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Contemporary Development With Functional Programming

The Schnapsen Log

February 10, 2017

Carpe Diem

Martin Tompa

The game against your dangerous Uncle Tibor continues, with your clever Uncle Hans looking on. After the earlier disastrous deal that left you behind with the game point scores 1:4, you scored 2 game points on the next one, bringing both of you within striking distance of winning the whole game. One deal later, you find yourself in the following position:

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

No one has declared a marriage yet, but you do know from an earlier trump exchange that Tibor is holding A. You pull both hearts from your hand and show them to Tibor to claim the marriage, giving you 59 trick points. You are just about to return K to your hand when you pause and then, with both cards still in your outstretched hand, go into a trance. Finally coming out of it, you excitedly say, “Watch this, Hans!”, return the queen to your hand, and lead K.

Tibor thinks for a moment and then wins the trick with A. After drawing the last cards from the stock, this is the position:

Tibor: (27 points)
A
J
♣ K
AQ

You: (59 points)
KJ
Q
♣ —
TK

There is not much left that Tibor can do. He can cash one or two of his aces in order to get beyond 33, but eventually must concede the deal.

“Very nicely done, dear,” Tibor congratulates you as he gives you 1 game point to tie the score 1:1.

“Thanks, Tibor! Hans, did you notice the difference between leading Q and K?” you inquire happily. “I almost led the queen out of habit. But then I realized that Tibor could discard his losing Q on it. And then, unless I make the very lucky draw of A from the stock, I would have been on lead in a position like this.” You move some cards around on the table.

Tibor: (12 points)
AJ
AJ
♣ K

You: (65 points)
K
K
♣ —
ATK

“I can’t make another trick from this position, and Tibor will be the one to score a game point,” you conclude. “The same is true if I draw ♣K or J from the stock instead of A.”

“Very true, dear,” Hans agrees. “Did you also think about what would have happened if Tibor had ducked your actual lead of K?”

“Yes, I did,” you reply. “With the K lead, Tibor can’t afford to discard his losing Q, because that gives me 66 points. His only possible discard is J, giving me 65 points. Any diamond I draw from the stock gives me 2 game points instead of 1. The other two cards left for me to draw are ♣K and A, either of which leaves me on lead in a position like this.” You move a few cards to illustrate.

Tibor: (12 points)
AJ

♣ K
AQ

You: (65 points)
K
AQ
♣ —
TK

“I can’t stop Tibor from passing 33 trick points,” you conclude. “He can cash his four winners to get to … let’s see … 12, 27, 32, 47, 62 … yes 62 trick points. Not quite enough. And then he has to lead Q, that key loser I didn’t want him to discard earlier. I win 1 game point, just like I actually did when Tibor didn’t duck.”

“A very thorough analysis of your play, dear,” Hans compliments you, causing you to beam at his uncharacteristic praise. “But did you have any better play?” he continues in more characteristic style.

Your smile fades. What does Hans have in mind? When you think you know, you are welcome to read my analysis.

© 2017 Martin Tompa. All rights reserved.


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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.

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Recent Columns

February
Carpe Diem, Feb 10
The Glass is 9/10 Full, Feb 2
January
The Battle and the War, Jan 17
December
If Worse Comes to Worst, Dec 14
April
Keep Calm, Apr 9
January
Homework on Expected Values, Jan 26

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