The Schnapsen Log

A Handful of Losers (solution)

Martin Tompa

You know by now that the first thing you should consider, when following to the last trick before the stock is exhausted, is ducking. It is much simpler, because you know what you will draw from the stock (♦T) and so you know exactly what the position will be one trick later.

The obvious discard to make on Katharina’s ♣A is ♠K, because this denies Katharina the possibility of cashing her valuable ♠T later. (There is nothing you can do about Katharina’s equally valuable ♣T, because you can’t discard both of your clubs on this one trick.) If you discard ♠K, one trick later Katharina will be on lead from this position:

Katharina: (34 points)
♠ TQ
♥ —
♣ TK
♦ Q

You: (36 points)
♠ —
♥ Q
♣ QJ
♦ TJ

Can you see what Katharina will do from here? She is going to begin a forcing defense by leading ♠Q for you to trump.

Katharina: (34 points)
♠ T
♥ —
♣ TK
♦ Q

You: (41 points)
♠ —
♥ Q
♣ QJ
♦ T

From this position, one possibility is for you to pull her trump and cash ♥Q. But she will discard ♣K, bringing your trick point total to only 61, and then she will take the last two tricks and win. If you lead anything other than ♦T from the diagrammed position, she will win the trick and force you again by leading ♠T, and trumping that will be the last trick you take. Either way, you lose 1 game point.

Back to trick 5, then, and let’s see if there is a better discard on Katharina’s ♣A. If the decision is going to come down to which of you takes the last trick, as now seems likely, then there is a subtle advantage to discarding ♣J rather than ♠K. Namely, this discard will leave Katharina with two nontrump suits that are longer than yours, spades and clubs. In the struggle for the last trick, these longer suits are a liability. If you discard ♣J, here is the position one trick later, with Katharina on lead:

Katharina: (32 points)
♠ TQ
♥ —
♣ TK
♦ Q

You: (36 points)
♠ K
♥ Q
♣ Q
♦ TJ

Katharina’s two tens will only get her to 59 trick points, so it looks as though the decision will indeed come down to which of you takes the last trick. There are two possible ways Katharina can proceed from this position. The first is to cash one of her tens (giving it up as an entry in the last trick struggle) and then force you to trump by continuing that suit. It doesn’t matter which of her tens she chooses to cash, so let’s assume that it is spades. After you trump the second spade, you will be on lead from this position:

Katharina: (46 points)
♠ —
♥ —
♣ TK
♦ Q

You: (41 points)
♠ —
♥ Q
♣ Q
♦ T

You now force her back by leading ♥Q, putting her on lead from this position:

Katharina: (52 points)
♠ —
♥ —
♣ TK
♦ —

You: (41 points)
♠ —
♥ —
♣ Q
♦ T

You have executed a tempo endplay: she will get to 65 trick points by cashing ♣T, but then you win the last trick and 1 game point.

Let’s go back to the position at trick 6 and pursue the only other play Katharina can make.

Katharina: (32 points)
♠ TQ
♥ —
♣ TK
♦ Q

You: (36 points)
♠ K
♥ Q
♣ Q
♦ TJ

She can lead her trump ♦Q, which will put you on lead from this position:

Katharina: (32 points)
♠ TQ
♥ —
♣ TK
♦ —

You: (49 points)
♠ K
♥ Q
♣ Q
♦ J

Do you recognize this position and do you remember how to win from here? This is the signature position of the tempo squeeze! You have a loser in each of Katharina’s two-card suits (spades and clubs), one trump, and one squeeze card (♥Q). In the race for the last trick, you do not want to lead any suit in which Katharina has more cards than you. So you lead ♥Q instead, and Katharina is squeezed. She must discard one of her small black cards, and whichever one she chooses, you exit in that same suit. For instance, suppose she discard ♠Q on your ♥Q. You then exit by leading ♠K, and that leaves Katharina on lead in this position:

Katharina: (46 points)
♠ —
♥ —
♣ TK
♦ —

You: (55 points)
♠ —
♥ —
♣ Q
♦ J

You have again executed a tempo endplay, and will win the last trick with your remaining trump. The conclusion of the ducking analysis, then, is that you should discard ♣J rather than ♠K, and you will win 1 game point.

The only other thing to consider is whether you can do better by winning Katharina’s ♣A rather than ducking. But there is not much to consider, because of your fistful of losers. If you trump her ♣A with your only trump, ♦J, you will have 49 trick points, but Katharina will have most of the high cards. The only way that you will win the deal is by drawing one of your marriage partners from the stock, either ♠Q or ♣K. In those two cases, you will win 2 game points immediately by declaring the marriage. But any of the other three possible draws from the stock will give you only one additional trick, and Katharina is certain to win the last trick and 1 game point. Therefore, your expected gain if you trump her ♣A is ⅖(+2) + ⅗(−1) = 1/5 game points. This is considerably less than the 1 game point you will gain by making the correct duck.

This was a lengthy analysis, but an interesting one that made use of a number of different endplays.

© 2015 Martin Tompa. All rights reserved.

Comments