40.7% (a priori) to
27.7%, and the possibility of the preemptor having 3 trump is reduced to 5% 
about onefifth of the 25% when opponent's distribution is unknown.
Further second suit distribution tables are found in "Probabilities &
Alternatives In Bridge", by Antonio Vivaldi and Gianni Barracho.
Card Distribution
(remaining two hands)
Hand Distribution
(suits within a hand)
High Card Point Count (HCPs in one hand)
Miscellaneous Probabilities
(assorted interesting odds)
Number of Cards (card quantity in
a suit)
Posteriori Probability (example
when additional information is known)
Suit Combinations (best lead and
plays)
Expected Controls (based on HCP)
Also see books on
Probabilities
