Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

October 14, 2012

Intuition (solution)

Martin Tompa

Since you are following to the last trick before the stock is exhausted, you should first consider ducking. The obvious card to discard is K. This would leave you in the following position, with Katharina on lead:

Katharina: (39 points)
AK
AK
♣ K

You: (18 points)

TQ
♣ AQJ

What do you expect will happen next? Katharina will lead some black card, and you will be thrown in. Whatever you do, you will ultimately have to open up the heart suit. This will give Katharina 28 additional trick points in hearts, for a total of 67. Even if you run all of your clubs before opening up the hearts, you won’t accumulate enough trick points.

That TQ in your hand should make you very nervous at the stage of the deal when the stock is nearly exhausted. It should scream “Endplay danger!” to you.

What can you do about it? You’re going to lose that T to Katharina’s A anyway. What would happen if, instead of discarding the obvious K on her T, you discarded Q, abandoning the idea of protecting T? Here would be the new position, with Katharina still on lead:

Katharina: (38 points)
AK
AK
♣ K

You: (18 points)

T
♣ AQJ
K

From this position, Katharina cannot win any trick other than A (provided you don’t let her win her ♣K), and that heart trick will bring her trick point total to only 59. You cannot reach 66 trick points either, but you are guaranteed to win the last trick, as long as you give up T early.

It seems counter-intuitive (at least to me) to bare your precious T in this way. But you’re going to lose it whatever you do, so baring it doesn’t cost you anything. In fact, it saves you from also handing Katharina your winning K as a discard.

We should also consider whether you can do better by trumping Katharina’s T rather than ducking. I will leave it as an exercise for you to convince yourself that you are worse off trumping. As a hint, no matter what card you draw from the stock, it’s very hard for you to score more than 1 game point.

© 2012 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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