Suit breaking probabilities

It isn’t necessary to know the exact percentages to manage this aspect of the game. What really matters is understanding a few basic rules so you know which way the balance leans, as Jean-Marc Roudinesco would say.

Notice in the table below that symmetrical distributions with an even number of missing cards are always less likely than slightly asymmetrical distributions (except for the 1-1 split when only 2 cards are missing).

Also note that a specific symmetrical layout is more likely than a specific asymmetrical one. It is the total number of asymmetrical layouts that makes those distributions more frequent overall. To sum up, assuming R-V-9-7 are missing in a suit :

• If someone asks you to bet on the distribution, bet on a 3-1 split.
• But if someone asks you to choose between these two specific layouts: R-V / 9-7 or R-V-9 / 7, bet on R-V / 9-7.

With an odd number of missing cards, however, the most symmetrical distribution is always the most likely.

How to read this table ?

This table shows the probabilities of suit splits between two opponents in bridge. With minor adjustments, these figures also apply to 3-player Tarot. The general tendencies remain valid in 4-player Tarot as well.

• The Missing cards column indicates the number of cards missing in the suit.
• The Split column shows the possible ways those cards may be divided between the two opponents.
• The Probability column gives the chance of each split occurring.
• The Number of combinations column shows how many specific card layouts produce that split. Example : 8 (4×2) means there are 4 possible layouts for each opponent, for a total of 8.
• The Frequency column expresses, as a percentage, the probability of each specific layout.

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