Opposition Hidden Cards

In bridge statistical probabilities play an important part. Different declarer play strategies will lead to success depending on the distribution of opponent’s cards. To decide which strategy has highest odds for success, the declarer should acquire a basic understanding of the probabilities of card distributions.

Hidden Card Distribution Odds


In the absence of any information from bidding or play to alter the odds the table below displays the odds of the hidden card distribution.

Generalisations about how the cards usually fall

Except for 2 cards the general rule is
1.) Odd cards probably do split as evenly as possible

2.) Even cards probably do not split evenly

An example of Information which changes the Odds in the Table Below

For example . Eg a hand which has preempted showing a 6 card spade suit has only 7 ‘vacant spaces’ for other suits while if declarer and dummy together have 5 spades the other defender has 2 spades leaving 11 vacant spaces in that hand. If there are 4 cards in another suit (say diamonds) in those hands the odds of them splitting 2-2 drops 5% while the hand with more vacant spaces is 5 times as likely than the other to hold 3 or 4 diamond suit cards

The Odds for Opponents Hidden Card Distribution

Opposition Holdings in a SuitSplit%ageSplit%ageSplit%ageSplit%ageSplit%age
2 cards1-152%2-048%
3 cards2-178%3-022%
4 cards2-241%3-150%4-010%
5 cards3-268%4-128%5-05%
6 cards3-335%4-249%5-115%6-02%
7 cards4-362%5-230%6-17%7-00.5%
8 cards4-433%5-347%6-217%7-13%8-00.2%
9 cards5-459%6-331%7-29%8-11%9-01%