In an earlier post, I showed you how to use my program to work out construction puzzles, wherein you are given a scenario and you must build a hand that fits it. Today’s post is about using my program to help you work out another very useful type of exercise: suit combination problems.
You can find suit combination problems everywhere in bridge literature. The official ACBL Encyclopedia of Bridge devotes 50 pages to a huge, comprehensive list of such problems in chapter 20. The Bridge World magazine springs them on you throughout each issue. You’re going along enjoying an article, letting the author do all the work, when BAM! No, it’s not Emeril Lagasse, it’s a suit combination problem appearing suddenly as a sidebar to the article you are reading. Oh my God, can’t I just read the article? You can, but you know, the editors of TBW will think less of you if you don’t take the time to noodle out the suit combo that they have inflicted upon you. Seriously, though, they are essential exercises for training your brain to think about percentages, what you do and don’t know based on the cards you can see, and how to play a hand.
Now, as with construction puzzles you can do all the work in your head, or work it out on paper, or even deal out some cards the way our primitive forebears did it. But we’re going to use my program to turbo charge the process. Let’s hop to it!
Let’s study Excercise 2 from page 14 of the book Playing Suit Combinations by Fred Gitelman and Jeff Rubens. In accordance with the copyright that allows reproduction of brief excerpts in reviews of the book, I am here to tell you that this is a fine and extremely useful book and you should go buy it.
Exercise 2 says that to fulfill your notrump contract, you need four diamond tricks. North has Q2 and South has AT943. You have adequate transportation and you surmise from other clues that diamonds are distributed 3-3 in the opponents’ hands. How do you make your four diamond tricks?
As with construction puzzles, suit combinations cry out for using the Manual Deal feature of my program. So select “Manual Deal” under Deal Type. Also, to make it more challenging, select “No” under Hands Visible After Deal. You will see how that comes into play in just a minute.
Now click the Deal button to go to the Manual Deal page. There, key in what we know about the deal from the suit combination description:
Note how I used the “B” in each diamond suit to specify an exact number of cards for each hand. You may observe correctly that I could have left off the “XXXB” in either West or East since the blank diamond hand would receive all of the leftovers, but remember what I have written in other posts: if it only costs you a few keystrokes, go ahead and be specific about what you want.
Now click the “Click here…” button and you will see one way this deal could come out:
Beautiful isn’t it? Just look at those…nothings! Where’s my cards, man?
Never fear, the cards are there. Remember, we chose to NOT make the hands visible after the deal. That is so we can challenge ourselves by limiting what we can see. But we do need to see something, don’t we. So now click anywhere in the blank area in South’s hand and you should see this:
Now, since the suit combination does give you both North and South, also click in North’s blank hand and now you see both:
What you now have is your North/South hands in an actual deal, with diamonds exactly as specified in the problem description.
This is the point where you should now take as long as you like to look at and think about the problem at hand. Look at the book, which immediately gives you a solution. The solutions to suit combinations rarely guarantee success. Instead, they are usually expressed in terms of making choices based on the known odds of this or that distribution of the unseen cards. In this case, the solution tells you that leading twice from dummy is the best solution, based on the odds.
Now, whether you arrived at that solution yourself or by reading the author’s explanation, let’s go ahead and see how it would work with this particular deal. Click West’s hand, and then click East’s hand, and all is revealed:
East and West each have one diamond honor and two small cards. The authors tell us that there are six possible variations on this distribution, and that leading twice from dummy is the way to win our four diamond tricks in notrump with this kind of distribution.
The authors also tell us that there are four distributions wherein West has both honors and one small card, and that leading twice from dummy will fail in those instances. You can use your imagination, or you can see it for yourself.
Lacking other evidence, knowing the above odds would tell you to lead twice from dummy, because the distribution in which that play would win is more likely than the other, by 6 to 4.
To see the less common distribution for yourself, you could keep this setup the same and just repeatedly press the “Deal” button to go back to the Manual Deal page, leave the template as is, and click “Click here…” to see another random deal that fits your template. That would eventually deliver a deal where West has KJ in diamonds. And in fact, since the study of suit combinations involves the study of percentages, you might want to do just that, keep generating deals with East/West getting random leftover diamonds until the KJ shows up in West. Then you can see how those 6-4 odds work out in practice.
I just did that, by the way, and it took at least a dozen tries to get the KJ in West’s diamonds. Draw no conclusions from my small sample size. You would have to try it some large number of times to arrive at true odds. A statistician could tell you how many times.
Or, if you take the authors’ word for it about the odds and you really just want to see a sample deal with KJ in West’s diamonds so you can think about card play, just tweak your Manual Deal template. Change West’s diamonds from “XXXB” to “KJXB” like so:
BAM! er…I mean there you have it. KJ in West, Put on Your Flak Vest (my first original bridge aphorism—possibly too specific to catch on any time soon):
I like having a computer assist me with visualizing these things. But ultimately, even with the computer assist, you still have to do the hard part: THINK!