\iftrue
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\font\top=cmbx10 scaled \magstep 2
\font\hbf=cmbx10 scaled \magstephalf
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\font\sc=cmcsc10
\font\top=cmbx10 scaled \magstep 2
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\newbox\colB
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\hsize=2.4in
\tolerance=5000
\hyphenpenalty=20
\linepenalty=200
\frenchspacing
\catcode`\@=13
\def@#1{%
\if s#1{$\spadesuit$}\else
\if h#1{$\heartsuit$}\else
\if d#1{\copy\Diam}\else
\if c#1{$\clubsuit$}\else
\if n#1{\sc nt}\else
\if -#1{$\bullet$}\fi\fi\fi\fi\fi\fi}
\def\>{$\Rightarrow$\ }
\catcode`\>=13
\def>{\ \tabb}
\def\x{{\sc x}}
\def\y{{\sc y}}
\def\z{{\sc z}}
\parskip=1pt
\parindent=0pt
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\setbox\plusbox\hbox{$^\plus$}
\ht\plusbox=0pt
\def+{\copy\plusbox}
\hoffset=-.3in
\voffset=-.5in
\advance\vsize by 1in
\def\jump{$j$}%\hat\jmath$}
\def\dbljump{$j\kern-2.5pt j$}%\hat{\hat\jmath}$}

\newbox\tmp
\catcode`\&=12

\catcode`\>=12
\def\startt{\widbid=0pt\def\build{}}
\def\endt{\widmean=\hsize \advance\widmean by -\widbid \relax \build}
\def\interject#1\\{\expandafter\def\expandafter\build\expandafter{\build
#1}}
\def\+#1\\{\edef\args{#1}\expandafter\parse\args\\}
\def\parse#1\tabb#2\\{\setbox\tmp\hbox{#1}%
\ifdim\wd\tmp>\widbid \widbid\wd\tmp\fi
\expandafter\def\expandafter\build\expandafter{\build
\hbox{\hbox to \widbid{\hfil #1}\vtop{\hsize=\widmean\relax
#2\par\kern1.5pt}}}}
\catcode`\>=13

\def\smallskip{\vskip2pt\relax}
%\catcode`\&=4
\let\tabb&
\newdimen\widbid
\newdimen\widmean
\def\heading#1{\smallskip\center{\bf #1}}
\def\Heading#1{\removelastskip\center{\hbf #1}}
\def\HEADING#1{\center{\top #1}\smallskip}
\def\then{\center{\vrule width .5\hsize height .4pt}}
\def\Then{\center{\vrule width .9\hsize height .8pt}\smallskip}
\def\center#1{\line{\hfil#1\hfil}}
\def\fone{{\sc f1r}}%For\-cing 1 round\kern-1pt.}}
\def\fgame{{\sc For\-cing to game.}}
\def\Game{\kern-1pt{\sc Game}}
\def\Slam{\kern-1pt{\sc Slam}}
\hfuzz=3pt
\hbadness=10000
%\raggedright
\nopagenumbers

\newbox\Ope\setbox\Ope=\hbox{(}\dp\Ope=0pt\ht\Ope=0pt
\newbox\Clope\setbox\Clope=\hbox{)}\dp\Clope=0pt\ht\Clope=0pt
\newbox\Diam\setbox\Diam=\hbox{$\diamondsuit$}\dp\Diam=0pt\ht\Diam=0pt
\catcode`\(=13\def({\noindent\copy\Ope\nobreak}
\catcode`\)=13\def){\penalty10000\copy\Clope}

\newcount\hours \newcount\minutes
\hours\time
\divide\hours by 60
\multiply\hours by 60
\minutes\time
\advance\minutes by -\hours
\divide\hours by 60
\newcount\column
\column=0
\output{\ifcase\column
\global\setbox\colA\box255
\global\column=1\relax
\or
\global\setbox\colB\box255
\global\column=2\relax
\or
\global\setbox\colC\box255
\setbox255=\vtop{\multiply\hsize by 3
\advance\hsize by 9pt
\hbox to \hsize{\box\colA\hfil\vrule\hfil\box\colB\hfil\vrule\hfil\box\colC}
%\vskip -.5in
$n$=Any level/$m$=Minimum bid/\jump=Single jump bid/% 
\dbljump=Double jump bid/ex=exactly/tx=tricks/$\tau$=transferred 
suit\par
{\sevenrm Bidding Cheat Sheet \the\day.\the\month.\the\year\ 
\number\hours:\number\minutes\quad 
\copyright\ 1993 Andrew Marc Greene}\par
}%
\shipout\box255
\global\setbox\colA=\vtop{}%
\global\setbox\colB=\vtop{}%
\global\setbox\colC=\vtop{}%
\global\column=0\relax
\fi
}

\HEADING{Opening Bids}
\startt
\+1@c@d > 13(12)+ pts, 3 cards, no 5-card major.  Usually stronger minor.\\
\+1@h@s > 13(12)+ pts, 5 cards (very rarely 4).  If 5-5 in majors,
prefer 1@h.\\
\+1@n > 15--17 pts, 3+ suits stopped, \hbox{4-3-3-3} or
\hbox{4-4-3-2}.\\
\+2@c > 20+ {\sc hcp}. \fone\\
\+2@d@h@s > 6--11 {\sc hcp}, ex 6 in \x, about 7 tx.\\
\+2@n > 20--22 pts, 4 suits stopped, \hbox{4-3-3-3}.\\
\+3\x\ > 6--11 {\sc hcp}, ex 7 in \x, about 7 tx.\\
\+4\x\ > 6--11 {\sc hcp}, ex 8 in \x, about 8 tx.\\
\endt
\Then
\HEADING{Takeout Doubles}
A direct double of 1\x{} is for takeout, and shows 12+~pts.\ with
support for all other suits, or 18+~pts.\ and any shape.  
(With 4 in 
each @h@s, it is permissible to double without support for the unbid 
minor.  With a singleton or void in \x{} one may shade to 10+~pts.
With 4-3-3-3 distribution one should avoid takeout doubles.)
\par
\heading{Responses}
If third hand passes, responses by doubler's partner are:\par
\startt
\+2\x\ > 13+\ pts, or 10--12 and 2 unbid 4+ majors, \fone\\
\+$m$\y\ > 0--9 pts, longest suit (pref.\ @h@s)\\
\+\jump \y\ > 10--12 pts, inv, 4+ if @h@s, 5+ if @c@d.\\
\+\dbljump \y\ > 0--9 pts, 6+ cards in \y\ (preempt)\\
\+1@n > 6--9(10), \x\ stopped, no 4+ unbid major.\\
\+2@n > 11(10)--12 pts, inv, \x\ stopped, no 4+ unbid
major\\
\+3@n > 13--16 pts, or 12 with a 5+ minor.\\
\endt
If third hand {\sc Rdbl}s, fourth hand may {\sc Pass};
if third hand bids, $m$\y\ indicates 6(5)--9 pts.\par
\heading{Doubler's Rebids}
If fourth hand jumped, cue-bid, or bid @n, further bidding is
natural.  Else:\par
\startt
\+{\sc Pass} > 0--15+ pts.\\
\+$m$\y\ > 16--18 pts.\ or so, 4+ cards in \y. If opener passes and
this bid is 3\y\ then 18--20 pts.\\
\+\jump\y\ > 19--20 pts.\ or so, 4+ cards in \y.\\
\+$m$\z\ > 18--20 pts, 5+ cards.  `\Game?'\\
\+\jump \z\ > 6+ good cards, 8--9 tricks.\\
\+1@n > 18--20 pts, \x\ stopped.\\
\+2@n > 19-21 pts (if a jump, 21-22 pts).\\
\+3@n > Better than 2@n, or 9 tricks.\\
\+$n$\x\ > 21+ pts, says nothing about \x, \fone\\
\endt
\eject

\HEADING{Responses to Notrump}
\startt
\+2@c > At least one 4-card major and 8+ pts, or a 5-card minor and
10+ pts. (Stayman)\\
\+2@d@h > 5 hearts\slash spades, 0+ pts.  If 5-4 in majors and 8+ pts,
use Stayman instead. Opener must bid 2@h/2@s. (Jacoby transfer)\\
\+2@s > 5-4 in minors, no 4-card major.  `\Game?'
(Minor-suit Stayman)\\
\+\lower\baselineskip\hbox{
\vbox{\hbox{2@n}\hbox{3@c}}%
\raise.5\baselineskip\hbox{$\Bigr\}$}}\ignorespaces
> 6(5) clubs\slash diamonds, 0+ pts. Opener must
bid 3@c/3@d. (Minor-suit transfer)\\
\endt
\Then
\Heading{Stayman}
\heading{Opener's Rebids after 2@c}
\startt
\+2@d > No 4-card major.\\
\+2@h > 4 hearts or 4 of both majors.\\
\+2@s > 4 spades, not 4 hearts.\\
\endt
\heading{Responder's Rebids}
\startt
\+2@h@s > 5-4 in majors, 8--9 pts.\\
\+2@n > 4 in an unbid major, 8--9 pts.\\
\+3@c@d > 5 cards, 10+ pts.\\
\+3@h@s > If a raise, 4 cards, 8--9 pts;
else, 5-4 in majors, 10--11 pts. `\Game!'\\
\+3@n > 4 in an unbid major, 10+ pts.\\
\+4@c > Gerber.\\
\endt
\Then
\Heading{Jacoby Transfers}
\heading{Responder's Rebids}
\startt
\+{\sc Pass} > 0--6 pts.\\
\+2@s > 6--9 pts, 5-5+ in @h@s. `\Game?'\\
\+2@n > 8--10 pts, \hbox{5-3-3-2}, `\Game?'\\
\+3@c@d > 10+ pts, 4-card minor, `\Game!'\\
\+3@h@s > (raise) 6-card suit, `\Game?'\\
\+3@h > (1@n-2@h-2@s-3@h) 5+-5+ in @h@s, 10+ pts. `\Game!'\\
\endt
\Then
\Heading{Minor-suit Stayman}
\heading{Opener's Rebids}
\startt
\+2@n > 15--16 pts, both @h@s stopped.
Doesn't deny 4-card minor.\\
\+3@c@d > 4 cards, 15--16 pts.\\
\+3@h@s > 16--17 pts, natural suit or stopper. `3@n?' Doesn't deny 4-card
minor.\\
\+3@n > 16--17 pts, both @h@s stopped.\\
\+4@c@d > 4 cards, 16--17 good pts, `\Slam?'\\
\endt
\heading{Responder's Rebids}
\startt
\+3@c@d > 5 cards.  (If 1@n-2@s-3@c-3@d, this is \fgame)\\
\+3@n > Signoff (natural)\\
\+4@c@d > 5 cards. (Unless 1@n-2@s-3@d-4@d, this is \fgame)
%(Note that 4@c is not Gerber!)
\\
\+4@h@s > If a raise, good 3-card support \\
\+\jump @h@s > else, singleton or void, `\Slam?'\\
\endt
\Then
%\eject
\Heading{Minor-suit Transfers}
\heading{Responder's Rebids}
\startt
\+{\sc Pass} > 0+ pts.\\
\+3\z\ > 1-ton or void, 6+ in $\tau$. `\Slam?'\\
\+3@n > Semi-balanced hand, mild slam interest.  Signoff unless opener
has 16--17 pts and a good fit.\\
\+\jump @c@d > Good distribution. `\Game?'\\
\+4@n > Better than 3@n. `\Slam?'\\
\+5$\tau$ > Signoff.  Weird distribution and few pts.\\
\endt
\eject

\HEADING{Suit Bidding}
\heading{Responses to 1@s@h@d@c}
\startt
\+1\y\ > 6+ pts.\ and a good suit; doesn't require weak \x.\\
\+1@n > 6--12 pts, no other good bid.  Often 6--8 pts.\
and a suit below \x. \fone\\
\+2\y\ > (below 2\x) 9(8)--11 pts, 4+ good cards; 
doesn't mean weak \x.\\
\+2\x\ > 6--10 pts, support of \x:
4 cards, 3 to an honor, or 2 of AKQ.\\
\+2\y\ > (above 2\x) 13+ pts, 4+ cards.\\
\+2@n > 13+ pts, balanced hand.\\  %after 1@h@s...
\interject\heading{Add'l Responses to 1@c@d}\\
\+3\x\ > 6--9 pts, 5(4) cards.\\
\interject\heading{Add'l Responses to 1@h@s}\\
\+3\x\ > %(Jump major ``limit'' raise) 
11--12 pts, `\Game?' (Limit raise).\\
\+\lower\baselineskip\hbox{\vbox{\hbox{3@s}\hbox{4@h}}%
\raise.5\baselineskip\hbox{$\Bigr\}$}}\ignorespaces
> 13--16 pts, 4 cards in \x, and a splinter: 
1-ton or void in \y; `\Game!'\\
\+2@n > 13+ pts, balanced hand, `\Game!'\\
\+3@n > 13--16 pts, 4+ in \x, no singleton or void.  {\sc For\-cing to
4\x}, `\Slam?'\\
\endt
\Then
\Heading{Responses to 2@c}
\startt
\+2@d > No valid response. (Don't {\sc pass}!)\\
\+\lower\baselineskip\hbox{
\vbox{\hbox{2@h@s}\hbox{3@c@d}}%
\raise.5\baselineskip\hbox{$\Bigr\}$}}\ignorespaces
> 8+ {\sc hcp} or $1{1\over2}$ quick tricks; and 5 cards led by Q+.\\
\+2@n > 8+ {\sc hcp}, balanced hand.\\
\endt
\heading{Opener's Rebids after 2@h@s@n/3@c@d}
Bidding is natural and {\sc forced to game}.  A bid of 3@n or game in
an agreed suit discourages slam.\par
\heading{Opener's Rebids after 2@d}
\startt
\+\lower\baselineskip\hbox{
\vbox{\hbox{2@h@s}\hbox{3@c@d}}%
\raise.5\baselineskip\hbox{$\Bigr\}$}}\ignorespaces
> 5 cards (or 4-4-4-1), \fone\\
\+2@n > 23--24 pts, 4-3-3-3, all stopped.\\
\+3@n > 25--27 pts, 4-3-3-3, all stopped.\\
\endt
The second negative is used by responder to respect the force.  The
cheaper minor rebid, or 3@n after 3@d, means 0--4 pts.\ and denies any
aces.  After this, bidding is natural; unless opener immediately
rebids his suit, this sequence is \fgame\par
\quad Any other response confirms 4 pts.\ and is \fgame\par
\Then
\Heading{Responses to 2@d@h@s}
\startt
\+2@n > 14(12)+ pts, `\Game?' \fone\\
\+3,4\x > ??? \\
\+{\sc Pass} > All other cases.\\
\endt
\heading{Opener's Rebids}
\startt
\+3\x\ > 5--8 pts.  Responder should {\sc pass}.\\
\+3@n > Suit \x\ was led by AKQ (AKJ).  Doesn't mean @n!\\
\+3\y\ > 8--11 pts, Q+ in \y.\\
\+4@c@d > (new suit) 8-11 pts, 5(4)-card side suit.  If 4 cards,
led by Q+.\\
\endt
\heading{Responder's Rebids}
\startt
\+3\x\ > (or 4@d after 2@d) `\Game???'\\
\+$n$\y\ > (below game) 5 cards. `\Game!'\\
\+3@n > Natural, signoff.  If \x\ was @h@s, opener may
correct to 4\x.\\
\+Game \tabb is a natural signoff.\\
\endt
\eject

\eject
%\Then
\HEADING{Slam bidding}
\heading{Blackwood}
A bid of 4@n is Blackwood unless:\par
{@-\ partner's last bid was in @n;\par 
\hangafter=1 \hangindent=1em
@-\ your last bid was 3@n and you had not agreed on @h@s as trump;\par
\hangafter=1 \hangindent=1em
@-\ partner has never bid or doubled, but you have;\par
\hangafter=1 \hangindent=1em
@-\ it's immediately after Stayman or a Jacoby Transfer bid.\par
}\heading{Responses to Blackwood}
\quad 5@c\ 0 (or 4) aces.\hfill5@h\ 2 aces.\quad\break
\null\quad 5@d\ 1 ace.\hfill5@s\ 3 aces.\quad\break
After interference, use DOPI:\par
\setbox\tmp=\hbox{\sc Pass}
\quad\hbox to \wd\tmp{\sc Dbl\hfil}\ 0 aces.\hfill 
Cheapest bid 2 aces.\quad\break
\noindent\null\quad\box\tmp\ 1 ace.\hfill
Next bid 3 aces.\quad\break
A void does not count as an ace.\par
\heading{Key-card Blackwood}
In this variant, the trump king counts as an ace, and 5@d shows 1 or 5
``key cards''.\par
\heading{Gerber}
A jump bid of 4@c when partner's last bid was a natural 1@n or 2@n is
Gerber.  Responses start at 4@d (0 or 4 aces).\par
\heading{Cue bids}
A cue bid displays interest in slam and indicates first-round control
(ace or void).  A minimum bid in a new suit for your side is a cue bid
if it is above 3 of your trump suit.  (However, if your trump
suit is @c@d and the new bid is 3@h@s, and another suit remains unbid,
then the bid of 3@h@s may be seeking a major-suit fit.)\par
\quad Returning to the agreed trump suit (or bidding 3@n) denies
interest in slam.  Any non-agreed suit that meets the above criteria
is another cue bid, and continues to be invitational.  Other options
are Blackwood or jumping directly to slam.\par

\HEADING{Overcalls}
An overcall does not require points, it requires tricks!\par
\startt
\+1y\ > 6(5)+ good cards, 6+ tricks.\\
\+1@n > Same as a 1@n opening.\\
\+2\y > (below 2\x) 6+ good cards, 7+ tricks.\\
\+$n$\y > 0--10 pts, 6+ cards. Defensively weak. $n$-3 tricks
(equal vuln.)  Bid it all now, then shut up.\\
\endt
\heading{More about weak jumps}
After a weak jump overcall, partner should pass\dots\par
\Then
\Heading{Followup Principles}
Bidding game is usually signoff.  Bidding one level beneath game is
usually invitational, and often expresses some slam interest.
\eject
\eject
\eject
\bye

