Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

July 17, 2012

To Duck and Not to Duck

Martin Tompa

Your Uncle Claudius has now claimed the seat across from you, with Uncle Hans kibitzing once again. You haven’t played against Claudius in quite a long time. You hope you can make Hans proud on this deal. It’s going to be tough, because you haven’t collected a single trick yet.

Unseen cards:
AQJ
T
♣ —
TQ

Your cards:
K
AKQ
♣ —
A

Trump: T
Stock: 1 face-down card
Game points: Claudius 4, You 6
Trick points: Claudius 38, You 0
On lead: Claudius

Claudius strokes his long beard for a while, tentatively fingers a few different cards, and finally leads Q. You remember that in this position, following to the last lead before the stock is exhausted, the first thing you should consider is ducking. It would pain you to break up that pretty marriage, but you steel yourself and dutifully consider discarding Q. This would bring Claudius to 44 and you would pick up T, leaving you in this position with Claudius still on lead:

Claudius: (44 points)
AQJ
T
♣ —
T

You: (0 points)
TK
AK
♣ —
A

You picture Claudius’s hand in your mind and try to imagine how play would proceed. Claudius’s only two possible tricks are A and Q, and A alone wouldn’t be enough to reach 66. So he would lead J to set up Q as a winner. You could then cash your two red aces but, however you play it, he would eventually capture your two kings with his two trumps. That would give him 22 more points for a total of exactly 66. And the most you could get would be 54.

Giving up only 1 game point isn’t too shoddy, given the fact that you haven’t taken a single trick yet. On the other hand, it’s easy to see that you won’t do any worse by winning this trick and declaring your marriage, and maybe you’ll draw something good from the stock. So you go ahead and take Claudius’s Q with your A. You now have 14 points and draw an unhelpful J from the stock, putting you on lead in this position:

Claudius: (38 points)
ATQ
T
♣ —
T

You: (14 points)
KJ
AKQ
♣ —

You remember that no trumps have been played yet, so Claudius has all three. You also remember that he holds T and it’s unprotected, so you cash A and show your marriage, bringing you to 55 points. But that’s it for you, as you cannot make any more tricks. Claudius records his 1 game point.

“Well, I did as well as I could,” you say proudly. “I remembered your advice, Hans, about considering ducking first, but it would have broken up my marriage and I would have lost that way too.”

“Yes, I had you that time,” Uncle Claudius replies with a tight nod. “You couldn’t recover from the lead I’d built up.”

Uncle Hans clears his throat and smiles at you wistfully. “I am very impressed that you could remember all of Claudius’s cards, dear, and that you could work through the play and the point counts in your head. That really is very impressive. But …” And here he pauses. “Are you certain there was no way to win the deal?”

“Of course I’m certain,” you insist. “I can’t win by ducking, and I can’t win by not ducking.”

What on earth does Hans have in mind? When you think you know, you are welcome to read my analysis.

© 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

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