The Schnapsen Log

A Multitude of Options (conclusion)

Martin Tompa

If you leave the stock open, your best lead is probably ♥A, which allows you to retain the lead without giving up your black suit elimination plays. This lead will bring your trick point total to at least 40. If you draw either of your marriage partners ♠Q or ♣K from the stock, or draw ♣A, you can easily cash your winners and collect 2 game points. If you draw any of the other 3 possible cards, it will turn out that you can always win 1 game point by throwing Peter in.

Let’s start with the draw of ♠T from the stock. The best discard Peter could make on your ♥A lead is either ♠Q or ♣J. In either case, you can throw him in with a spade. Both are very similar, so let’s assume he discarded ♠Q. This leaves you on lead in this position:

Peter: (20 points)
♠ —
♥ J
♣ AKJ
♦ J

You: (41 points)
♠ ATK
♥ —
♣ TQ
♦ —

You now exit with ♠K. Peter trumps and can cash ♥J, on which you discard ♠T. But then he is endplayed and must open up the club suit, after which your ♣T and ♠A give you enough trick points to win 1 game point.

Suppose next that you were to draw ♣J from the stock. Peter’s best discard on your ♥A is either ♠Q or ♣K. If he discards ♠Q, you are left on lead in this position:

Peter: (20 points)
♠ T
♥ J
♣ AK
♦ J

You: (41 points)
♠ AK
♥ —
♣ TQJ
♦ —

You cash ♠A and then lead ♠K to throw him in. He can again cash ♥J, but then must open up the club suit and give you 1 game point.

If, instead, Peter discards ♣K on your ♥A, this is the resulting position:

Peter: (20 points)
♠ TQ
♥ J
♣ A
♦ J

You: (42 points)
♠ AK
♥ —
♣ TQJ
♦ —

This time, instead of throwing him in with a spade, you throw him in by leading ♣J. He can cash both of his jacks, on which you discard your remaining clubs, but is then endplayed and must yield both spade tricks to you for 1 game point.

The final case to consider is when you draw ♥J from the stock. In this case, you can eliminate spades and force Peter to open up the club suit and give you 1 game point. I’ll leave the details for you to work out.

The open-stock summary, then, is that if you lead ♥A, you will gain 2 game points if any of 3 cards remains in the stock, and will gain 1 game point if any of the other 3 remains in the stock. Therefore, your expected gain is ½(+2) + ½(+1) = 3/2.

It is an interesting question now to compare the best result if you close the stock with that if you leave the stock open. If you leave the stock open, you cannot lose the game and expect to gain 1.5 game points. If you close the stock, you can lose the whole game with probability 1/6, but gain 2 game points with probability 5/6. Which outcome would you prefer?

I actually think that it’s a very close decision. I have a slight preference for leaving the stock open and not risking losing the game on this deal.

© 2013 Martin Tompa. All rights reserved.

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