# The Schnapsen Log

## Threats (solution)

#### Martin Tompa

When the deal was over, Tibor told me he first considered ducking my ♥Q lead, which is absolutely the right first thing to try when following to the last trick before the stock is exhausted. He reconstructed this as the position after ducking, with me still on lead:

Peter:(25 points)

♠ AK

♥ J

♣ AQ

♦ —

Tibor:(35 points)

♠ TQ

♥ T

♣ KJ

♦ —

It looks like a position with endplay potential until you realize that neither player is going to reach 66 trick points. And with his spades and clubs dominated by mine, he could not possibly win the last trick. This means ducking would cost Tibor 1 game point, and he would do no worse by winning the trick. So he took my ♥Q with his ♥T.

Unfortunately for him, Tibor drew ♠A from the stock, so he was on lead from this position:

Peter:(20 points)

♠ K

♥ J

♣ AQJ

♦ —

Tibor:(48 points)

♠ ATQJ

♥ —

♣ K

♦ —

The only further trick Tibor could win was ♠A, and he lost his 1 game point just the same as if he had ducked.

Tibor was disappointed, because he had worked out that there were 3 cards he could have drawn from the stock, ♣AQ and ♠K, that would have allowed him to reach 66 trick points without giving me another trick, so he would have gained 2 game points. Drawing either of the other two, ♠A or ♥J, would cause him to lose 1 game point. I then asked Tibor if he recalled how to work out the expected number of game points he would gain and was pleased to see that he did it correctly: ⅗(+2) + ⅖(−1) = 4/5.

I then recreated the position on the table when I had led ♥Q at trick 5:

Unseen cards:

♠ AK

♥ QJ

♣ AQ

♦ —

Tibor’s cards:

♠ TQJ

♥ T

♣ K

♦ —

Trump:♣J

Trick points:Peter 20, Tibor 35

I asked him if he could see any other play he could have made. It did not take him long to arrive at the idea: if ducking was wrong, and winning with ♥T was wrong, the only other possibility was winning with ♣K. This is the play that you and I used to call a ducking ruff, and I told Tibor about how we discovered it. The advantage, I said, is that he would retain his ♥T as a winner for later. I rearranged the cards to construct what the position would have been, for instance, if he would draw the ♠A from the stock as had happened:

Peter:(20 points)

♠ K

♥ J

♣ AQJ

♦ —

Tibor:(42 points)

♠ ATQJ

♥ T

♣ —

♦ —

His eyes lit up when he saw the difference: though he had fewer trick points this way, he still had two trick he could cash, ♥T and ♠A, instead of just one, and these two tricks would have gotten him to 69 trick points. He would have gained 2 game points instead of losing 1.

We went through the other possible cards he might have drawn from the stock. Three of them, ♠K, ♣A, and ♥J had the same outcomes as the way Tibor had played, +2 for each of the first two and −1 for ♥J. I then rearranged the cards so that we could study the final case, in which he drew ♣Q:

Peter:(20 points)

♠ AK

♥ J

♣ AJ

♦ —

Tibor:(42 points)

♠ TQJ

♥ T

♣ Q

♦ —

This is an interesting position, and I let Tibor work it out on his own. After a few moments he had found the elimination play: cash ♥T to eliminate my heart exit card and then throw me in by leading ♣Q. I can cash my clubs and ♠A to reach 52 trick points, but eventually I must let him win his ♠T and 68 trick points. This is the only draw from the stock in which the ducking ruff is slightly worse than simply winning trick 5 with ♥T, 1 game point gained instead of 2.

We then worked through the expected gain if Tibor uses the ducking ruff, which is ⅗(+2) + ⅕(+1) + ⅕(−1) = 6/5 game points, somewhat better than the 4/5 game points we calculated earlier for winning trick 5 with the ♥T. Tibor seemed quite pleased to learn a brand new play.

With kisses from both of us,

your Peter.

© 2013 Martin Tompa. All rights reserved.