A Bridge Oddity: Odds in the Game of Bridge

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 3^rd and 4^th 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

Suit Combinations

There are more than 600 suit combinations listed in the Encyclopaedia of Bridge.[1] 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.

Here’s a few examples:

If you are missing an uneven number of cards in a suit, the odds say they will be divided as evenly as possible. And conversely, if you are missing an even number of cards, odds favour them splitting as oddly as possible.

So if you have 5 spades and dummy has 3 spades, that leaves 5 missing – odds say they will more likely split 3-2 (3 in one hand and 2 in the other) than 4-1.

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. [2] The Standard Plays of Card Combinations (BaronBarclay), 16 Suit Combinations (FlashCard Machine), Study Bridge 101: Card Combinations (ProProfs).

Finesse Odds

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%.

In a classic finesse, you lead towards a ‘tenace’ hoping to trap the opponent’s honour. For example, you are in your hand, dummy has the AQXX of spades. You lead from your hand and hope your left hand opponent (LHO) has the King. If they play it, you can win with your ace and the queen is good. If they don’t play it, you insert the Q and it wins. There are many many examples of a finesse but this capture’s its essence.

A tenace is a specific holding of two non-consecutive high cards in the same suit, where a player is missing the card or cards that rank between them. AQ is a tenace, but so is KJ and even Q10 – When I was learning I used to think of them as a sandwich missing the meat and hoping it was ‘onside’

50% of the time, supposedly, the missing meat will be onside to the finesse. But this isn’t a hard and fast rule of course. If you know the person on your right has a bunch of high card points, or if they actually bid the suit during the auction – the missing honour will probably be offside.

And here’s another useful ‘odds’ rule of thumb. If you’re missing an honour in a suit, odds favour it being in the hand with the most cards in that suit. It makes sense really. If I have 4 spades I have 4 chances to have the missing K – if I have only 2 spades I have only 2 chances of holding it.

Bridge odds get complicated and of course there are zillions, and they change with every bid and every card played. But as you play more they will become more and more useful.

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.

SpillOdds.com is Norway’s biggest online casino portal for Odds bonuses, Oddstips and reviews of gaming companies – a great place to get started playing in the world of online betting. Written in Norwegian.

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