Life So Short, the Craft So Long to Learn

The Schnapsen Log

November 9, 2012

Entries from Thin Air (solution)

Martin Tompa

This is a very interesting endgame position for you. Did you work out that this last deal of the tournament is going to hinge on who wins the very last trick? The maximum set of winners Katharina can hope to cash consists of A, ♣A, and K, on which you will discard K, ♣K, and Q, giving her a grand total of 64 trick points. The maximum set of winners you can find consists of K (if you can trump her K) and AT, on which Katharina will discard KJ, giving you the exact same grand total of 64 trick points. (Only one of K and Q can be a winner for you: if you trump K with K, then Katharina has a trump remaining to trump your Q.) This really is a tight match, isn’t it?

Winning the last trick looks somewhat promising, since your hand seems to have three entries, K and AT (if you can use K to trump) and Katharina’s seems to have only two, A and ♣A. Your strategy to win the last trick, as usual, is to lead out losers and retain your winners as entries back to your hand.

The obvious loser to lead is ♣K. Let’s see what will happen if you do that. Katharina will win and lead K, leaving you on lead in this position:

Katharina: (42 points)
♣ —

You: (37 points)

♣ —

What happened to your two heart entries? The answer is that Katharina executed a tempo endplay by knocking out your trump, forcing you to open up the heart suit and give her the last trick with A.

Things are no better for you if you start out with three rounds of hearts in order to force her in trumps:

Katharina: (41 points)

♣ A

You: (56 points)

♣ K

From this position, she will again lead K, and you will have to concede the last club trick.

This leaves only one possibility for you, and it is counterintuitive. What happens if you give up on the idea of retaining your sole trump K as an entry to your hand, and lead it out as though it’s a loser? This will put Katharina on lead from this position

Katharina: (42 points)

♣ A

You: (29 points)

♣ K

She can cash her K, on which you will discard Q, at any time she likes. But the remaining entries are exactly as we counted originally: you have two entries in hearts, and she has only one entry in clubs. Whatever she does, you will win the last trick with a heart.

How did the counterintuitive lead of K perform this magic? The answer is that it denied Katharina the possibility of trumping your Q, particularly on the last trick as happened in her tempo endplay. This in turn prevented her tempo endplay, creating your two heart entries practically out of thin air. You traded in one entry (K) for two (AT), a good deal for you.

© 2012 Martin Tompa. All rights reserved.


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About the Author

Martin Tompa

Martin Tompa (

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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