Probabilities of distribution

It's not necessary to know the probabilities with exact percentages to control this aspect of the game, it's only necessary to understand some basic rules to know on which side leans the balance, as would say Jean-Marc Roudinesco.

Notice in the table below how the symmetrical distributions for an even residue are always less probable than the slightly asymmetrical distributions (except for the 1-1 distribution for 2 missing cards).

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Notice also that a particular symmetrical combination is more likely than a particular asymmetrical combination. It's the total of the asymmetrical combinations which makes these distributions more probable. To summarize, and by supposing that it misses R-V-9-7 in a suit:

For an odd residue however, the most symmetrical distribution is always more likely.

How to read this table ?

The table indicates the probabilities of distribution of opponents residues in bridge game, it should thus correspond (with small adjustments) to the probabilities of the tarot with 3 players. The tendencies observed are however valid for the tarot with 4 players.

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Probabilities of distribution of opponents residue
Residue   Split   Probabilities Combinations
Number Frequency
1 0-1 100 % 2 (1x2) 50 %
2 0-2 48 % 2 (1x2) 24 %
1-1 52 % 2 26 %
3 0-3 22 % 2 (1x2) 11 %
1-2 78 % 6 (3x2) 13 %
4 0-4 10 % 2 (1x2) 4,7 %
1-3 50 % 8 (4x2) 6,2 %
2-2 40 % 6 6,7 %
5 0-5 4 % 2 (1x2) 1,9 %
1-4 28 % 10 (5x2) 2,8 %
2-3 68 % 20 (10x2) 3,4 %
6 0-6 1,5 % 2 (1x2) 0,7 %
1-5 14,5 % 12 (6x2) 1,2 %
2-4 48,5 % 30 (15x2) 1,6 %
3-3 35,5 % 20 1,7 %
7 0-7 0,5 % 2 (1x2) 0,3 %
1-6 6,8 % 14 (7x2) 0,5 %
2-5 30,5 % 42 (21x2) 0,7 %
3-4 62 % 70 (35x2) 0,9 %
8 0-8 0,2 % 2 (1x2) 0,1 %
1-7 2,9 % 16 (8x2) 0,2 %
2-6 17,1 % 56 (28x2) 0,3 %
3-5 47,1 % 112 (56x2) 0,4 %
4-4 32,8 % 70 0,5 %
9 0-9 0,05 % 2 (1x2) 0,02 %
1-8 1,1 % 18 (9x2) 0,06 %
2-7 8,5 % 72 (36x2) 0,12 %
3-6 31,5 % 168 (84x2) 0,19 %
4-5 58,9 % 252 (126x2) 0,23 %
10 0-10 0,01 % 2 (1x2) 0,005 %
1-9 0,35 % 20 (10x2) 0,017 %
2-8 3,8 % 90 (45x2) 0,04 %
3-7 18,5 % 240 (120x2) 0,08 %
4-6 46,1 % 420 (210x2) 0,11 %
5-5 31,1 % 252 0,12 %

Updated: 07/02/2016

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