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The Schnapsen Log

August 11, 2013

The Last Place You Look

Martin Tompa

“All right, Emmi,” you say, looking her in the eye. “This ends now.” If only your success could be as certain as your words, you think, as you look back down at your cards.

Unseen cards:
AQ
J
♣ Q
AK

Your cards:
K
K
♣ A
TQ

Trump: Q
Stock: 1 face-down card
Game points: Emmi 2, You 1
Trick points: Emmi 20, You 31
On lead: You

Your clever Uncle Hans has taught you that the first thing you should consider, when on lead at the last trick before the stock is exhausted, is closing the stock. An elimination play looks possible if you close the stock, so you think it through. You could cash your K and ♣A and then throw Emmi in with a spade so that, assuming she holds both A and K, you would win your T. You add up the trick points you would accumulate, but the total frustratingly comes to 65, unless you are lucky enough that J is the last card face-down in the stock. With only a 1/6 probability of winning, you abandon the idea of closing the stock.

With the stock left open, you certainly don’t want to open up that diamond suit, nor squander your master trump or your only ace. It would seem a windfall if you could persuade Emmi to win this trick so that you pick up the royal marriage. With all this in mind, you lead K. Emmi doesn’t fall for this simple trap, though, and discards ♣Q. You now hope for a good draw from the stock, and don’t feel disappointed when you draw A. This leaves you on lead from this position:

Emmi: (20 points)
Q
QJ
♣ —
AK

You: (38 points)
A
K
♣ A
TQ

If you force Emmi by leading ♣A, you can see that she will lead her last trump and eventually take the last trick with a diamond. In fact, you realize that you are doomed to lose the last trick whatever you do, because Emmi has more entries than you do: two diamonds and a trump for her versus one spade and a trump for you. You also cannot get anywhere near 66 trick points with only A and K as winners. You throw down your hand in frustration and tell her to score her game point.

“That’s too bad, my dear,” your Uncle Hans says to you. “Once Emmi made the good choice to unload her ♣Q liability on your K lead, there wasn’t much you could draw from the stock that would have allowed you to win. Only drawing J or A would have admitted a win for you, and even with those draws you would have had to proceed very carefully.”

“Then I did as well as I could have, Hans?” you inquire hopefully.

Hans hesitates, but you know what his hesitation means: you had a better play, but it pains him to hurt your feelings by telling you so. Nor is Hans capable of withholding edification from you: “You might have had a better lead than K at trick 5,” he says quietly.

Once you have found the better lead, be sure you have a plan for whatever Emmi plays on that lead. When you’ve made your plans, you are welcome to read my analysis.

© 2013 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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