The Schnapsen Log

Protection (solution)

Martin Tompa

Despite your training, I know how tempting it is to take Peter’s juicy ♣T with your ♣A. But what if you draw something useless such as ♣J from the stock?

No, let’s start where you know by now that you should start, by considering what happens if you duck this trick. If you duck with the obvious discard of ♠K, the only card that doesn’t look essential, this will be the position after drawing from the stock:

Peter: (45 points)
♠ —
♥ Q
♣ KJ
♦ AK

You: (21 points)
♠ —
♥ KJ
♣ A
♦ TQ

Looking at your ♦TQ, even one trick earlier, should make you very nervous. This is a holding that screams, “Endplay danger”. What do you imagine is going to happen from this position? Peter will lead either a heart or a club to throw you in. You can then cash all your hearts and clubs, which will bring you up to 47 trick points. But after that you will be forced to open up the diamond suit, and Peter will score enough points to win 1 game point.

Let’s not abandon the idea of ducking trick 5 just yet. Is there another discard you can find on Peter’s lead of ♣T? The only other possible discard is a diamond. Probably you felt that you can’t discard ♦Q, because you need it as protection for your ♦T. But what we’ve just seen from Peter’s throw-in play is that ♦Q is useless as protection in this situation. You might as well consider discarding it on his ♣T then. The advantage of this is that you don’t hand Peter the points of your discarded ♠K in addition to your ♦TQ later. Here is the position if you discard ♦Q on his ♣T.

Peter: (44 points)
♠ —
♥ Q
♣ KJ
♦ AK

You: (21 points)
♠ K
♥ KJ
♣ A
♦ T

The only trick Peter can make after this is ♦A, capturing your unprotected ♦T and bringing his trick point total to only 65. This means that the winner is going to be the player who takes the last trick. As long as you lead your losing ♦T as soon as you gain the lead, you cannot be stopped from winning all the other tricks, and in particular the last one. Ducking with ♦Q means you win 1 game point rather than losing. This is a good result for you.

Are we done with the analysis? Not quite. Because Peter only had 31 trick points when he led ♣T at trick 5, there is a possibility that you might be able to win 2 game points by taking this trick rather than the 1 game point you will win by ducking. You probably don’t want to win this trick with a ducking ruff (that is, by trumping ♣T), because that would use up your master trump ♥K. So let’s consider instead what will happen if you win the trick in the obvious way with ♣A. This will bring your trick point total to 42, and eventually cashing your master trump will add another 6 trick points for 48.

The result will now depend on what you draw from the stock. If it is either ♥Q or ♦K, the resulting marriage would give you enough trick points, and you will earn 2 game points. If you draw ♣J you will lose 1 game point. This will be the position with you on lead:

Peter: (31 points)
♠ —
♥ QJ
♣ K
♦ AK

You: (42 points)
♠ K
♥ K
♣ J
♦ TQ

You do have an elimination play from this position, but it isn’t quite sufficient. You can cash ♥K for your 48 trick points and then throw Peter in by leading ♠K.

Peter: (38 points)
♠ —
♥ —
♣ K
♦ AK

You: (48 points)
♠ —
♥ —
♣ J
♦ TQ

While it’s true that Peter would have to be the one to open up the diamond suit from this position, it doesn’t give you enough points. He can lead ♦K immediately and then will take the last two tricks and 1 game point.

If, instead of drawing ♣J from the stock, you draw ♣K, this is the resulting position:

Peter: (31 points)
♠ —
♥ QJ
♣ J
♦ AK

You: (42 points)
♠ K
♥ K
♣ K
♦ TQ

♣K is just enough of a draw to make the elimination work. You cash ♥K and ♣K, resulting in this position:

Peter: (31 points)
♠ —
♥ Q
♣ —
♦ AK

You: (54 points)
♠ K
♥ —
♣ —
♦ TQ

Now when you lead ♠K to throw Peter in, he must open up the diamond suit, and winning your ♦T will give you enough trick points and 1 game point.

The last possible card you can draw from the stock is ♦A, which would result in this position:

Peter: (31 points)
♠ —
♥ QJ
♣ KJ
♦ K

You: (42 points)
♠ K
♥ K
♣ —
♦ ATQ

You cannot reach 66 trick points from here, because ♥K and ♦A are your only winners. But Peter cannot reach 66 trick points either, and careful play will get you the last trick. Cash ♥K and lead ♠K to put Peter on lead from this position:

Peter: (38 points)
♠ —
♥ —
♣ KJ
♦ K

You: (48 points)
♠ —
♥ —
♣ —
♦ ATQ

There is nothing Peter can do to prevent you from taking the last trick with a diamond. He can cash two clubs first, but his trick point total will be only 57.

Let’s put this all together now and calculate the expected number of game points you will win if you take ♣T with ♣A at trick 5. There are two cards (♥Q, ♦K) you can draw to win 2 game points, two cards (♣K, ♦A) you can draw to win 1 game point, and one card (♣J) you can draw to lose 1 game point. Your expected gain is thus ⅖(+2) + ⅖(+1) + ⅕(−1) = 1 game point, exactly the same as if you discarded ♦Q on Peter’s ♣T. Discarding ♦Q does act as a safety play, protecting you against the possibility of drawing the losing ♣J. On the other hand, winning his ♣T offers you the possibility of gaining 2 game points with lucky draws. What the expected game point analysis shows is that, in the long run, these two plays will average out to be equivalent.

© 2013 Martin Tompa. All rights reserved.

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