Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

February 2, 2017

The Glass is 9/10 Full (solution)

Martin Tompa

“Here’s something I could have done differently,” you reply sourly. “I could have joined the others instead of playing cards.”

“True,” Hans replies, “but then you would have missed out on a chance to hear me lecture. Let’s go all the way back to trick 1, when Tibor led J.” Hans reconstructs your starting hand on the table for all to see.

Your cards:
KQ

♣ A
AQ

“You should plan your play carefully before acting,” Hans continues. “With your beautiful hand, you fully intend to win this trick, close the stock, and score 3 game points. That’s all good.

“But now is the time to view your glass as 1/10 empty rather than 9/10 full. What can go wrong? If Tibor doesn’t have both missing trumps, as is very likely, you cannot miss: your trump lead knocks out any trump he might hold and then, whatever he leads, you can win the trick and cash your aces for enough points. So you should assume that Tibor does hold both missing trumps, and see if you can find a safety play that will help in this situation. Tibor will surely pull your last trump and then the danger is easy to foresee: he could cash some number of hearts and you will have to discard winners and hope for a miracle.”

Hans stops and waits for you to catch up. “All right,” you admit, “it’s not so hard to predict the bad things that might happen, even as early as the first trick. But what could I have done about it?”

Gently, Hans asks, “Did you consider any different action at the first trick? It’s very natural to win it as cheaply as you can, saving your A for later. But it’s worth considering winning that first trick with A instead. The advantage is that you score the points for that ace immediately, rather than risk having to discard it later. Here is how your hand would have looked after you close the stock and declare the royal marriage.” Hans rearranges the cards on the table.

Your cards:
KQ

♣ AJ
Q

Trump: J
Trick points: Tibor 0, You 53
On lead: You

Hans continues his lecture. “Tibor can pull 2 rounds of trumps and cash some hearts. But notice that you have 53 trick points instead of the 45 that you had at this point with your play. As long as Tibor holds any club whatsoever in his hand, you are guaranteed to get to 66 trick points. You might still be unlucky, of course, and find him clubless. But you have decreased the probability of suffering from your bad luck.”

“A very nice safety play, Hans,” Uncle Tibor chimes in. “If it had been me, I don’t think it would have occurred to me to win the first trick with anything other than Q.”

© 2017 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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April
Homework on Expected Values, Apr 26
March
Thoughtful Actions, Mar 25
Noble Sacrifice, Mar 4
February
Carpe Diem, Feb 10
The Glass is 9/10 Full, Feb 2
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The Battle and the War, Jan 17

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