How to use statistics when 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 of them reach a certain level of expertise and then hit a plateau. Their game stops improving.
What is responsible for this plateau? For many, the answer is statistics. Or to be more precise, a lack of understanding or knowledge of how to use stats when playing.
What do statistics have to do with the game of bridge, I hear you ask? The answer is “a lot”. They can be, and often are, an obstacle to becoming a better bridge player.
Let’s say, for example, that you are a declarant. Once the opponents have made their opening, the dummy’s hand is exposed for all to see. You know which cards you hold and which cards the dummy holds.
Now assume you are playing a trump contract. Dummy holds 5 trump cards and you hold 4, for a total of 9 cards. This means your opponents hold 4 trump cards between them.
You have to plan your game. Depending on the cards you hold in the trumps, you may have to try and figure out how the trumps are distributed among the opponents. A 4-0 split can mean the game plays out much differently than it would if there was a 2-2 split.
You can’t know for sure how the cards are dealt 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 game. This won’t always work, but in a number of games it will give you a better chance of winning more games.
As you can imagine, there are many statistics associated with the game of bridge. The best players will have memorized and used all of them. Those of us who are more modest, home or club players will only remember a few – the ones we think will be most useful to us and which we will be able to figure out how to use.
So, back to our division of trumps. As we plan our game, it may seem to us that a 4-0 trump split between opponents will require us to play differently than a 2-2 or 3-1 split. We cannot know how they split up and we may not be able to plan for all 3 scenarios. So which one 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 apparent early on that the cards are split that way, you’ll want to rethink your plan.
In a scenario where a 4-0 split could have a big effect on the number of tricks you win, you may feel like testing the split early in the game by drawing a round of trumps (or whatever suit you are interested ). If one of the opponents shows up in the first round, then you know you’re up against a 4-0 split and you can re-plan your game.
If split testing isn’t possible, then you’ll probably want to do the percentage play and hope your approach pays off.
If 5 cards of a suit are missing, the chance percentage changes. The probability of a 5-0 split is only 4% (and your opponents may have helped you know if this was likely to be the case by offering this suit). The probability of a 4-1 split is 28%, but the probability of a 3-2 split is 68%. You’ll probably want to make your initial plan based on the 3-2 spread.
Planning your game is an essential skill and knowing some basic stats will help you plan. But bridge is a dynamic game, and you have to be ready to rethink your plan if your opponents mess you up or the stats don’t work in your favor.
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