Life So Short, the Craft So Long to Learn

The Schnapsen Log

June 25, 2013

Trumpless (solution)

Martin Tompa

You try to imagine how you can take tricks with both A and ♣T, which would give you enough trick points to win the deal. The best chance would be if you can endplay your sister and force her to open up the club suit. Wouldn’t that feel great?

You remember your clever Uncle Hans’s advice: when you are on lead at the last trick before the stock is exhausted, the first thing to consider is closing the stock. Can you possibly afford to close the stock when you have no trump and Emmi probably has one? Sure: her trump will be key in your plan to endplay her.

With all this in mind, you close the stock, lead A, and hold your breath. When Emmi follows suit with K, you exhale noisily and relax a little. Next you lead J, which she trumps with K.

Unseen cards:


Your cards:

♣ TQ

Trick points: Emmi 26, You 57

At this point you lay down your hand face up and say, “The worst that can happen is that you cash J and ♣A, on which I can discard Q and ♣Q, respectively. But after that you’ll have to let me win my ♣T and that will give me enough points.” You happily record 2 game points for yourself.

“That was a beautiful throw-in, dear,” your Uncle Hans beams. “It takes courage and insight to close the stock with no trumps in your hand. But tell me, did you think about what would have happened if the last trump was face-down in the stock? In that case, the throw-in would fail and your sister wouldn’t open up the club suit so nicely for you.”

“Yes, Hans, I did think about that,” you reply proudly. “I had 57 trick points when I won my A. If Emmi didn’t have the trump, my QJ would both have been winners, and Emmi would have had to discard two jacks at least. That would have brought me to 66 trick points on the nose. The only way my play would fail is if K was the last card in the stock. The throw-in would still work, but Emmi would have trumped my A and I wouldn’t collect enough trick points to get to 66.”

“Very good, dear.”

Let’s calculate the expected number of game points you will gain by this play. With probability 5/6 (the probability that any of the 6 unseen cards other than K is in the stock) you will gain 2 game points, and with probability 1/6 you will lose 2 game points. Therefore your expected gain is ⅚(+2) + ⅙(−2) = 4/3. Your expected gain is slightly less, ⅘(+2) + ⅕(−2) = 6/5, if you know Emmi holds K because of an earlier trump exchange. Either way, you’ve done well with your trumpless hand.

© 2013 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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