Psellos
Contemporary Development With Functional Programming

The Schnapsen Log

July 5, 2014

The Big Trumps (solution)

Martin Tompa

The first thing you should consider when on lead to the last trick before the stock is exhausted is closing the stock. You have the top winner in each of the nontrump suits. If Tibor happen to be holding all of the three unseen nontrump cards K, Q, and ♣Q, you can cash all three winners and get to 69 trick points. But if any of those three unseen cards is still in the stock, you will fall short, and Tibor’s three trumps will take the remaining tricks. Since Tibor already has 39 trick points, you stand to gain less by closing than you stand to lose. In this particular case, you will win 1 game point if any of the three trumps is face-down in the stock, and lose 2 game points if any of the three nontrump cards is face-down. Usually, this is a bad situation in which to close the stock.

Let’s then consider what will happen if you leave the stock open. At first glance, the outcome seems a little unpredictable. What will Tibor do if you lead J or Q? It seems to depend on the exact five cards he is holding.

Let’s suppose that Tibor is already holding the three big trumps and look at the deal from his point of view. He already has 39 trick points, and those three big trumps will bring his total up to 64, plus whatever you contribute to those three tricks. That means that it’s easy for him to see that he should trump whatever you lead and will be guaranteed to score 2 game points. This is a nice, simple example of what I have earlier called role reversal.

You must assume, then, that one of those big trumps is still face-down in the stock, because otherwise you will lose 2 game points whether you close the stock or not. And if one of those big trumps is still in the stock, you should close the stock, because in that case you are guaranteed to be able to cash your three winners and gain 1 game point.

This is something of a desperation play, then, because you must proceed on the assumption that certain cards remain in the stock. Let’s calculate your expected gain if you close the stock. Three of the six unseen cards, if in the stock, will cause you to gain 1 game point, and the remaining three will cause you to lose 2 game points. Therefore, your expected gain is ½(+1) + ½(−2) = −1/2. All this work, and you expect to lose half a game point! Still, it’s better than the alternative: if you leave the stock open, Tibor may win your trick even if he is missing one of the big trumps, and his reward will be to draw that big trump from the stock and go on to win 2 game points.

© 2014 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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