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How to Use Statistics in Playing Cards

Millions of people enjoy playing bridge and millions of players understand the basic rules of the game. They practice and play every day. Many reach a certain level of expertise and then plateau. Their game stops improving.

What’s responsible for this plateau? For many the answer is statistics. Or to be more accurate, a lack of understanding or knowledge of how to use statistics when you are playing.

What do statistics have to do with playing bridge, I hear you ask? The answer is “a lot”. They can be, and often are, the barrier to becoming a better bridge player.

Let’s assume, for example, that you are declarer. Once the opponents have made their opening lead dummy’s hand is exposed for all to see. You know which cards you hold and which cards dummy holds.

Now assume that you are playing a trump contract. Dummy holds 5 cards in trumps and you hold 4, a total of 9 cards. That means that your opponents hold 4 trump cards between them.

You need to plan your play. Depending on which cards you hold in trumps you may need to try and work out how the trumps are split between the opponents. A 4-0 split may mean the game plays very differently from the way it would play if there was a 2-2 split.

You can’t know for certain how the cards split in any given situation, but you can use statistics to give you a better chance. Then you can play for the most likely scenario – the percentage play. This won’t always work, but over a number of games it will give you the better chance of winning more games.

As you might imagine, there are a lot of statistics associated with playing bridge. The best players will have memorised and will use all of them. Those of us who are more modest, home or club players will just remember a few – the ones that we think will be most useful to us and that we will be able to understand use.

So, back to our trump split. While we are planning our play it may seem to us that a 4-0 trump split between the opponents will need us to play differently from a 2-2 split, or a 3-1 split. We can’t know how they split and we might not be able to plan for all 3 scenarios. So which should we choose as the most likely?

Statistics tell us that the probability of a 4-0 split is 10%. However, the provability of a 2-2 split is 40% and the probability of a 3-1 split is 50%. It probably doesn’t make sense to plan for a 4-0 split – although if it becomes obvious early on that the cards split that way, you will want to rethink your plan.

In a scenario where a 4-0 split could have a major effect on the number of tricks you win, you may feel that you want to test the split early on in the game by drawing a round of trumps (or whichever suit is of concern). If one of the opponents shows out in the first round, then you know you are up against a 4-0 split and can replan your play.

If testing the split isn’t possible, then you will probably want to make the percentage play and hope your approach pays off.

If there are 5 cards missing from a suit, the percentage chances change. The probability of a 5-0 split is just 4% (and the opponents may have helped you work out if that is likely to be the case by bidding that suit). The probability of a 4-1 split is 28%, but the probability of a 3-2 split is 68%. You will probably want to make your initial plan on the assumption of a 3-2 split.

Planning your play is an essential skill, and knowing some basic statistics will help you plan. But bridge is a dynamic game and you need to be prepared to rethink your plan if the opponents wrong foot you, or the statistics don’t work in your favor.