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Contemporary Development With Functional Programming

The Schnapsen Log

March 7, 2012

Safety First (solution)

Martin Tompa

Since you hold all the top trumps and Katharina is getting so close to 66 trick points, it feels right to win this trick with your T and start building up your own point count. You will draw the face-down “mystery card”, and it might be something that helps. Imagine if it were K, giving you the royal marriage! It could be ♣A, and then you would have the two highest clubs to cash after you “pull” (i.e., extract) all of Katharina’s trumps. It can’t be K, because Katharina already showed you that card, but even picking up Q would be an additional winner once you’ve pulled trumps.

In fact, the only card that you might draw that looks useless is J. What if that’s the card you draw? Let’s count up how many trick points you could collect in that case. Here is what things would look like after you win T, draw J, and Katharina draws J:

Katharina: (50 points)
KJ
Q
♣ A
K

You: (30 points)
ATQ
J
♣ T

Notice that we’ve already added 20 to Katharina’s points for the marriage and 13 to your points for Q and T in your tricks. You can run your trumps, ATQ, collecting KJ and K from your opponent. (Being a Schnapsen master, Katharina has kept track of exactly what cards remain in your hand and knows that K is useless and can be discarded.) Let’s add all these points to your count. You have 30, and these three tricks will bring you another 34, for a total of 64 points. Not quite enough. And you are left with two losers, J and ♣T, and nothing you can do about them. If you try to rearrange your play to take the last trick, Katharina will cash two winners and easily exceed 66 points. You are going to lose this deal and the game.

It’s not all that bad, though, right? If you were to draw any of the three other possible cards (K, Q, or ♣A), you would make one more trick and well over 66 points. So there is only a 1/4 probability of losing the deal and game, since only 1 of the 4 possible cards you might draw is a loser. Not bad at all.

But why take even this small risk, when there is a play that guarantees you the win? You don’t have to beat Katharina’s Q back at trick 5. You can discard something from your hand instead. That ♣T you are holding is a liability, because it will likely fall to Katharina’s ♣A. Why not pitch it on the Q? That’s a lot of points to give away voluntarily, but it will only bring her total up to 63. If you do this, Katharina draws the mystery card and you draw the J, resulting in this position:

Katharina: (63 points)
K
QJ
♣ A
K

You: (17 points)
ATQJ

♣ —
T

Quite a change in your hand from the position shown earlier, right? In fact, despite Katharina’s 63-17 lead, she cannot take another trick. You will collect all the remaining tricks, and plenty of points (77 in total) to win. You win with probability 100%, not just 75%.

In bridge, this type of play is known as a safety play. You may enjoy the thrill of drawing the mystery card, but I would rather play it safe.

© 2012 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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