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The Schnapsen Log

September 2, 2022

Sidestep a Few Landmines (solution)

Martin Tompa

Concealed cards:
A
AQ
♣ Q
KQ

Your cards:

TJ
♣ AK
A

Trump: J
Stock: Open, 1 face-down card
Game points: Tibor 4, You 4
Trick points: Tibor 20, You 25
On lead: You

Even though Tibor only has 20 trick points, the diamond marriage, the certainty of Tibor’s ace of trumps, and the missing A combine to make your situation very precarious. What do you think will happen if you leave the stock open? Whatever you lead, there is a real danger that Tibor will take this trick. If he does, his two aces plus the marriage will bring his trick point total to at least 20+11+2+11+2+20 = 66 and you will lose 2 game points. You could try leading ♣K and hope Tibor ducks, but you know him to be an aggressive player and it’s likely he would trump it.

It looks like you have to close the stock and hope that one of those important concealed cards is still in the stock, making this a desperation play. To have any hope of getting to 66 trick points, you will need to win all three of your big cards, A, ♣A, and T. Assuming that Tibor holds A, you will only be able to win T by coercing Tibor to lead hearts, that is, an elimination play.

Your hope is that the last face-down card is a diamond. Let’s assume for concreteness that K is still in the stock. You cash A, eliminating Tibor’s safe exit card Q. Your trick point total is now 25+11+3 = 39. When you cash ♣A, your total is 39+11+3 = 53 and this is the resulting position:

Tibor: (20 points)
A
AQ
♣ —

You: (53 points)

TJ
♣ K

Now you throw Tibor in by leading ♣K, which he must trump, leaving him with nothing to lead but hearts. No matter which one he leads, you will eventually win his Q with your T, bringing your total to exactly 53+10+3 = 66 and earning you 2 game points.

Notice that this play will also work if the last face-down card in the stock is A. Since there are 5 possible cards that could still be in the stock (A is excluded, since you know Tibor holds it) and 3 of those 5 cards cause you to win the deal, the probability that you win by closing the stock is 3/5. That’s quite good, as desperation plays go.

© 2022 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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September
Sidestep a Few Landmines, Sep 2
June
Two Last-Trick Problems, Jun 27
May
More Extremes of Luck, May 21
April
Grasping at Straws, Apr 4
March
A New Scheme for Remembering Cards, Mar 23
September
As Luck Would Have It, Sep 9

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