The Schnapsen Log
On the Brink of Success (solution)
Martin Tompa
You may be far ahead in trick points, but the only useful winner in sight for your future is ♥T. You might turn ♣K into a winner if you draw ♣J from the stock to protect it, but even if you succeed it will only bring you another 7 trick points, which is not enough. Your best chance is to focus on ♥T. But what is your best chance of turning ♥T into a winner?
Whatever card you might lead, there is a good chance that Katharina holds the winner in that suit. More precisely, there is a 5/6 probability that she does. What will happen if she wins this trick? I foresee a flurry of winners she will run. Count up the trick points she will accumulate if she cashes the top card in each suit. They sum up to a whopping 62 trick points that she will add to the 5 she already has, enough to win the deal without giving up a single trick.
What else can you do? What is it that you are supposed to consider first when you are on lead at the last trick before the stock is exhausted? Right, the first thing you should consider is closing the stock. How can that help you prevent Katharina from accumulating those 62 additional trick points? The answer is that any of those 4 top cards (♠T, ♥A, ♣T, ♦A) might still be in the stock when you close it. If so, the greatest number of additional trick points Katharina can pick up before leading ♥Q is 57, which would bring her total to only 62. All you have to do is hold on to ♥TK as long as you can; your other cards can all be discarded.
There is one more thing we need to consider: what card will you lead after closing the stock? You might be tempted to lead ♥K, in order to set up your ♥T as a winner. But this would be a mistake. If ♥A is in the stock, ♥Q will be Katharina’s contribution to the last trick you will take. Any lead other than a heart will be fine.
If you close the stock with either queen still in it, you will lose 2 game points. In the other four cases, you will win 2 game points. This means that the expected number of game points you will gain by closing the stock is ⅔(+2) + ⅓(−2) = 2/3. Compared to the 1 game point you will likely lose if you don’t close the stock, this is a good outcome.
© 2012 Martin Tompa. All rights reserved.
