Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

April 9, 2012

The Mother of Invention (solution)

Martin Tompa

Despite your considerable lead in trick points, things are looking bleak for this game. What you can see looming is that club marriage, and it doesn’t seem as though there’s much you can do to prevent it, or in fact to prevent Peter from winning the deal. I predict that Peter will take whatever you lead with one of his aces (except for ♣J, which he might trump with J), declare the marriage (simultaneously knocking out your ♣A), and then get back in to cash his other ace and ♣K. Count up the trick points he will have accumulated after the marriage, A, A, and ♣K. You should arrive at a total of 68. Don’t forget to add in the points for the cards you will contribute to these three tricks.

Is there anything you can do to alter this future? Other than your desperate plan to spill Peter’s coffee in his lap and steal some of his tricks in the resulting confusion, is there any hope for this game at all?

The only part of my prediction that isn’t inevitable is what Peter has in his hand to play on this trick. If one of those aces is still in the stock rather than in his hand, then you can alter the future I’ve predicted. If it’s A in the stock, that would suggest that leading K might work. But of course it won’t: if A is in the stock, then Peter is holding the club marriage in his hand and will want to trump K with J in order to declare the marriage. In the process, he will pick up A from the stock and have plenty of points to win.

Your only hope is that A is the last card remaining in the stock. In that case you must lead Q, which is the master trump right now, and the only card in your hand that Peter cannot beat. He will discard J, leaving this position:

Peter: (13 points)
A

♣ KQ
TJ

You: (39 points)
TK

♣ AJ
A

You can now cash your two aces, picking up his J and ♣Q, which will bring your trick point total to exactly 66.

It’s a lot to hope for, that the one mystery card in the stock is the trump ace. Since there are 6 cards you haven’t seen and you need one particular one to be in the stock, the probability of success is only 1/6. But it’s the only hope you have, so lead out that Q with authority, as though you know it’s a winner.

This play is at the opposite extreme from the safety play we saw in an earlier column. The safety play is designed to avoid a small probability of failure. Today’s play is designed to grab a small probability of success. I would call it a desperation play.

When the only way you can win (or the only way you can cross the 33 point threshold, or the only way you can take your first trick before your opponent wins) is to assume a certain distribution of the cards, it is a necessity for you to assume that distribution. And you know what they say about necessity.

© 2012 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

December
Singleton Tens, Dec 1
November
Complete Information, Nov 28
September
Gamble, Sep 30
April
Homework on Expected Values, Apr 26
March
Thoughtful Actions, Mar 25
Noble Sacrifice, Mar 4

Archives

2018
2017
2016
2015
2014
2013
2012