Using probabilities to help your card play
Missing an odd number of cards a suit will probably break the way you want it to. Missing an even number of cards the suit will probably not behave.
Knowing a few bridge probabilities can help you choose between two lines of play when you are declarer. In this lesson I'll show you an easy way to remember the odds then we'll play through a hand to put it all into practice.
Rule of thumb for bridge odds
If you're missing an even number of cards the suit probably won't break evenly. For example, missing 6 cards the suit will probably not break 3-3.
If you're missing an odd number of cards the suit will probably break nicely. For example, missing 5 cards, there will probably be 3 in one hand and 2 in the other.
9 card fit
With a 9 card fit you're missing 4 cards. Those 4 cards could be distributed 2 in one opponent's hand and 2 in the other. Bridge players would call that a 2-2 break. There might be 3 cards in one hand and 1 in the other which we'd call a 3-1 break or there might be 4 in one hand and none in the other which would be a 4-0 break.
8 card fit
With an 8 card fit you're missing 5 cards. Those cards could be 3-2, 4-1 or 5-0
Our odds rule of thumb says that missing an odd number of cards the suit will probably break nicely. So, go ahead and take a guess! What are the chances of a 32 break?
7 card fit
With a 7 card fit you're missing 6 cards. Those cards could be 3-3, 4-2, 5-1 or 6-0
Our odds rule of thumb says that missing an even number of cards the suit will probably not break nicely. What's more likely - a 3-3 break or a 4-2 break?
21 high card points. Nice!
This is a 2NT opening bid and when North raises to 3NT that's high enough. I've already shown my strength so it's North's job to decide how high to bid.
Planning the play in 3NT
The lead is the ♠Q. Let's take a look. So we're going to make a couple of spade tricks. We've got the ♥A, ♥K, ♥Q so that's three heart tricks. We're up to five! We've got the ADA, ♦K and the ♣A. So that's eight. We need one more trick.
In the diamonds we've got the jack of diamonds, so we could hope that West has got the ♦Q. We could just play ♦5, and if West plays low, we'll play the ♦J. And if West does have the ♦Q, we are going to make that one extra trick in the diamond suit.
The other thing we could do is just keep on playing clubs and eventually, hopefully, the opposition are going to run out. What would it require for the opposition to run out of clubs and give us one extra club trick? We'd need the suit to be three, two. So if one of our opponents has three and the other has two and we just keep playing the clubs, we're eventually going to be the only one with any clubs left and our last club will win.
Choosing between two lines of play
Which of those two lines is best? Are we going to try the diamond finesse or are we going to try and set up the clubs? We don't need a whole lot of complicated maths for this. You know that finesse works 50% of the time. Maybe you feel like it doesn't work 50% of the time, but really West is going to have the ♦Q 50% of the time. Does playing clubs give us a better chance than 50%?
In the club suit, we are missing an odd number of cards. We've got eight, they've got five. Missing an odd number of cards the suit probably will break the way we want it to, and that's all we need to know! Clubs breaking is more likely than the 50% finesse.
So I'm just going to win the ♠K and duck a round of clubs, I'm going to have to lose two clubs at some point but most of the time I'm going to be able to eastablish that last club as a winner.