Psellos
Life So Short, the Craft So Long to Learn

The Schnapsen Log

July 10, 2013

Measure Twice, Act Once (solution)

Martin Tompa

Recall the frequent advice when following to the last trick before the stock is exhausted: first consider what happens if you duck, because in that case you know what you will draw from the stock (the face-up trump) and exactly what both hands will look like one trick later. In the current case, you have three queens from which you can choose your discard on Emmi’s K. It looks as though they are all equivalent, each being a loser. But don’t be in a rush to choose one at random. There is a big difference among them, and only one of them is the right choice. Do you see which one it is, and why?

Suppose you choose to discard Q on Emmi’s K. Here is the situation one trick later, with Emmi on lead:

Emmi: (39 points)
TK
T
♣ Q
A

You: (21 points)
Q

♣ TKJ
Q

Emmi can now cash A and T, coming to 66 trick points exactly and scoring 2 game points. Discarding Q instead of Q has the same unfortunate result.

That leaves only Q. Why is Q the right queen to discard? Because only this discard denies Emmi the possibility to cash her ace. If you discard Q on Emmi’s K, here is the situation with Emmi on lead:

Emmi: (39 points)
TK
T
♣ Q
A

You: (21 points)
Q
Q
♣ TKJ

Now all Emmi can do is cash her two tens, which leaves her just shy at 65 trick points. She cannot arrange to take the last trick either, because your 3 trumps guarantee you’ll have one left to win the last trick, provided you lead one of your queens whenever you are on lead.

You are guaranteed to win 1 game point if you discard Q, but you will lose 2 game points if you discard either of the other queens. What a difference the choice of discard and 1 small trick point can make! The lesson is to count carefully.

Since Emmi hasn’t passed the 33 trick point threshold yet at the time of her K lead, you should also consider what will happen if you trump rather than ducking. But there is not much to consider. With those 3 losing queens, the only card you can draw from the stock that will give you a win of the deal is ♣Q for the royal marriage. Those are not good odds. Your expected gain is ⅙(+2) + ⅚(−1) = −1/2. If in fact you saw Emmi exchange ♣J for ♣Q, you have no chance of winning at all. Either way, trumping has a much lower expected gain than the correct duck.

© 2013 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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