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Contemporary Development With Functional Programming

The Schnapsen Log

September 4, 2019

The Horns of a Dilemma (solution)

Martin Tompa

Concealed cards:

ATQ
♣ A
TQ

Your cards:
Q
K
♣ —
AKJ

Trump: J
Stock: 1 face-down card
Game points: Tibor 2, You 1
Trick points: Tibor 13, You 33
On lead: You

What is the first play to consider when on lead to the last trick before the stock is exhausted? Right, you should think about closing the stock. If you close the stock and Tibor is holding TQ, then you will want him to open the diamond suit. That suggests an elimination play. You begin by cashing Q so that Tibor cannot exit by playing hearts for you to trump. Assuming Tibor doesn’t discard a diamond on Q, you exit next by leading K. Tibor may have one more heart or club to cash after this trick, on which you can discard J. After that, he will have nothing but his two diamonds left, and you will win both of those tricks. Will that give you enough trick points? Even if Tibor had both red queens in his hand, your final trick point count will be 33+3+3+3+4+10+11 = 67 and you will win the game.

Notice, though, that you need Tibor to have both missing diamonds in order to accumulate enough trick points. If one of those diamonds is still in the stock, instead of exiting with K, your winning play would be to cash your diamonds starting with A, which would give you enough points. The problem is that you don’t know which of these two plays will succeed. The only information you have to guide you is what Tibor discards on your Q. If he discards Q, you have learned almost nothing: he could still have either one or two diamonds left in his hand, and you are left on the horns of a dilemma.

To make matters worse, if Tibor doesn’t hold T, he is quite capable of making the deceptive discard of T on your Q. You will infer from this discard that Q is the last face-down card in the stock and that the elimination play will work, whereas in fact it won’t.

Wanting to avoid the dilemma’s horns, you should now consider what happens if you leave the stock open. You need only 1 game point to win the game, and Tibor has only 13 trick points, so perhaps you can afford to leave the stock open and still win the game.

You probably want to retain Q to pull trumps after the stock is open, and you should be reluctant to open the diamond suit. This leaves only one candidate to lead, so let’s see what happens if you lead K with the stock open.

If Tibor wins this trick, say with A, he will be on lead from this position:

Tibor: (28 points)

TQ
♣ A
TQ

You: (33 points)
QJ

♣ —
AKJ

The only trick Tibor will take after this is T. You will win all the other tricks and the game.

Thus, Tibor must duck your K lead, and his best discard is Q. This will bring your trick point total to 40. Your Q will pull his last trump for 45, and your A will make the total at least 59 trick points. If you draw A, ♣A, or either diamond from the stock, you will easily make enough trick points to win the game. The only questionable card you can draw from the stock is T. If that is the case, you will be on lead from this position:

Tibor: (13 points)
J
A
♣ A
TQ

You: (40 points)
Q
T
♣ —
AKJ

From here, an elimination play nearly identical to the one discussed earlier is waiting for you. You draw Tibor’s trump with Q and exit with T. Tibor is now on lead from this position:

Tibor: (34 points)


♣ A
TQ

You: (45 points)


♣ —
AKJ

Tibor can cash ♣A, but then is forced to open the diamond suit, and you are rewarded with 73 trick points and the game.

© 2019 Martin Tompa. All rights reserved.


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About the Author

Martin Tompa

Martin Tompa (tompa@psellos.com)

I am a Professor of Computer Science & Engineering at the University of Washington, where I teach discrete mathematics, probability and statistics, design and analysis of algorithms, and other related courses. I have always loved playing games. Games are great tools for learning to think logically and are a wonderful component of happy family or social life.

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The Horns of a Dilemma, Sep 4
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