Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

February 10, 2017

Carpe Diem (solution)

Martin Tompa

Concealed cards:
A
AJ
♣ K
AQ

Your cards:
K
KQ
♣ —
TK

Trump: J
Stock: 1 face-down card
Game points: Tibor 1, You 2
Trick points: Tibor 12, You 39
On lead: You

“What am I always telling you is the first thing to think about when you are on lead with one face-down card in the stock?” Hans asks.

You look a little shame-faced as you quietly respond, “Close the stock. I considered it, but not very long because of all the losers in my hand.”

“That’s right, dear,” Hans continues. “You did hold mostly losers. But, to balance that, the marriage would bring your trick point total to 59, so one winner might be all you need to locate.”

“I see it now,” you say. “Close the stock, declare the marriage, lead either one, and hold on to my diamonds for dear life. Since Tibor had only 12 trick points, closing the stock and succeeding would give me 2 game points and the whole game.”

“Right again, my dear,” Hans nods. “As long as that last face-down card isn’t the critical Q, you will eventually win a trick with your T and plenty of points to win the deal and the game. Even if you lead K after declaring the marriage and Tibor holds the best cards possible, as long as those cards include Q you will eventually win. Tibor will take the trick with his A, but the most he can accumulate after that is 12 + 4 + 11 + 11 + 4 + 4 + 3 + 11 + 4 = 64 trick points. After cashing all those winners, his last card will be Q and your last card will be T.”

“Wait, Hans,” you interject. “I see a glitch in your plan. What if the last face-down card is A? Then, even if I’ve led K, Tibor’s J only brings me to 65 trick points.”

“Well done, dear! That is indeed something else to consider. But, in that case, anything you lead next will give Tibor the trick, and eventually you will have to make some more trick points.

“What make closing the stock a much better play than leaving it open,” Hans concludes, “are the game point score and the nature of your opponent. Your play with the stock open guaranteed you 1 game point, leaving the score at 1:1. If you instead close the stock, this deal will end the whole game one way or the other. Only 1 of the 5 cards you haven’t seen, Q, can foil your plan if it is the last face-down card in the stock. (Remember that you have seen A and know it to be in Tibor’s hand.) That means there is a 1/5 probability of losing the game and a 4/5 probability of winning it. Are your chances of winning the game that good if you play one more deal at 1:1? Not against an opponent who plays as well as Tibor does! No, this was the moment to seize the day.”

© 2017 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

September
Gamble, Sep 30
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

Archives

2017
2016
2015
2014
2013
2012