The Schnapsen Loghttp://psellos.com/schnapsen/blog/Martin Tompa2017-06-23T22:21:43ZXML::Atom::SimpleFeedHomework on Expected Valueshttp://psellos.com/schnapsen/blog/2017/04/136-homework.html2017-04-26T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">April 26, 2013</div>
<h2 id="homeworkonexpectedvalues">Homework on Expected Values</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- expectation -->
<p>For regular readers of this column, I apologize for the fact that I
have been producing columns at a slower rate recently. The slow rate
is probably going to continue for the next few months. I haven’t been
idle on the Schnapsen front, however. I am busy teaching a <a href="http://www.cs.washington.edu/education/courses/cse312/13sp/">course on
Probability and Statistics</a>, and am using Schnapsen as a
running example of applications of Probability. It’s been fun
teaching Schnapsen to a large group of students who had never
encountered it before.</p>
<p>In the course, we are just up to the topic of <em>expected value</em> now, so
it seems appropriate to give them a homework exercise that involves
<a href="http://psellos.com/schnapsen/blog/2013/04/../../2012/04/010-expected.html">expected game points</a>. Today’s column is that homework
exercise. This means that I won’t be posting my analysis until one
week from now, when the homework will be due.</p>
<hr></hr>
<p>You have just started a new game against the Maestro. On the
very first deal, you reach the following interesting position:</p>
<blockquote>
<p><strong>Unseen cards:</strong> <br />
<big>♠</big> Q <br />
<span style="color:red">♥</span> KJ <br />
♣ TK <br />
<span style="color:red"><big>♦</big></span> A </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> A <br />
<span style="color:red">♥</span> ATQ <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> T </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Maestro 7, You 7 <br />
<strong>Trick points:</strong> Maestro 21, You 18 <br />
<strong>On lead:</strong> Maestro </p>
</blockquote>
<p>The Maestro fingers each card in his hand in turn, and finally leads
<span style="color:red"><big>♦</big></span>A. There have been no marriages declared, and no one did a trump
exchange. You should assume that each of the five cards you haven’t
seen is equally likely to be the last face-down card in the stock.</p>
<p>Plan your play for the rest of the hand. In particular, answer
the following questions:</p>
<p>(a) How will the deal play out if you <a href="http://psellos.com/schnapsen/blog/jargon.html">duck</a> this trick?
Who will win, and how many game points?</p>
<p>(b) How will the deal play out if you win this trick? In this case,
you will draw the random, face-down card from the stock and the
Maestro will draw the face-up <big>♠</big>J. Consider each of the five cards
you might draw and, for each one, find your best play and the
resulting number of game points you will win or lose. Combine these
appropriately to determine the <a href="http://psellos.com/schnapsen/blog/2013/04/../../2012/04/010-expected.html">expected number of game
points</a> that you will win.</p>
<p>(c) Based on your answers, will you duck the Maestro’s <span style="color:red"><big>♦</big></span>A or trump
it? Why?</p>
<p>Once your homework has been turned in a week from now, you will be
able to read my <a href="http://psellos.com/schnapsen/blog/2013/04/063-homework-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2013 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Thoughtful Actionshttp://psellos.com/schnapsen/blog/2017/03/135-thoughtful.html2017-03-25T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">March 25, 2017</div>
<h2 id="thoughtfulactions">Thoughtful Actions</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- tempo squeeze -->
<p>You have begun another game against Uncle Tibor. In the very first
hand, you reach a point where some thought seems required.</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> AQ <br />
<span style="color:red">♥</span> Q <br />
♣ TQ <br />
<span style="color:red"><big>♦</big></span> T </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> K <br />
<span style="color:red">♥</span> AJ <br />
♣ K <br />
<span style="color:red"><big>♦</big></span> K </p>
<p><strong>Trump:</strong> <span style="color:red"><big>♦</big></span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Tibor 7, You 7 <br />
<strong>Trick points:</strong> Tibor 33, You 20 <br />
<strong>On lead:</strong> Tibor </p>
</blockquote>
<p>There have been no marriages declared and no trump exchange.
Tibor does his fair share of thinking and then leads <span style="color:red">♥</span>Q.</p>
<p>This will be a two-part puzzle. For now, just decide what card you
will play on this trick. When you have an answer, you are welcome to
read my <a href="http://psellos.com/schnapsen/blog/2017/03/135-thoughtful-decision.html">analysis</a>. Once we have finished this trick, I will give
you a second puzzle to work on.</p>
<blockquote>
<p>© 2017 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Noble Sacrificehttp://psellos.com/schnapsen/blog/2017/03/134-noble.html2017-03-04T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">March 4, 2017</div>
<h2 id="noblesacrifice">Noble Sacrifice</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- desperation, elimination, unblock -->
<p>Your game against Uncle Tibor must draw to a close with this deal,
because the game point score is now tied 1:1.</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> TQ <br />
<span style="color:red">♥</span> Q <br />
♣ AT <br />
<span style="color:red"><big>♦</big></span> T </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> AKJ <br />
<span style="color:red">♥</span> K <br />
♣ J <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Trump:</strong> ♣Q <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Tibor 1, You 1 <br />
<strong>Trick points:</strong> Tibor 32, You 15 <br />
<strong>On lead:</strong> Tibor </p>
</blockquote>
<p>Tibor thinks a bit and then, to your dismay, closes the stock. Your
prospects do not look good and you feel your pulse start to race.</p>
<p>Tibor plays ♣A followed by ♣T. What is your plan? When you are
ready, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2017/03/134-noble-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2017 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Carpe Diemhttp://psellos.com/schnapsen/blog/2017/02/133-carpe.html2017-02-10T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">February 10, 2017</div>
<h2 id="carpediem">Carpe Diem</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close -->
<p>The game against your dangerous Uncle Tibor continues, with your
clever Uncle Hans looking on. After the earlier disastrous deal that
left you behind with the game point scores 1:4, you scored 2 game
points on the next one, bringing both of you within striking distance
of winning the whole game. One deal later, you find yourself in the
following position:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> A <br />
<span style="color:red">♥</span> AJ <br />
♣ K <br />
<span style="color:red"><big>♦</big></span> AQ </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> K <br />
<span style="color:red">♥</span> KQ <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> TK </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Tibor 1, You 2 <br />
<strong>Trick points:</strong> Tibor 12, You 39 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>No one has declared a marriage yet, but you do know from an earlier
trump exchange that Tibor is holding <big>♠</big>A. You pull both hearts from
your hand and show them to Tibor to claim the marriage, giving you 59
trick points. You are just about to return <span style="color:red">♥</span>K to your hand when you
pause and then, with both cards still in your outstretched hand, go
into a trance. Finally coming out of it, you excitedly say, “Watch
this, Hans!”, return the queen to your hand, and lead <span style="color:red">♥</span>K.</p>
<p>Tibor thinks for a moment and then wins the trick with <span style="color:red">♥</span>A. After
drawing the last cards from the stock, this is the position:</p>
<blockquote>
<p><strong>Tibor:</strong> (27 points) <br />
<big>♠</big> A <br />
<span style="color:red">♥</span> J <br />
♣ K <br />
<span style="color:red"><big>♦</big></span> AQ </p>
<p><strong>You:</strong> (59 points) <br />
<big>♠</big> KJ <br />
<span style="color:red">♥</span> Q <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> TK </p>
</blockquote>
<p>There is not much left that Tibor can do. He can cash one or two of
his aces in order to get beyond 33, but eventually must concede the deal.</p>
<p>“Very nicely done, dear,” Tibor congratulates you as he gives you 1
game point to tie the score 1:1.</p>
<p>“Thanks, Tibor! Hans, did you notice the difference between leading
<span style="color:red">♥</span>Q and <span style="color:red">♥</span>K?” you inquire happily. “I almost led the queen out of
habit. But then I realized that Tibor could discard his losing <span style="color:red"><big>♦</big></span>Q on
it. And then, unless I make the very lucky draw of <span style="color:red">♥</span>A from the
stock, I would have been on lead in a position like this.” You move
some cards around on the table.</p>
<blockquote>
<p><strong>Tibor:</strong> (12 points) <br />
<big>♠</big> AJ <br />
<span style="color:red">♥</span> AJ <br />
♣ K <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>You:</strong> (65 points) <br />
<big>♠</big> K <br />
<span style="color:red">♥</span> K <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> ATK </p>
</blockquote>
<p>“I can’t make another trick from this position, and Tibor will be the
one to score a game point,” you conclude. “The same is true if I draw
♣K or <span style="color:red">♥</span>J from the stock instead of <span style="color:red"><big>♦</big></span>A.”</p>
<p>“Very true, dear,” Hans agrees. “Did you also think about what would
have happened if Tibor had ducked your actual lead of <span style="color:red">♥</span>K?”</p>
<p>“Yes, I did,” you reply. “With the <span style="color:red">♥</span>K lead, Tibor can’t afford to
discard his losing <span style="color:red"><big>♦</big></span>Q, because that gives me 66 points. His only
possible discard is <span style="color:red">♥</span>J, giving me 65 points. Any diamond I draw from
the stock gives me 2 game points instead of 1. The other two cards
left for me to draw are ♣K and <span style="color:red">♥</span>A, either of which leaves me on lead
in a position like this.” You move a few cards to illustrate.</p>
<blockquote>
<p><strong>Tibor:</strong> (12 points) <br />
<big>♠</big> AJ <br />
<span style="color:red">♥</span> — <br />
♣ K <br />
<span style="color:red"><big>♦</big></span> AQ </p>
<p><strong>You:</strong> (65 points) <br />
<big>♠</big> K <br />
<span style="color:red">♥</span> AQ <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> TK </p>
</blockquote>
<p>“I can’t stop Tibor from passing 33 trick points,” you conclude. “He
can cash his four winners to get to … let’s see … 12, 27, 32, 47,
62 … yes 62 trick points. Not quite enough. And then he has to
lead <span style="color:red"><big>♦</big></span>Q, that key loser I didn’t want him to discard earlier. I win
1 game point, just like I actually did when Tibor didn’t duck.”</p>
<p>“A very thorough analysis of your play, dear,” Hans compliments you,
causing you to beam at his uncharacteristic praise. “But did you have any
better play?” he continues in more characteristic style. </p>
<p>Your smile fades. What does Hans have in mind? When you think you
know, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2017/02/133-carpe-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2017 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->The Glass is 9/10 Fullhttp://psellos.com/schnapsen/blog/2017/02/132-glass.html2017-02-02T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">February 2, 2017</div>
<h2 id="theglassis910full">The Glass is 9/10 Full</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close, safety -->
<p>All your aunts and uncles and cousins are at your home again
today for a cheerful, boisterous gathering. As usual, there is a card
game involved. You are once again pitted against your Uncle Tibor,
with clever Uncle Hans looking over your shoulder. Midway through the
game you shuffle, deal out the cards, and look down at this starting
hand: </p>
<blockquote>
<p><strong>Your cards:</strong> <br />
<big>♠</big> KQ <br />
<span style="color:red">♥</span> — <br />
♣ A <br />
<span style="color:red"><big>♦</big></span> AQ </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Stock:</strong> 9 face-down cards <br />
<strong>Game points:</strong> Tibor 4, You 3 <br />
<strong>Trick points:</strong> Tibor 0, You 0 <br />
<strong>On lead:</strong> Tibor </p>
</blockquote>
<p>Your pulse quickens as you think about the possibilities. Any hand
containing the royal marriage and two outside aces is a beautiful
starting hand. You have a real chance of landing 3 game points and
the whole game. Wouldn’t it be something to beat Uncle Tibor for
once? As Tibor contemplates his opening lead, your one concern is
that he may lead a heart. But, joy of joys, he finally leads <span style="color:red"><big>♦</big></span>J and
you grin. You can taste the sweet victory already.</p>
<p>You win the trick with your <span style="color:red"><big>♦</big></span>Q and draw the useless ♣J from the
stock, but this doesn’t dampen your glee at all. You close the stock
and show your trump marriage, fully expecting to score both of your
aces for plenty of points. </p>
<p>To your surprise, Tibor plays <big>♠</big>A and follows it with <big>♠</big>T, pulling
your last trump and leaving you with these cards:</p>
<blockquote>
<p><strong>Your cards:</strong> <br />
<big>♠</big> — <br />
<span style="color:red">♥</span> — <br />
♣ AJ <br />
<span style="color:red"><big>♦</big></span> A </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Trick points:</strong> Tibor 28, You 45 <br />
<strong>On lead:</strong> Tibor </p>
</blockquote>
<p>Your smile fades and you suddenly feel a bit dizzy. Tibor leads <span style="color:red">♥</span>Q,
on which you discard ♣J. And then Tibor leads <span style="color:red">♥</span>T, and your own
heart sinks. You are forced to discard one of your beautiful aces.
What is much worse is that your only remaining hope of reaching 66 is
that Tibor’s last card is ♣T or <span style="color:red"><big>♦</big></span>T and you’ve saved the right ace.
You have gone from riches to rags in 10 seconds!</p>
<p>You see very little evidence to help you choose which ace to discard.
Finally, thinking that it would be like your aggressive Uncle Tibor to
have led the jack from <span style="color:red"><big>♦</big></span>TJ at trick 1, you discard ♣A on his heart.
To add insult to severe injury, Tibor’s last card is ♣T, and he is
the one who scores 3 game points.</p>
<p>You turn to Uncle Hans, who has watched the whole deal and is fully
ready for your outburst. “Can you believe my luck, Hans?” you
whine. “That Tibor should have both high trumps, plus two hearts?
And that he should choose to play out those two hearts and squeeze me?
And then I still had a chance to win, and guessed the wrong ace to
discard. Have you ever seen anyone with such bad luck?”</p>
<p>Kind Uncle Hans commiserates. “That was indeed some of the worst luck
imaginable, dear,” he says. “The odds of Tibor having all those
terrible cards were tiny.” Hans pauses for a moment before going on.
“And yet, my dear, can you think of something you could have done
differently that might have saved you?”</p>
<p>Do you see what Hans has in mind? When you have your answer ready,
you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2017/02/132-glass-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2017 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->The Battle and the Warhttp://psellos.com/schnapsen/blog/2017/01/131-heat.html2017-01-17T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">January 17, 2017</div>
<h2 id="thebattleandthewar">The Battle and the War</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close -->
<p>You are near the end of a very tight game against a lucky opponent.
Each of you is within 1 or 2 game points of winning when you find
yourself on lead in the following position: </p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> Q <br />
<span style="color:red">♥</span> AKJ <br />
♣ AKQ <br />
<span style="color:red"><big>♦</big></span> J </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> AK <br />
<span style="color:red">♥</span> TQ <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> A </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Stock:</strong> 3 face-down cards <br />
<strong>Game points:</strong> Opponent 1, You 2 <br />
<strong>Trick points:</strong> Opponent 7, You 32 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>No one has declared a marriage or exchanged the trump. What should
you do? When you have your answer ready, you are welcome to read my
<a href="http://psellos.com/schnapsen/blog/2017/01/131-heat-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2017 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->If Worse Comes to Worsthttp://psellos.com/schnapsen/blog/2016/12/130-worse.html2016-12-14T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">December 14, 2016</div>
<h2 id="ifworsecomestoworst">If Worse Comes to Worst</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close, elimination -->
<p>It has been a long time since I have written a column, for which I
apologize to you, my dear reader. I promise to restart with a gentle
puzzle and solution.</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> — <br />
<span style="color:red">♥</span> KJ <br />
♣ TKJ <br />
<span style="color:red"><big>♦</big></span> J </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> AT <br />
<span style="color:red">♥</span> Q <br />
♣ AQ <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Opponent 7, You 7 <br />
<strong>Trick points:</strong> Opponent 30, You 26 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>You are playing against an opponent who you believe does not play as
well as you do. You find yourself on lead in the diagrammed
situation. No one has declared a marriage. What would you do? When
you have your answer ready, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2016/12/130-worse-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2016 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Keep Calmhttp://psellos.com/schnapsen/blog/2016/04/129-calm.html2016-04-09T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">April 9, 2016</div>
<h2 id="keepcalm">Keep Calm</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- desperation, inference, role reversal -->
<p>In this third round of the regional tournament you have been pitted
against Rudi, whom you have found to be an exceptionally challenging
opponent. In the previous deal you finally took over the game point
lead, and both of you are now within striking distance of winning the
game. And then this disaster occurs:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> TQ <br />
<span style="color:red">♥</span> TKQJ <br />
♣ AQ <br />
<span style="color:red"><big>♦</big></span> TQ </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> AK <br />
<span style="color:red">♥</span> A <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> AJ </p>
<p><strong>Trump:</strong> ♣J <br />
<strong>Stock:</strong> 5 face-down cards <br />
<strong>Game points:</strong> Rudi 3, You 2 <br />
<strong>Trick points:</strong> Rudi 60, You 0 <br />
<strong>On lead:</strong> Rudi </p>
</blockquote>
<p>How did you get to a trick point score of 60:0 after only two tricks?
The answer is obvious: Rudi declared the royal marriage at trick 1,
led the king, and continued with the ten of trumps at 2. You
discarded a jack and a king on these two tricks, which comes to 60
trick points. In the diagrammed position, Rudi now does what you
feared: he closes the stock, which means that this deal will decide the
entire game. He then leads <big>♠</big>T.</p>
<p>Things look decidedly bleak, but it won’t do you any good to panic or
despair. What is your plan? When you think you have a good one, you
are welcome to read my <a href="http://psellos.com/schnapsen/blog/2016/04/129-calm-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2016 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Homework on Expected Valueshttp://psellos.com/schnapsen/blog/2016/01/129-homework.html2016-01-26T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">April 26, 2013</div>
<h2 id="homeworkonexpectedvalues">Homework on Expected Values</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- expectation -->
<p>For regular readers of this column, I apologize for the fact that I
have been producing columns at a slower rate recently. The slow rate
is probably going to continue for the next few months. I haven’t been
idle on the Schnapsen front, however. I am busy teaching a <a href="http://www.cs.washington.edu/education/courses/cse312/13sp/">course on
Probability and Statistics</a>, and am using Schnapsen as a
running example of applications of Probability. It’s been fun
teaching Schnapsen to a large group of students who had never
encountered it before.</p>
<p>In the course, we are just up to the topic of <em>expected value</em> now, so
it seems appropriate to give them a homework exercise that involves
<a href="http://psellos.com/schnapsen/blog/2013/04/../../2012/04/010-expected.html">expected game points</a>. Today’s column is that homework
exercise. This means that I won’t be posting my analysis until one
week from now, when the homework will be due.</p>
<hr></hr>
<p>You have just started a new game against the Maestro. On the
very first deal, you reach the following interesting position:</p>
<blockquote>
<p><strong>Unseen cards:</strong> <br />
<big>♠</big> Q <br />
<span style="color:red">♥</span> KJ <br />
♣ TK <br />
<span style="color:red"><big>♦</big></span> A </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> A <br />
<span style="color:red">♥</span> ATQ <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> T </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Maestro 7, You 7 <br />
<strong>Trick points:</strong> Maestro 21, You 18 <br />
<strong>On lead:</strong> Maestro </p>
</blockquote>
<p>The Maestro fingers each card in his hand in turn, and finally leads
<span style="color:red"><big>♦</big></span>A. There have been no marriages declared, and no one did a trump
exchange. You should assume that each of the five cards you haven’t
seen is equally likely to be the last face-down card in the stock.</p>
<p>Plan your play for the rest of the hand. In particular, answer
the following questions:</p>
<p>(a) How will the deal play out if you <a href="http://psellos.com/schnapsen/blog/jargon.html">duck</a> this trick?
Who will win, and how many game points?</p>
<p>(b) How will the deal play out if you win this trick? In this case,
you will draw the random, face-down card from the stock and the
Maestro will draw the face-up <big>♠</big>J. Consider each of the five cards
you might draw and, for each one, find your best play and the
resulting number of game points you will win or lose. Combine these
appropriately to determine the <a href="http://psellos.com/schnapsen/blog/2013/04/../../2012/04/010-expected.html">expected number of game
points</a> that you will win.</p>
<p>(c) Based on your answers, will you duck the Maestro’s <span style="color:red"><big>♦</big></span>A or trump
it? Why?</p>
<p>Once your homework has been turned in a week from now, you will be
able to read my <a href="http://psellos.com/schnapsen/blog/2013/04/063-homework-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2013 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->An Endplay with Holeshttp://psellos.com/schnapsen/blog/2015/11/128-endplay.html2015-11-21T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">November 21, 2015</div>
<h2 id="anendplaywithholes">An Endplay with Holes</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close, elimination -->
<p>The game point scores against Rudi are getting closer in this third
round of the regional tournament. In the next deal, you find yourself
in the following position:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> TQJ <br />
<span style="color:red">♥</span> T <br />
♣ KJ <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> AK <br />
<span style="color:red">♥</span> K <br />
♣ Q <br />
<span style="color:red"><big>♦</big></span> Q </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Rudi 3, You 4 <br />
<strong>Trick points:</strong> Rudi 19, You 43 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>Plan your play. When you have a good plan, you are welcome to read my
<a href="http://psellos.com/schnapsen/blog/2015/11/128-endplay-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Maintain Controlhttp://psellos.com/schnapsen/blog/2015/11/127-maintain.html2015-11-05T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">November 5, 2015</div>
<h2 id="maintaincontrol">Maintain Control</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- last trick, force -->
<p>You have made a small comeback against Rudi in this third round of the
regional tournament. You then find yourself in the following endgame
position: </p>
<blockquote>
<p><strong>Rudi:</strong> (28 points) <br />
<big>♠</big> A <br />
<span style="color:red">♥</span> Q <br />
♣ K <br />
<span style="color:red"><big>♦</big></span> TK </p>
<p><strong>You:</strong> (31 points) <br />
<big>♠</big> QJ <br />
<span style="color:red">♥</span> T <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> AQ </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span> <br />
<strong>Stock:</strong> Exhausted <br />
<strong>Game points:</strong> Rudi 3, You 5 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>The stock is exhausted and the trick point scores are low. What is
your plan? When you have come up with a good one, you are welcome to
read my <a href="http://psellos.com/schnapsen/blog/2015/11/127-maintain-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Homework on Expected Valueshttp://psellos.com/schnapsen/blog/2015/10/126-homework.html2015-10-24T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">April 26, 2013</div>
<h2 id="homeworkonexpectedvalues">Homework on Expected Values</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- expectation -->
<p>For regular readers of this column, I apologize for the fact that I
have been producing columns at a slower rate recently. The slow rate
is probably going to continue for the next few months. I haven’t been
idle on the Schnapsen front, however. I am busy teaching a <a href="http://www.cs.washington.edu/education/courses/cse312/13sp/">course on
Probability and Statistics</a>, and am using Schnapsen as a
running example of applications of Probability. It’s been fun
teaching Schnapsen to a large group of students who had never
encountered it before.</p>
<p>In the course, we are just up to the topic of <em>expected value</em> now, so
it seems appropriate to give them a homework exercise that involves
<a href="http://psellos.com/schnapsen/blog/2013/04/../../2012/04/010-expected.html">expected game points</a>. Today’s column is that homework
exercise. This means that I won’t be posting my analysis until one
week from now, when the homework will be due.</p>
<hr></hr>
<p>You have just started a new game against the Maestro. On the
very first deal, you reach the following interesting position:</p>
<blockquote>
<p><strong>Unseen cards:</strong> <br />
<big>♠</big> Q <br />
<span style="color:red">♥</span> KJ <br />
♣ TK <br />
<span style="color:red"><big>♦</big></span> A </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> A <br />
<span style="color:red">♥</span> ATQ <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> T </p>
<p><strong>Trump:</strong> <big>♠</big>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Maestro 7, You 7 <br />
<strong>Trick points:</strong> Maestro 21, You 18 <br />
<strong>On lead:</strong> Maestro </p>
</blockquote>
<p>The Maestro fingers each card in his hand in turn, and finally leads
<span style="color:red"><big>♦</big></span>A. There have been no marriages declared, and no one did a trump
exchange. You should assume that each of the five cards you haven’t
seen is equally likely to be the last face-down card in the stock.</p>
<p>Plan your play for the rest of the hand. In particular, answer
the following questions:</p>
<p>(a) How will the deal play out if you <a href="http://psellos.com/schnapsen/blog/jargon.html">duck</a> this trick?
Who will win, and how many game points?</p>
<p>(b) How will the deal play out if you win this trick? In this case,
you will draw the random, face-down card from the stock and the
Maestro will draw the face-up <big>♠</big>J. Consider each of the five cards
you might draw and, for each one, find your best play and the
resulting number of game points you will win or lose. Combine these
appropriately to determine the <a href="http://psellos.com/schnapsen/blog/2013/04/../../2012/04/010-expected.html">expected number of game
points</a> that you will win.</p>
<p>(c) Based on your answers, will you duck the Maestro’s <span style="color:red"><big>♦</big></span>A or trump
it? Why?</p>
<p>Once your homework has been turned in a week from now, you will be
able to read my <a href="http://psellos.com/schnapsen/blog/2013/04/063-homework-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2013 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->When to Strikehttp://psellos.com/schnapsen/blog/2015/10/125-strike.html2015-10-15T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">October 15, 2015</div>
<h2 id="whentostrike">When to Strike</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- duck, squeeze -->
<p>You have progressed, admittedly struggling, to the third round of this
regional tournament by beating Katharina and others in the second.
You are now pitted against Rudi, a musician that you don’t know very
well. After the first few deals, you find yourself in this position:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> ATKQ <br />
<span style="color:red">♥</span> — <br />
♣ TQ <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> J <br />
<span style="color:red">♥</span> AQ <br />
♣ AK <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Rudi 3, You 7 <br />
<strong>Trick points:</strong> Rudi 25, You 21 <br />
<strong>On lead:</strong> Rudi </p>
</blockquote>
<p>Rudi has gotten an early game point lead, but in the current deal the
trick point scores are still low. Rudi considers his options and
finally leads <big>♠</big>K. Your mind races with possibilities for an endplay
in clubs, inferences about the last card in the stock, and wondering
if it will come down to who will win the last trick. What are you
going to do? When you have devised a good plan, you are welcome to
read my <a href="http://psellos.com/schnapsen/blog/2015/10/125-strike-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->To Close or Not To Closehttp://psellos.com/schnapsen/blog/2015/10/124-close.html2015-10-06T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">October 6, 2015</div>
<h2 id="tocloseornottoclose">To Close or Not To Close</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close, role reversal -->
<p>My friend Jeff showed me a very interesting hand he’d been dealt
recently, and we spent quite some time analyzing it. Here’s the
hand.</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> AKQJ <br />
<span style="color:red">♥</span> KJ <br />
♣ TKQJ <br />
<span style="color:red"><big>♦</big></span> TKQJ </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> T <br />
<span style="color:red">♥</span> AT <br />
♣ A <br />
<span style="color:red"><big>♦</big></span> A </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>Q <br />
<strong>Stock:</strong> 9 face-down cards <br />
<strong>Game points:</strong> Opponent 7, You 7 <br />
<strong>Trick points:</strong> Opponent 0, You 0 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>I’ve given you Jeff’s hand. It is the first trick of the first deal
of the game. You’ve been dealt this monster and you have the lead.
Should you close the stock? </p>
<p>It’s almost twice as likely that the critical <big>♠</big>A is still in the
stock than in your opponent’s hand, since your opponent holds only 5
cards and there are 9 cards face-down in the stock. If this is the
case and you close the stock, then you will take all 5 tricks
(starting with your trumps, of course). You have 53 trick points in
your hand, so you expect to get to 66 without breaking a sweat.</p>
<p>What if you close the stock and are unlucky enough that your opponent
holds <big>♠</big>A? Even in this case, if you run your other 4 winners
(starting with your trumps, of course), Jeff pointed out that your
opponent may well feel squeezed, if he or she holds one of those other
tens, ♣T or <span style="color:red"><big>♦</big></span>T. Your opponent will have to decide whether to hold
onto the ten or <big>♠</big>A, and in some cases may discard the wrong one and
your <big>♠</big>T will become a winner.</p>
<p>What are you going to do, close the stock or not? When you have made
your decision, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2015/10/124-close-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Judging the Book by its Coverhttp://psellos.com/schnapsen/blog/2015/09/bookcover.html2015-09-27T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">September 27, 2015</div>
<h2 id="judgingthebookbyitscover">Judging the Book by its Cover</h2>
<h4 id="martintompa">Martin Tompa</h4>
<div class="screenminiature" style="float:left; padding-right:5px; width:50%">
<a href="https://www.createspace.com/5627448">
<img src="http://psellos.com/schnapsen/blog/2015/09/cover.png" alt="Winning Schnapsen cover" width="100%"></img>
</a>
</div>
<p>In the most recent Schnapsen Log column I proudly announced my brand
new book <a href="http://psellos.com/schnapsen/blog/2015/09/../../2015/09/book.html"><em>Winning Schnapsen</em></a> and gave a detailed description
of what’s on the inside of the book. In today’s column I am excited
to discuss what’s on the outside: the artwork on the cover.</p>
<p>The artist who designed the cover is <a href="http://saulutions.com/">Saul Perkes</a>. I prefer to
call him “the wizard who designed the cover”, because when I look
at the cover what I see are ordinary playing cards that have been
enchanted.</p>
<p>All you Schnapsen players will readily identify the scene as a
standard Schnapsen hand containing the 20-point heart marriage. But
Saul has enchanted the marriage partners, bringing them to
life. They are happily married, holding hands and smiling at each
other. The King has his sword drawn, ready to attack your
opponent.</p>
<p>Let’s look at the original inanimate cards from which Saul started,
side by side with his animated marriage. The <a href="http://byronknoll.blogspot.com/2011/03/face-cards.html">original cards</a>,
shown below on the left, were generously placed in the public domain
by Byron Knoll. The instance of the marriage shown below on the
right comes from the spine of my book, where Saul placed it in
miniature.</p>
<div class="screenminiature" style="width:100%">
<img src="http://psellos.com/schnapsen/blog/2015/09/marriage.png" alt="Before and After" width="100%"></img>
</div>
<p>I particularly love the way Saul brought the Queen to life. He turned
her whole upper body to face her King, inclined her head slightly so
that we see more of her hair and headdress, and put a sweet smile on
her lips and in her eyes. The way both partners have broken out of
the confines of their cards is pure enchantment.</p>
<p>I am impressed with Saul’s talent in creating this Schnapsen imagery.
I am extremely grateful that he created it for the cover of my book.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Winning Schnapsenhttp://psellos.com/schnapsen/blog/2015/09/book.html2015-09-22T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">September 22, 2015</div>
<div class="screenminiature" style="float:right; width:30%">
<a href="https://www.createspace.com/5627448">
<img src="http://psellos.com/schnapsen/blog/2015/09/order-now-button.png" alt="Order Now" width="100%"></img>
</a>
</div>
<h2 id="winningschnapsen"><em>Winning Schnapsen</em></h2>
<h4 id="martintompa">Martin Tompa</h4>
<!--
Oct. 27: Amazon just put *Winning Schnapsen* on sale for $13.59,
instead of the list price of $16.99. I don't know how long this sale
will last, but it's a great discount. [Order
here](http://www.amazon.com/dp/1515377369/).
-->
<div class="screenminiature" style="float:left; padding-right:5px; width:40%">
<a href="https://www.createspace.com/5627448">
<img src="http://psellos.com/schnapsen/blog/2015/09/cover.png" alt="Winning Schnapsen cover" width="100%"></img>
</a>
</div>
<p>I am proud to announce my book, <em>Winning Schnapsen</em>, about the
most fascinating two-player card game. No one has ever written a book
about the intriguing winning strategy of Schnapsen, despite the game’s
300+ year history and despite certain similarities to the card game
Bridge, about which hundreds of books have been written. <em>Winning
Schnapsen</em> will be the definitive book on this game.</p>
<p>Schnapsen and its variants are popular throughout continental
Europe. Schnapsen is, in fact, the national card game of Austria,
where tournaments are played regularly. <em>Winning Schnapsen</em>
now brings the game to a global audience.</p>
<p>You do not need to know anything about the game when you start reading
<em>Winning Schnapsen</em>. Schnapsen is simple to learn, and the
book begins with the complete rules and some very general tips on
how to play. Each of the following chapters focuses on one particular
type of winning endgame play. The strategies are introduced
entirely through the use of thought-provoking, concrete examples from
the game, in a manner very similar to the daily newspaper’s bridge or
chess columns. Each such example is posed as a fun and challenging
puzzle on which you can test your mastery of that chapter’s strategy.
There are more than 100 of these puzzles in the book, each with an
illuminating analysis.</p>
<p>The analyses early in the book are simple and just require counting
and logical thinking. Later ones are more challenging, some using
elementary concepts from Probability Theory such as Mathematical
Expectation. These concepts are explained simply from first
principles, and understanding them does not require any math
background. Chapters 9-11 introduce some advanced endgame plays
that, until now, have been known only to a select group of Schnapsen
masters.</p>
<p><strong>Chapter 1</strong>, “Introduction to the Game”, introduces the wonderful
game of Schnapsen. The complete rules of the game are given in eight
easy-to-read pages. If you have never played a card game that
involves tricks and trumps, those basic concepts are explained in
simple terms. Chapter 1 closes with some very general strategy
guidelines, particularly aimed at beginners who are unfamiliar with
similar games.</p>
<p><strong>Chapter 2</strong>, “Basic Plays”, contains 9 puzzles that illustrate simple
but important endgame strategies. These include the safety play,
designed to protect the player against a small probability of failure,
and the diametrically opposite desperation play, designed to seize a
small probability of success by assuming the only distribution of
cards that would allow success.</p>
<p><strong>Chapter 3</strong>, “Force and Counterforce”, contains 9 puzzles that deal with
the critical issue of trump control in the endgame, and the means of
gaining such control when you do not already have it. The forcing
defense is the strategy of coercing your opponent to trump one of your
cards each time you obtain the lead. The counterforce play is an
interesting strategy that, in the right circumstances, counteracts the
forcing defense. The forcing defense comes from bridge, but the
counterforce is peculiar to Schnapsen and has no analogy in bridge.</p>
<p><strong>Chapter 4</strong>, “Throw-In and Elimination”, contains 12 puzzles that deal
with what is certainly the most important and most frequent endgame
coup. The idea will be familiar to advanced bridge players: you
orchestrate everything to put your opponent on lead in a position in
which he or she is compelled to lead from a vulnerable suit.</p>
<p><strong>Chapter 5</strong>, “Expectation”, uses 15 puzzles to introduce and practice an
important concept from Probability Theory that is used to deal with
the fact that you usually have imperfect information about the
distribution of the unseen cards. In most situations, some of these
distributions will lead to a win for you and some will lead to a
loss. When this is the case for each of two lines of play you could
choose, how should you decide which of them is superior? The answer
is given by the concept of Mathematical Expectation.</p>
<p><strong>Chapter 6</strong>, “Ducking Ruff”, contains 3 puzzles illustrating a play
peculiar to Schnapsen. In the ducking ruff play, it is advantageous
to trump a lead voluntarily that you could have won without using a
valuable trump.</p>
<p><strong>Chapter 7</strong>, “Tempo and the Last Trick”, contains 6 puzzles that
focus on the important rule that the winner of the very last trick
wins the deal, if neither player could claim a win before that trick.
The strategy for winning the last trick is subtle, and often quite
different from the rest of Schnapsen’s endgame strategy. You will
learn how to recognize situations where the decision will come down to
the last trick, and how to jockey for position to win it.</p>
<p><strong>Chapter 8</strong>, “Inference”, uses 4 puzzles to illustrate the advanced
topic of inferring the cards your opponent holds from the plays your
opponent has made.</p>
<p><strong>Chapter 9</strong>, “Squeezes”, contains 11 puzzles that illustrate a variety
of squeeze plays. These are advanced plays in which you reel off a
sequence of winning cards; in the process, your opponent is coerced to
discard something that, either directly or indirectly, establishes one
or more new winning cards in your hand. These plays are related to,
but necessarily different from, squeeze plays in bridge.</p>
<p><strong>Chapter 10</strong>, “Role Reversal”, contains the most challenging sorts
of analyses in the book, related to the inferences of Chapter 8. In
these analyses, illustrated by 4 puzzles, you must put yourself in
your opponent’s position and imagine which cards might be concealed
from your opponent and what your opponent would play in such a
situation.</p>
<p><strong>Chapter 11</strong>, “Deception”, contains another advanced strategy, in
which you make an unusual play whose purpose is to deceive your
opponent. This play can only succeed against an expert opponent who
is capable of drawing inferences (of the type discussed in Chapter 8)
about your cards from your play. The purpose of deception is to
induce your opponent to draw the wrong inference about your cards and
thereby make the wrong play.</p>
<p>Finally, <strong>Chapter 12</strong>, “Endgame Review and Family Tale”, contains 31
puzzles that test your knowledge of endgame strategy from the previous
ten chapters. In those earlier chapters, you often had the artificial
advantage of knowing what sort of play to look for, based on the topic
of the chapter. Each puzzle in this final long series tests one or
more techniques that were introduced earlier. This is the realistic
situation that you face every time you are at the battlefield of the
Schnapsen table.</p>
<p>Something other than Schnapsen makes this book utterly unique and
personal. The 31 puzzles of this final chapter are bound together by
stories of my father’s family history in the turbulent years of Europe
from the aftermath of World War I in 1919 to the aftermath of World
War II in 1947. The stories deal with politics, the White Terror of
Hungary, persecution, arrests, bribery, deportations, the rise and
fall of Nazism, religion, danger, youth, mathematics, family bonds
and, of course, Schnapsen. The integration of family history and
games combines two passions of mine.</p>
<!--
**Appendices** provide a glossary of Schnapsen jargon, the synopses of
three technical mathematical publications that have a bearing on
Schnapsen strategy, and a survey of variants on the Schnapsen rules.
-->
<p>Using concrete examples and clear explanations, <em>Winning
Schnapsen</em> presents techniques that will increase your playing
skill, no matter how experienced you are. You can improve your game
dramatically by working through just one of the book’s puzzles each
day. If you do that, it will be as if I were your private tutor in
the comfort of your own home.</p>
<div class="screenminiature" style="float:right; width:30%">
<a href="https://www.createspace.com/5627448">
<img src="http://psellos.com/schnapsen/blog/2015/09/order-now-button.png" alt="Order Now" width="100%"></img>
</a>
</div>
<p><strong>Product Details:</strong></p>
<ul>
<li>452 pages</li>
<li>List price: $16.99</li>
<li>Trim size: 6 ⨯ 9 inches</li>
<li>Language: English</li>
<li>ISBN-10: 1515377369</li>
<li>ISBN-13: 978-1515377368</li>
</ul>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Nothing to Sparehttp://psellos.com/schnapsen/blog/2015/09/123-nothing.html2015-09-19T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">September 19, 2015</div>
<h2 id="nothingtospare">Nothing to Spare</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- elimination, last trick -->
<p>In this second round of the tournament, you are still 1 game point
away from vanquishing the formidable Katharina and moving on to the
next round. Meanwhile, she is slowly closing the gap.</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> AQ <br />
<span style="color:red">♥</span> TJ <br />
♣ KJ <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> TJ <br />
<span style="color:red">♥</span> AKQ <br />
♣ — <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Trump:</strong> <span style="color:red"><big>♦</big></span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 3, You 1 <br />
<strong>Trick points:</strong> Katharina 28, You 28 <br />
<strong>On lead:</strong> Katharina </p>
</blockquote>
<p>It’s a close game, with the trick point score exactly tied. Katharina
ponders for a few moments and then leads ♣K. You have no card you
feel you can spare from your hand. What are you going to do? When
you think you have a good plan, you are welcome to read my
<a href="http://psellos.com/schnapsen/blog/2015/09/123-nothing-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->The Glass is Slightly Fullhttp://psellos.com/schnapsen/blog/2015/09/122-glass.html2015-09-13T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">September 13, 2015</div>
<h2 id="theglassisslightlyfull">The Glass is Slightly Full</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- desperation -->
<p>You are close to vanquishing the formidable Katharina in the second round
of this tournament. Focus: it’s not time to rest on your laurels
quite yet!</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> AT <br />
<span style="color:red">♥</span> A <br />
♣ TQ <br />
<span style="color:red"><big>♦</big></span> Q </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> QJ <br />
<span style="color:red">♥</span> K <br />
♣ AK <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 4, You 1 <br />
<strong>Trick points:</strong> Katharina 33, You 33 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>You just need 1 more game point to win the game and move on to the
next round. Katharina declared the diamond marriage earlier in the
deal, and the trick point score is now exactly tied. What do you think
of your prospects? When you think you have a good plan, you are
welcome to read my <a href="http://psellos.com/schnapsen/blog/2015/09/122-glass-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Collector's Itemshttp://psellos.com/schnapsen/blog/2015/09/121-collectors.html2015-09-07T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">September 7, 2015</div>
<h2 id="collectorsitems">Collector’s Items</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close, force -->
<p>You have just passed Katharina’s game point score in the second round
of this tournament, but it could still be anyone’s game. In the middle
of the next deal, you are on lead from this position:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> ATK <br />
<span style="color:red">♥</span> A <br />
♣ TK <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> — <br />
<span style="color:red">♥</span> TQ <br />
♣ AQJ <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 4, You 3 <br />
<strong>Trick points:</strong> Katharina 14, You 25 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>You are missing the master trump and it doesn’t look as if you will be
able to run your club suit. How would you proceed? When you think
you have a good plan, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2015/09/121-collectors-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->A Handful of Losershttp://psellos.com/schnapsen/blog/2015/09/120-handful.html2015-09-02T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">September 2, 2015</div>
<h2 id="ahandfuloflosers">A Handful of Losers</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- duck, force, tempo endplay, tempo squeeze -->
<p>In the second round of the tournament, you continue what feels like an
interminable game against the flamboyant champion Katharina. You are
beginning to find it difficult to keep your focus, but you know that
one lapse could be fatal.</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> TQ <br />
<span style="color:red">♥</span> — <br />
♣ ATK <br />
<span style="color:red"><big>♦</big></span> Q </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> K <br />
<span style="color:red">♥</span> Q <br />
♣ QJ <br />
<span style="color:red"><big>♦</big></span> J </p>
<p><strong>Trump:</strong> <span style="color:red"><big>♦</big></span>T <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 4, You 4 <br />
<strong>Trick points:</strong> Katharina 19, You 36 <br />
<strong>On lead:</strong> Katharina </p>
</blockquote>
<p>Staring at your handful of losing cards, you find it difficult to
stifle a groan. But stifle you must, because you don’t want to give away
any useful information. Katharina concentrates on her cards for a
while and finally leads ♣A. Plan your play. When you think you have
a good plan, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2015/09/120-handful-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->The Best of All Worldshttp://psellos.com/schnapsen/blog/2015/08/119-best.html2015-08-28T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">August 28, 2015</div>
<h2 id="thebestofallworlds">The Best of All Worlds</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- elimination, tempo endplay, expectation -->
<p>Unfortunately, you got unlucky in the previous deal and Katharina
picked up 2 more game points. This put her slightly ahead of you
again. And then the next deal finds you in this position:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> AK <br />
<span style="color:red">♥</span> — <br />
♣ AKJ <br />
<span style="color:red"><big>♦</big></span> K </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> QJ <br />
<span style="color:red">♥</span> Q <br />
♣ TQ <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 4, You 5 <br />
<strong>Trick points:</strong> Katharina 19, You 42 <br />
<strong>On lead:</strong> Katharina </p>
</blockquote>
<p>No marriages have been declared. Katharina ponders for a long moment
and then leads <big>♠</big>A. Plan your play. When you think you have a good
plan, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2015/08/119-best-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->Rote Behaviorhttp://psellos.com/schnapsen/blog/2015/08/118-rote.html2015-08-23T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">August 23, 2015</div>
<h2 id="rotebehavior">Rote Behavior</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close, expectation -->
<p>You have pulled slightly ahead of the masterful Katharina in round 2
of the tournament. The next deal finds you on lead in this position:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> K <br />
<span style="color:red">♥</span> Q <br />
♣ AQ <br />
<span style="color:red"><big>♦</big></span> AK </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> — <br />
<span style="color:red">♥</span> T <br />
♣ TK <br />
<span style="color:red"><big>♦</big></span> QJ </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 6, You 5 <br />
<strong>Trick points:</strong> Katharina 12, You 41 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>No marriages were declared and neither player did a trump exchange.
Plan your play. When you think you have a good plan, you are welcome
to read my <a href="http://psellos.com/schnapsen/blog/2015/08/118-rote-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->On Leadhttp://psellos.com/schnapsen/blog/2015/08/117-lead.html2015-08-19T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">August 19, 2015</div>
<h2 id="onlead">On Lead</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- close, force -->
<p>In the very next deal of the tournament you find yourself on
lead in the following situation:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> — <br />
<span style="color:red">♥</span> TKQJ <br />
♣ AQ <br />
<span style="color:red"><big>♦</big></span> — </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> — <br />
<span style="color:red">♥</span> A <br />
♣ K <br />
<span style="color:red"><big>♦</big></span> AKJ </p>
<p><strong>Trump:</strong> ♣J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 6, You 7 <br />
<strong>Trick points:</strong> Katharina 25, You 48 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>This is a precarious position for you. Katharina probably has trump
control and a long suit to run, including a potential marriage. If
she were on lead, it’s a good bet that she would close the stock, pull
your trump, knock out your <span style="color:red">♥</span>A, and win the deal by running her
hearts. But Katharina is not on lead, you are. What is your plan?
When you think you have a good one, you are welcome to read my
<a href="http://psellos.com/schnapsen/blog/2015/08/117-lead-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->A Second Ounce of Preventionhttp://psellos.com/schnapsen/blog/2015/08/116-second.html2015-08-15T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">August 15, 2015</div>
<h2 id="asecondounceofprevention">A Second Ounce of Prevention</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- throw-in, unblock -->
<p>You have advanced to round 2 of the regional tournament. After a few
other opponents, you are pitted once again against Katharina. This is
the situation in the very first deal:</p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> A <br />
<span style="color:red">♥</span> T <br />
♣ AQ <br />
<span style="color:red"><big>♦</big></span> AK </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> J <br />
<span style="color:red">♥</span> — <br />
♣ KJ <br />
<span style="color:red"><big>♦</big></span> TQ </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 7, You 7 <br />
<strong>Trick points:</strong> Katharina 13, You 54 <br />
<strong>On lead:</strong> Katharina </p>
</blockquote>
<p>Your wonderful trick point score is due to a spade marriage at the
beginning of the deal. Katharina ponders for a moment, her eyes
concealed by a palm frond hanging down from her hat. She gives her
head a small shake to get the frond out of her way and, to your
surprise, closes the stock. She cashes <big>♠</big>A and then leads <span style="color:red">♥</span>T.</p>
<p>What is your plan? When you think you have a good one, you are
welcome to read my <a href="http://psellos.com/schnapsen/blog/2015/08/116-second-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->An Ounce of Preventionhttp://psellos.com/schnapsen/blog/2015/08/115-ounce.html2015-08-11T11:00:00-08:00<!--#include virtual="${Base_URL}/templates/header.html" --><h1 class="page-title">The Schnapsen Log</h1><div class="date">August 11, 2015</div>
<h2 id="anounceofprevention">An Ounce of Prevention</h2>
<h4 id="martintompa">Martin Tompa</h4>
<!-- safety -->
<p>In a regional tournament, you have survived nearly to the end of round
1 when you find yourself pitted against Katharina, whom you know to
be an intimidating opponent. On her head she sports another of her
outlandish hats, with vegetation and fruits sprouting out at
impossible angles. </p>
<blockquote>
<p><strong>Concealed cards:</strong> <br />
<big>♠</big> QJ <br />
<span style="color:red">♥</span> A <br />
♣ TK <br />
<span style="color:red"><big>♦</big></span> J </p>
<p><strong>Your cards:</strong> <br />
<big>♠</big> — <br />
<span style="color:red">♥</span> K <br />
♣ AQJ <br />
<span style="color:red"><big>♦</big></span> A </p>
<p><strong>Trump:</strong> <span style="color:red">♥</span>J <br />
<strong>Stock:</strong> 1 face-down card <br />
<strong>Game points:</strong> Katharina 2, You 1 <br />
<strong>Trick points:</strong> Katharina 47, You 48 <br />
<strong>On lead:</strong> You </p>
</blockquote>
<p>It has been a close match, and you need just one more game point. The
reason the trick point scores are so high is that you each declared a
marriage earlier in the deal, Katharina’s in spades and yours in
diamonds. You picked up that <span style="color:red">♥</span>K by a trump exchange.</p>
<p>Not to put any pressure on you, but a win of the current game is
critical to your tournament progress. What is your plan? When you
think you have a great one, you are welcome to read my <a href="http://psellos.com/schnapsen/blog/2015/08/115-ounce-solution.html">analysis</a>.</p>
<blockquote>
<p>© 2015 Martin Tompa. All rights reserved.</p>
</blockquote>
<hr></hr>
<!--#include virtual="${Base_URL}/templates/sb-footer.html" -->