The Schnapsen Log

The Best of All Worlds (solution)

Martin Tompa

What is the first thing you should consider when following to the last trick before the stock is exhausted? Right, you should first consider ducking, because when you duck you know exactly what the position will be one trick later. So let’s start there.

The obvious discard is ♠J. If you make that discard, then one trick later Katharina will be on lead from this position:

Katharina: (32 points)
♠ K
♥ —
♣ AKJ
♦ K

You: (42 points)
♠ Q
♥ QJ
♣ TQ
♦ —

Do you see what is going to happen from here? Katharina has an elimination play. She will cash ♠K to remove your only safe exit card and then will lead ♦K to throw you in. You will be left on lead from this position:

Katharina: (39 points)
♠ —
♥ —
♣ AKJ
♦ —

You: (49 points)
♠ —
♥ J
♣ TQ
♦ —

You are endplayed: either this trick or the next you will have to open up the club suit, giving Katharina 28 more trick points for a total of 67.

That means we need to go back to your discard of ♠J at trick 5, which didn’t work. Your only other possible discard is ♣Q. I know, you hate the thought of leaving your ♣T unprotected. But from the elimination play we just witnessed, how much protection was your ♣Q really providing?

If you were to discard ♣Q on Katharina’s ♠A at trick 5, she would be on lead from this position one trick later:

Katharina: (33 points)
♠ K
♥ —
♣ AKJ
♦ K

You: (42 points)
♠ QJ
♥ QJ
♣ T
♦ —

You have deprived Katharina of one club trick, which is critical. If she were to cash ♠K and ♣A, she would only reach 60 trick points, not enough. So the decision is going to come down to which player wins the last trick. Remember how this works? Both players want to lead their losers, but avoid leading suits where the other player has more cards.

In this case, you want to avoid leading clubs. Katharina will begin by leading her losing ♦K for you to trump. You will then lead your losing ♠J, leaving Katharina on lead from this position:

Katharina: (39 points)
♠ —
♥ —
♣ AKJ
♦ —

You: (49 points)
♠ Q
♥ J
♣ T
♦ —

By avoiding the club suit, you have executed a tempo endplay. Katharina has no choice but to open up the club suit, after which you will take the remaining tricks and gain 1 game point. See how much better the ♣Q discard worked at trick 5?

Are we done thinking? Is there anything else to consider before playing to trick 5? Yes, there certainly is: Katharina has only 19 trick points, so it is possible that you can do better than winning 1 game point if you trump her ♠A rather than duck it.

If you do trump it, your own trick point total will be 56. Now we have to consider each of the 5 possible cards you could draw from the stock after winning the trick. If you draw ♣A, you can cash it immediately for 13 more trick points and a win of 2 game points. If you draw either ♣K or ♠K, that will complete your marriage and you will likewise win 2 game points.

The other two cards you might draw from the stock are ♦K and ♣J, which are both useless. Let’s assume you draw ♣J; the play if you draw ♦K is exactly the same. This is the position at trick 6, with you on lead:

Katharina: (19 points)
♠ K
♥ J
♣ AK
♦ K

You: (56 points)
♠ QJ
♥ —
♣ TQJ
♦ —

Clearly your only possible winner is ♣T, which would give you enough points. So you must lead ♠J to throw Katharina in. She can cash her spade, heart, and diamond, which will bring her to only 36 trick points. But then she will have to open up the club suit, and you will get your ♣T and 1 game point.

It is clear, then, that trumping Katharina’s ♠A at trick 5 is the best of all worlds: you will gain 2 game points with any of 3 draws from the stock, and will gain 1 game point with either of the other 2 draws. Therefore, your expected gain is ⅗(+2) + ⅖(+1) = 1.6 game points.

© 2015 Martin Tompa. All rights reserved.

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