What is the true value of a card? - Diamond article
December 16, 2014
Spade Article - Counting Winners Part 2
January 1, 2015
Counting winners – Part 2
Now that we understand the basics of counting winners, let’s delve into some of the more subtle aspects. There are two factors that determine the strength of the cards we hold: how many high cards we have and our shape.
In Counting Winners Part 1, we discussed high cards. Shape has an equal, if not greater, impact on our winners. What do I mean by shape? I mean the length or shortness of our suits. When counting winners, we focus on length.
We take tricks by playing cards. Thus, the number of times we can play a card from a suit is the maximum number of tricks we can take. Let’s look at some examples:
We have the top four cards in hearts. It would be logical to count our winners as four. But, when we look closer, we realize that we can only play hearts twice, which means we can only take two tricks.
Why can we only play hearts twice? Because we have to follow suit! When you lead the A from dummy, you will have to follow suit from your hand. Whichever card you play (the Q or the J) will be swallowed by your A.
The same thing will happen when you lead the K. You cannot avoid this because you must follow suit.
When our high cards play together on the same trick, it’s called “crashing”. Unfortunately, because we have to follow suit, it is inevitable that our A will crash with the Q or J and our K will crash with the remaining high card, yielding only two tricks.
You can only play this suit two times because your length (in both hands) is two. Since you will have to play a heart from both hands, after two tricks, you won’t have any.
If we add some little cards, notice how the number of winners we have changes:
Now we do have four winners, because we can play the suit four times! How did I come up with four? Because we have four cards in each hand. In order to play a card, you have to have a card. The number of cards you have equals the number of times you can play them. But, remember we have to follow suit, so even though we have eight hearts we can only play them four times.
This time when we lead the A, we can play the 2.
When we lead the K, we can play the 4.
After taking those two tricks, we can lead two more and be sure to win them, because the Q and the J are the high hearts.
The sides do not have to be even as in the above example. If they are uneven (meaning we have a different number of cards in the two hands), the number of times we can play the suit is determined by the longer side.
In this case, we can take four spade tricks because we have the top four spades and the length of our longest side is four. We can play the A on the 3.
The K on the 4.
The Q on the 5.
Then lead the J (after getting to that hand some other way).
When you are trying to determine the maximum potential winners a suit has, remember that that number can never exceed the number of cards you have on the longest side.
Look at the following suits and determine how many winners you can take. For the purposes of these exercises, assume that transportation (the ability to lead from the hand you want to lead from) is not a problem.
1. You have three winners. In this case, you have the top five cards but can only take three tricks because your longest side is three. You cannot play the suit more than three times and therefore cannot take more than three tricks. Remember that you have to follow suit, so when you play your A, K, and Q, they will crash against your J and T.
2. You have four winners. You have the top four high cards and can play the suit four times (the number of cards in the hand with the longest hearts is four). This means you can take all four tricks and should count four winners.
3. You have six winners. You have the top ten cards in the suit, but can only lead the suit six times. Even though you have ten high cards, you can only take six tricks because after the sixth trick, you will be out of the suit. Remember that we can only take a trick by playing a card, so when we are out of cards, we are out of tricks.
4. You have four winners. You have the top six cards, but can only lead the suit four times because the length of your longest side is four.
5. You have two winners. Despite the fact that you have the top four cards in the suit, you will only be able to take two tricks. Why? Because you can only play the suit two times. You will have to follow suit each time and so your high cards will crash (play together).
Next time, we will continue to discuss how length affects winners, but we will focus on the power of long suits to make little cards good.