Life So Short, the Craft So Long to Learn

The Schnapsen Log

June 7, 2012

Close Call (solution)

Martin Tompa

What do you consider first when following to the last trick before the stock is exhausted? Right, you first consider ducking, because it involves fewer cases. Let’s do that.

There is only one smart card to discard, Q. Not because it preserves your marriage: Itell can break up that marriage once the stock is exhausted. Rather because it deprives Itell the chance to cash A after the stock is exhausted. You will draw the last trump from the stock, leaving this position with Itell on lead:

Itell: (33 points)

♣ A

You: (24 points)

♣ KQ

There are only two ways Itell can proceed from here. He can begin a forcing defense with K, but this will allow you to declare your marriage and reach 66 before he can even regain the lead. You will trump his K with Q, cash A, and declare the marriage, resulting in exactly 66 trick points. It is more likely that he will cash ♣A first to break up your marriage and then force you with K. You will still trump with Q and you will be on lead in this position:

Itell: (47 points)

♣ —

You: (31 points)

♣ K

It is going to be a race for the last trick. It is critical that you force Itell right back by leading ♣K, or else his forcing defense will succeed and he will have the last trump. He will trump with T for 61 points, but that will be his last trick and you will win the deal.

We are done with the ducking analysis: it results in a gain of 1 game point for you no matter how Itell plays. That’s good news. Is there any reason to consider winning his original lead of Q instead of ducking? Sure there is: Itell has only 27 trick points, so there may be chances for winning 2 game points rather than only 1. Suppose you trump Q with Q, bringing you to 30 trick points. Itell will draw J from the stock. A and the club marriage guarantee you a point total of at least 63, but you will need to draw something good from the stock to make up those last few points. Drawing T or A would certainly do it. Drawing ♣A isn’t helpful, because in that case Itell has no clubs in hand. You might think that drawing K from the stock for the diamond marriage would do it, but you cannot declare both marriages. This would be the situation:

Itell: (27 points)

♣ A

You: (30 points)

♣ KQ

Whichever marriage you declare, Itell can lead his ace to break up the other before you get a chance to declare it. You will lose 1 game point in this case.

The last card you could draw from the stock is K. Although this will lead to a win for you, you won’t be able to do it without letting Itell win a trick, so you will gain only 1 game point rather than 2. Ah, this means you shouldn’t have squandered your Q to trump Itell’s Q. You should trump with A instead, so that if you draw K from the stock you can declare the royal marriage and gain 2 game points. Go back and be sure you see that trumping with A will still allow you to gain 2 game points if you draw T or A from the stock.

All right, we’re now ready to put together the analysis for your expected number of game points if you trump Q with A. There are 3 cards (T, K, A) you can draw to gain 2 game points and 2 cards (♣A, K) to lose 1 game point. Therefore the expected number of game points you will gain is ⅗(+2) + ⅖(-1) = 4/5. Compare this to a guaranteed gain of 1 game point if you duck. This gives you two good reasons to duck: your expected gain is slightly greater (1 vs. 4/5) and you don’t suffer the 2/5 probability of being knocked out of the tournament. Take your game point and move on to the next battle against Itell.

This was a complicated analysis. There is a lot to work out and keep straight in your head in order to make the right decision. It will take practice for you to be able to do this at the table, and you will probably overlook some lines of play. But it is a skill you can master, and it pays off in the long run.

© 2012 Martin Tompa. All rights reserved.


blog comments powered by Disqus

About the Author

Martin Tompa

Martin Tompa (

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.


Getting Started

Links for Schnapsen and Sixty-Six

Links in German

Links in Hungarian

Recent Columns

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