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Contemporary Development With Functional Programming

The Schnapsen Log

September 30, 2017

Gamble (solution)

Martin Tompa

Concealed cards:

T
♣ AKJ
TK

Your cards:
K
AJ
♣ T
A

Trump: J
Stock: 1 face-down card
Game points: Tibor 1, You 2
Trick points: Tibor 11, You 48
On lead: You

What is the first thing to consider when on lead to the last trick before the stock is exhausted? Right, you should consider closing the stock. It is particularly appealing here, because you can freeze Tibor’s trick points so that, if you succeed, you will win 2 game points and the whole game. Wouldn’t that be a thrill, to beat Uncle Tibor, and right in front of your mentor Uncle Hans?

With the stock closed, your obvious hope is that Tibor holds T. If that is the case, you can simply cash A and win the game. That seems easy enough. But if you are unlucky and T is the last face-down card in the stock, this would be the position:

Tibor: (11 points)


♣ AKJ
TK

You: (48 points)
K
AJ
♣ T
A

From this position, the only trick you can win is A. You can start with a spade or heart lead, but Tibor will trump, cash his ♣A, and force you with ♣J. After you trump that lead with your A, Tibor has the last trump and a winning club left. You will have lost the game, reaching only 61 trick points.

Still, it’s a good gamble, isn’t it? The probability that Tibor holds the key card T is 5/6, since there are 6 cards you have not seen and Tibor is holding 5 of them. You should jump at a 5/6 chance of beating a superior opponent. You reach over to close the stock.

And then you remember Hans’s lessons. You draw back the hand that was about to close the stock, sit on it, and consider whether you can possibly do better with the stock left open.

The only room for improvement, of course, is to win the 2 game points with probability 1 rather than probability 5/6. Is that possible? With the stock open, if you lead a spade or heart, Tibor can trump it and cash his ♣A, crossing the 33-trick-point threshold and holding your gain to at most 1 game point. You could lead A but, if that last face-down card is the T, which is the situation you are trying to handle, you won’t take another trick and will lose the game.

That leaves only one possible lead, the unintuitive ♣T. But as soon as you focus on that, you begin to sense that it is a brilliant lead. Tibor cannot afford to duck it, because that would bring you to at least 60 trick points and leading your trump ace would then win the game. He must win your lead of ♣T, and even if he does it with ♣A that will bring his trick point total to only 32. He will then be on lead from this position:

Tibor: (32 points)

T
♣ KJ
TK

You: (48 points)
K
AJ
♣ —
AJ

Whatever Tibor leads, you can win the trick and cash your A, with full certainty that he now holds the T.

“Leaving the stock open and leading ♣T was inspired!” your Uncle Hans exclaims as soon as the last card falls.

You beam with appreciation at the rare compliment and respond, “I was thinking of what you taught me, Hans. It was a safety play, protecting myself against the one unlucky case that the T was still in the stock.”

“That’s right,” Hans replies. “By leading ♣T, you gave Tibor one more chance to draw T from the stock, if he didn’t have it already.”

© 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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Gamble, Sep 30
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