Psellos
Life So Short, the Craft So Long to Learn

The Schnapsen Log

December 15, 2012

Postponing Defeat (conclusion)

Martin Tompa

We can assume that Emmi will discard ♣J on your Q if she has it, and J if not. In either case, you will have 26 trick points at the end of that trick.

If you draw either A or K from the stock, running your winners will give you enough trick points: your AT will collect Emmi’s KJ, bringing you to 53 trick points. After that, cashing either A or KJ will force Emmi to discard T, giving you plenty of trick points to win. Here is the position if you draw K, in case you are having trouble visualizing it:

Emmi: (55 points)
AT
Q
♣ —
KJ

You: (26 points)
J
KJ
♣ —
AT

At the other extreme, if you draw either T or Q, your only winners are AT and you will end at 53 trick points. As soon as you lead either a spade or heart, Emmi will cash A to win, so be sure to cross the 33 trick point threshold beforehand. With each of these two draws, you lose 1 game point.

That leaves us to analyze the two jacks you might draw from the stock, and those are the ones where things get interesting. Let’s start with drawing ♣J, and assume that Emmi discarded J on your Q, since J is useless to her. This leaves you on lead in this position:

Emmi: (55 points)
AT
KQ
♣ —
K

You: (26 points)
J
J
♣ J
AT

What will happen when you run AT and ♣J, which is really the only way you can proceed? If Emmi discards T and Q, trying to preserve winners in each suit, you will reach 66 trick points exactly. So she is squeezed into discarding both of KQ, which sets up a new winner for you, the lowly J. When you cash that extra winner, she must finally discard T anyway, giving you plenty of trick points.

It’s easy to see that the same squeeze will develop if you draw J from the stock instead of ♣J: just substitute J for ♣J in the diagram above and think it through.

This type of squeeze is different from ones we have encountered before. Setting up the critical new winner J requires squeezing Emmi out of two higher hearts rather than just one. Because you have to squeeze her out of two cards, you need two squeeze cards yourself, T and whichever jack you drew. Bridge players call this type of squeeze an extended squeeze.

Let’s conclude by calculating the expected number of game points you will win. There are 4 possible draws that each give you 1 game point, and 2 possible draws that each cause you to lose 1 game point. Therefore, your expected gain is ⅔(+1) + ⅓(−1) = 1/3 game point. It’s not a lot, but at least it’s positive, your reward for working out the extended squeeze.

© 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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