A Bridge Oddity: Odds in the Game of Bridge
By Alex J. Coyne © 2018 Great Bridge Links
Bridge is a game of skill, strategy and wit – but behind that, we’re looking at a great deal of probability and mathematics. You might have wondered about the odds of certain plays and oddities occurring in the game of bridge, or you might want to be in the process of improving your bridge strategy. Here’s more about bridge odds, bridge hands, suit combinations and improving the odds for your game.
What are the Odds Of?
For the sake of both interest and strategy, you might have wondered about the odds of various plays and odds occurring during a game. We found some of these bridge probabilities mentioned on Bridge Hands, and we’re quoting some of them here.
The number of different hands a named player can receive = 635, 013, 559, 600
The number of different hands a second player can receive = 8, 112, 425, 444
The number of different hands the 3rd and 4th players can receive = 10, 400, 600
The odds against receiving a perfect hand = 169, 066, 442 to 1
The odds against a hand with no Aces = 2 to 1
The odds against being dealt four Aces = 378 to 1
There are more than 600 suit combinations listed in the Encyclopaedia of Bridge. Card combinations in the game of bridge can be compared to chess moves; there are several possible options, but there are certain standard moves that can be committed to memory to make strategies easier to calculate when you are in the game.
If you want to learn the standard suit combinations, you’ll find various in most introductory bridge books and courses. Also recommended is Suit Combinations in Bridge by Sally Brock and the Official ACBL Encyclopaedia of Bridge.
Flash cards are a huge help.  The Standard Plays of Card Combinations (BaronBarclay), 16 Suit Combinations (FlashCard Machine), Study Bridge 101: Card Combinations (ProProfs). Here’s a quiz taken from the Encyclopaedia of Bridge (not currently available) about suit combinations.
In contract bridge, a finesse is one of the first things you learn about – and it can give you the advantage you need. What do the odds say about finessing? The chances of a finesse succeeding are 50%.   The double finesse (or deep finesse) has a 25% chance instead. Faking this move – a little bit like a football player dodging to the side, or a poker player twitching over a mock bad-hand – is known as the Chinese Finesse.
According to this article from Sports Illustrated first published in the 1960’s, it’s called the Chinese Finesse “based on the absurd canard that the Chinese deal and play their cards backward—counterclockwise.” What are the odds of that? Well…
These Bridge Calculators
Bridge calculators are fun – and they’re useful. They can help you to figure out the odds of bridge puzzles you’ve always wondered about, and it can be a great help when you’re sitting down to analyse a game that you (or someone else) has played before.
Some of the best contract bridge calculators are available on Richard Pavlicek’s website. You can find them all by clicking here.
Here’s another bridge calculator from Automaton that’ll analyse missing cards and give you a play-evaluation table from your input. Again, this is useful when you need to evaluate a past game.
SuitPlay is a freeware program for Windows designed to tell you the best play for your suit combinations.
Books about Bridge Odds
There are plenty of more resources that are great for learning about the odds behind bridge. Here are our recommended options.
- Bridge, Probability & Information (Robert F. MacKinnon)
- Bridge Odds: Complete Probabilities in Contract Bridge (Frederick H. Frost)
- Practical Odds at Bridge (Alexander Traub)
- The Mathematical Theory of Bridge (Emile Borel)
- Bridge Odds for Practical Players (Hugh Walter Kelsey)
- Complete Book on Hand Evaluation in Contract Bridge (Mike Lawrence)
- The Encyclopaedia of Bridge