The Schnapsen Log

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 very large group of students who had never encountered it before.

In the course, we have recently covered the topic of expected value, 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 twelve days from now, when the homework will be due. A similar homework exercise appeared as a column last year.

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

Concealed cards:
♠ KJ
♥ T
♣ AT
♦ Q

Your cards:
♠ T
♥ AJ
♣ Q
♦ K

Trump: ♦J
Stock: 1 face-down card
Game points: Maestro 7, You 7
Trick points: Maestro 28, You 20
On lead: Maestro

There have been no marriages declared. Earlier in the deal, the face-up trump had been ♦Q, which the Maestro exchanged with the ♦J, so you know one of the Maestro’s cards is ♦Q. The Maestro fingers each card in his hand in turn, and finally leads ♣A. You should assume that each of the four cards you haven’t seen (♠K, ♠J, ♥T, ♣T) is equally probable 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 ♦J. Consider each of the four 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 twelve days from now, you will be able to read my analysis.

© 2017 Martin Tompa. All rights reserved.