The Schnapsen Log

Precarious Position (solution)

Martin Tompa

We know two of Phyllis’s five cards for a certainty: ♦K and ♠K. If I lead any card that she can trump with her ♦K, the game is over. The only lead she may not be able to take is my ♦T, if ♦A is still in the stock. Since there are 8 cards whose whereabouts are unknown, and 5 of them are still in the stock, the probability that ♦A is still in the stock is 5/8. (Peter will explain if you are confused by this.)

Now, if I do not close the stock and lead ♦T, my only hope of crossing the 33 trick point threshold is to draw either ♦A or ♥Q (for the marriage) from the stock immediately. Since I can draw any of the 8 unseen cards, only 2 of which give me a success, my probability of getting to 33 without closing the stock is only 2/8, not so good. (In fact, it is somewhat less than 2/8, because drawing the ♥Q still requires ♦A to be somewhere in the stock.) But if I instead close the stock and the ♦A is still in it, can I get to 66 trick points? With the worst hand Phyllis might be holding (meaning the fewest trick points to contribute to me) the position would look like this. (Remember that I knew two of her cards.)

Phyllis: (65 points)
♠ KJ
♥ TJ
♣ —
♦ K

Me: (13 points)
♠ —
♥ AK
♣ AT
♦ T

Notice that I have given her the ♥T so that my ♥K is not a winner. If I cash my four winners (♦T first, of course), I will end up with my original 13 points plus 42 from my hand plus at least 12 from Phyllis’s, which comes to 67 trick points, just enough to win the game.

Given the choice of closing the stock and winning the game with probability 5/8, or leaving the stock open and not immediately losing with probability less than 2/8, it was an easy choice. I closed the stock. It is a form of desperation play, grasping my only chance of success, that the ♦A is still in the stock.

Let Phyllis’s play be a lesson to all of you: if you declare the trump marriage at trick 1 and have even the possibility of another marriage, lead the trump king rather than queen. That way, if your opponent discards a jack, the next marriage will give you 66 rather than 65 trick points and you will win 3 game points rather than risk losing 1.

With additional kisses,
your Hans.

© 2013 Martin Tompa. All rights reserved.

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