Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

August 11, 2015

An Ounce of Prevention (solution)

Martin Tompa

Prospects look uncharacteristically good for you to win this game. You are on lead, have 48 trick points, and hold two aces. You surely want to consider closing the stock and cashing those two aces.

With the stock closed, the ♣A is a sure winner, because there are two clubs you haven’t seen and only one card face-down in the stock. If Katharina is holding J, then your A is also a winner and you will amass enough trick points to win by cashing your aces. This is a good plan: there are 5 cards that could still be face-down in the stock (Q cannot be, since you saw it in Katharina’s hand when she declared the marriage), and only 1 of those 5 (J) foils the plan. Therefore, your probability of winning the whole game is 4/5, which is good. Unfortunately, if your plan fails, then Katharina will score enough game points to win the whole game; that happens with probability 1/5.

It’s a good plan, but it’s not a great plan. A great plan would guarantee you the win. Did you search for such a plan?

What would happen if you left the stock open and led K? This seems like a crazy plan at first, since you may be giving up a valuable trump, or you may be giving Katharina a chance to jettison her J before you can cash A. What makes this plan sane is that you are already so close to 66 trick points.

Let’s consider Katharina’s possible responses to K. If she ducks, that will bring you to at least 54 trick points. Even if you then draw a club from the stock, you will still be able to cash ♣A for enough trick points and the game. So she cannot duck K.

Well, then, she must win your K lead with A to defeat you. This will put her on lead from the following position:

Katharina: (62 points)
QJ

♣ TK
J

You: (48 points)

J
♣ AQJ
A

Whatever she leads next, you are guaranteed to be able to cash both of your aces and win the game.

Leaving the stock open and leading K at trick 5 is a safety play, protecting you against the 1/5 probability that the last face-down card in the stock is J. That play is the proverbial ounce of prevention.

© 2015 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

June
Two Last-Trick Problems, Jun 27
May
More Extremes of Luck, May 21
April
Grasping at Straws, Apr 4
March
A New Scheme for Remembering Cards, Mar 23
September
As Luck Would Have It, Sep 9
December
What's in the Stock?, Dec 5

Archives

2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012