The Schnapsen Log

Postponing Defeat (conclusion)

Martin Tompa

We can assume that Emmi will discard ♣J on your ♦Q if she has it, and ♦J if not. In either case, you will have 26 trick points at the end of that trick.

If you draw either ♠A or ♥K from the stock, running your winners will give you enough trick points: your ♦AT will collect Emmi’s ♦KJ, bringing you to 53 trick points. After that, cashing either ♠A or ♥KJ will force Emmi to discard ♠T, giving you plenty of trick points to win. Here is the position if you draw ♥K, in case you are having trouble visualizing it:

Emmi: (55 points)
♠ AT
♥ Q
♣ —
♦ KJ

You: (26 points)
♠ J
♥ KJ
♣ —
♦ AT

At the other extreme, if you draw either ♠T or ♥Q, your only winners are ♦AT and you will end at 53 trick points. As soon as you lead either a spade or heart, Emmi will cash ♠A to win, so be sure to cross the 33 trick point threshold beforehand. With each of these two draws, you lose 1 game point.

That leaves us to analyze the two jacks you might draw from the stock, and those are the ones where things get interesting. Let’s start with drawing ♣J, and assume that Emmi discarded ♦J on your ♦Q, since ♦J is useless to her. This leaves you on lead in this position:

Emmi: (55 points)
♠ AT
♥ KQ
♣ —
♦ K

You: (26 points)
♠ J
♥ J
♣ J
♦ AT

What will happen when you run ♦AT and ♣J, which is really the only way you can proceed? If Emmi discards ♠T and ♥Q, trying to preserve winners in each suit, you will reach 66 trick points exactly. So she is squeezed into discarding both of ♥KQ, which sets up a new winner for you, the lowly ♥J. When you cash that extra winner, she must finally discard ♠T anyway, giving you plenty of trick points.

It’s easy to see that the same squeeze will develop if you draw ♦J from the stock instead of ♣J: just substitute ♦J for ♣J in the diagram above and think it through.

This type of squeeze is different from ones we have encountered before. Setting up the critical new winner ♥J requires squeezing Emmi out of two higher hearts rather than just one. Because you have to squeeze her out of two cards, you need two squeeze cards yourself, ♦T and whichever jack you drew. Bridge players call this type of squeeze an extended squeeze.

Let’s conclude by calculating the expected number of game points you will win. There are 4 possible draws that each give you 1 game point, and 2 possible draws that each cause you to lose 1 game point. Therefore, your expected gain is ⅔(+1) + ⅓(−1) = 1/3 game point. It’s not a lot, but at least it’s positive, your reward for working out the extended squeeze.

© 2012 Martin Tompa. All rights reserved.

Comments