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The Schnapsen Log

May 21, 2022

More Extremes of Luck

Martin Tompa

In today’s column I will continue my tales of probability extremes and woe against Doktor Schnaps. I was at the end of a tight game. We’re down to the last deal with the game point score 1:1. I’m on lead having been dealt the ace of trumps and ATKQ in an outside suit. What to do? If Doktor Schnaps has 0 or 1 trump, I can close the stock and win the game by cashing the trump, declaring the marriage, and running the rest of that suit. If Doktor Schnaps has 2 or 3 trumps, I’ll lose the game by closing. I don’t fancy my chances much with the stock open; it’s never a good starting hand to have four cards in a nontrump suit, because the opponent will gain the lead and keep playing cards from the remaining suits. I wish I knew what the probability was that Doktor Schnaps has 0 or 1 trump. I get out a piece of paper and start to work it out, but I’m concerned that I won’t be able to compute the probability quickly enough before my game times out. My hunch is that my probability of winning is pretty good. With 5 cards in its hand, 9 face-down cards in the stock, and 3 trumps I can’t see, the expectation is certainly for Doktor Schnaps to have 1 trump. So I close the stock, play the ace of trumps (Doktor Schnaps following suit), and declare the marriage, which Doktor Schnaps trumps. Game lost.

I’m thinking that I really need to work out that probability for the future, but first just one more game before I quit. I’m losing the next game with the game point score 3:1 when I’m on lead having been dealt the ace of trumps and ATKQ in an outside suit! What to do? Now the decision seems even easier, because 3:1 is a horrible score and here’s a chance to win the whole game. I close the stock, play the ace of trumps (Doktor Schnaps following suit), and declare the marriage, which Doktor Schnaps trumps. Second game lost.

I worked out the probability after that game. My probability of winning in this situation by closing the stock is 0.725. My probability of losing twice in this situation is 0.0755.

© 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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Recent Columns

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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