Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

December 28, 2012

The Homewrecker

Martin Tompa

“Ready for the next deal?” your aunt, Polite Polona, asks sweetly. She shoots a quick look at your Uncle Hans, who is kibitzing you, as if to warn him to behave.

Unseen cards:
TQ
AQ
♣ KQ

Your cards:
AK
J
♣ —
AT

Trump: J
Stock: 1 face-down card
Game points: Polona 2, You 2
Trick points: Polona 34, You 12
On lead: You

You know that the first thing you should consider, when on lead to the last trick before the stock is exhausted, is closing the stock. You take a quick inventory of your tricks and decide that closing the stock is nearly hopeless. Your current 12 trick points just isn’t enough of a starting platform, even if you could manage to collect 2 diamond and 2 spade tricks.

Thinking about the cards you haven’t yet seen, you take note of the mixed news. The good news is that Polona has no trumps in her hand. The bad news is that she might already be holding the club marriage. In fact, you realize, there is a 2/3 probability that she is, since any of the 4 other cards out of the 6 you haven’t seen could equally well be face-down in the stock. This means that leading J is probably out.

But since your aunt has no trumps, this could be an opportune time to cash A and hope for a good draw from the stock. You count trick points again. Your current 12, plus AT and A, plus at least 8 points contributed by Polona, comes to 52 trick points. If you draw either spade or A, that would give you enough to reach 66. Even if Polona doesn’t hold the club marriage and you draw ♣K, you think you can see a way to take the last trick. That’s good enough odds for you.

You lead your A and Polona discards Q. Unfortunately, you draw the miserable Q from the stock, putting you on lead in this position:

Polona: (34 points)
T
A
♣ KQ
J

You: (26 points)
K
QJ
♣ —
AT

“Oh well,” you sigh, showing everyone your hand. “That Q was an unlucky draw for me. I’ll pull a round of trumps so that I pass 33 points, but then I’m stuck. I can still make one more trump trick after that, but the remaining tricks are yours, Polona. One game point for you.”

“It was a valiant effort, dear,” your aunt tells you, “but it wasn’t meant to be.”

“Or perhaps it was meant to be,” Uncle Hans puts in quietly, unable to keep it to himself.

What is it that Uncle Hans has in mind? Once you have thought about it, you are welcome to read my analysis.

© 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.

Read about Winning Schnapsen, the very first and definitive book on the winning strategy for this fascinating game.

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