Contemporary Development With Functional Programming

The Schnapsen Log

January 26, 2016

Homework on Expected Values

Martin Tompa

I am once again teaching a course on Probability and Statistics, using Schnapsen as a running example of applications of Probability. It’s been fun teaching Schnapsen to a large group of students who had never encountered it before.

In the course, we are just up to the topic of expected value now, so it seems appropriate to give them a homework exercise that involves expected game points. Today’s column is that homework exercise. This means that I won’t be posting my analysis until about ten days from now, when the homework will be due. A similar homework exercise appeared as a column last October.

You have just started a new game against the Maestro. On the very first deal, you reach the following interesting position:

Concealed cards:
♣ Q

Your cards:
♣ A

Trump: Q
Stock: 1 face-down card
Game points: Maestro 7, You 7
Trick points: Maestro 21, You 17
On lead: Maestro

The Maestro fingers each card in his hand in turn, and finally leads A. There have been no marriages declared, and no one did a trump exchange. You should assume that each of the five cards you haven’t seen is equally likely to be the last face-down card in the stock.

Plan your play for the rest of the deal. In particular, answer the following questions:

(a) How will the deal play out if you duck this trick, using your best possible discard? Who will win, and how many game points?

(b) How will the deal play out if you win this trick? In this case, you will draw the random, face-down card from the stock and the Maestro will draw the face-up Q. Consider each of the five cards you might draw and, for each one, find your best play and the resulting number of game points you will win or lose. Combine these appropriately to determine the expected number of game points that you will win.

(c) Based on your answers, will you duck the Maestro’s A or trump it? Why?

Once your homework has been turned in about ten days from now, you will be able to read my analysis.

© 2016 Martin Tompa. All rights reserved.

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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Recent Columns

Imperfect Information, Jun 24
Singleton Tens, Dec 1
Complete Information, Nov 28
Gamble, Sep 30
Homework on Expected Values, Apr 26
Thoughtful Actions, Mar 25