Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

February 5, 2013

Imperfect Information

Martin Tompa

In the Café Abeles with your good friend Peter on this wintry day, you look a little sadly at your dwindling piece of Haselnusstorte and your cup of coffee, which not even an optimist would call half full. “Ah well”, you think, “I’m sure they have more in the kitchen.” Meanwhile, you are only a few tricks into the next deal when you find yourself in this situation:

Unseen cards:

TQ
♣ ATK
TKJ

Your cards:
AK
AK
♣ Q

Trump: J
Stock: 3 face-down cards
Game points: Peter 5, You 5
Trick points: Peter 13, You 38
On lead: You

We haven’t looked at too many positions this early in the deal. When you are at trick 6, you have perfect information about your opponent’s hand, assuming you’ve remembered the played cards correctly. When you are at trick 5, you have nearly perfect information about your opponent’s cards, since there is only one card concealed in the stock and the other 5 are held by your opponent. But at trick 4, where you find yourself now, your information is quite incomplete: nearly half the cards you haven’t yet seen are still in the stock.

How should you proceed from this position? Once you have a good plan, you are welcome to read my analysis.

© 2013 Martin Tompa. All rights reserved.


Comments

blog comments powered by Disqus

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.

Subscribe

Getting Started

Links for Schnapsen and Sixty-Six

Links in German

Links in Hungarian

Recent Columns

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
January
The Battle and the War, Jan 17

Archives

2017
2016
2015
2014
2013
2012