The Schnapsen Log

Homework on Expected Values

Martin Tompa

For regular readers of this column, I apologize for the fact that I have been producing columns at a slower rate recently. The slow rate is probably going to continue for the next few months. I haven’t been idle on the Schnapsen front, however. I am busy teaching a course on Probability and Statistics, and am 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 one week from now, when the homework will be due.

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

Unseen cards:
♠ Q
♥ KJ
♣ TK
♦ A

Your cards:
♠ A
♥ ATQ
♣ —
♦ T

Trump: ♠J
Stock: 1 face-down card
Game points: Maestro 7, You 7
Trick points: Maestro 21, You 18
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 hand. In particular, answer the following questions:

(a) How will the deal play out if you duck this trick? 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 ♠J. 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 a week from now, you will be able to read my analysis.

© 2013 Martin Tompa. All rights reserved.