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orcish-club.tex
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orcish-club.tex
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\documentclass{report}
\usepackage{fullpage, url}
\newcommand{\fs}{1st/2nd}
\newcommand{\tf}{3rd/4th}
\newcommand{\hcp}{\textsc{hcp}}
\newcommand{\bal}{\textsc{bal}}
\newcommand{\ak}{\textsc{ak}}
\newcommand{\gf}{\textsc{gf}}
\newcommand{\inv}{\textsc{inv}}
\newcommand{\nf}{\textsc{nf}}
\newcommand{\ph}{\textsc{ph}}
\newcommand{\uph}{\textsc{uph}}
\renewcommand{\c}{\ensuremath{\clubsuit}}
\renewcommand{\d}{\ensuremath{\diamondsuit}}
\newcommand{\h}{\ensuremath{\heartsuit}}
\newcommand{\s}{\ensuremath{\spadesuit}}
\newcommand{\nt}{\textsc{nt}}
\newcommand{\p}{\textsc{pass}}
\newcommand{\x}{\textsc{x}}
\newcommand{\y}{\textsc{y}}
\newcommand{\art}{\textsc{art}}
\newcommand{\nat}{\textsc{nat}}
\newcommand{\+}{\ensuremath{^+}}
\newcommand{\M}{\textsc{m}}
\newcommand{\OM}{\textsc{om}}
\newcommand{\modifications}{\paragraph{Modifications from Revision.}}
\newcommand{\zoom}{\underline}
\newcommand{\OR}{\textbf{or}}
\newcommand{\hsmash}[1]{\hbox to 0pt{#1\hss}}
\title{The Orcish Club}
\begin{document}
\maketitle
\tableofcontents
\listoffigures
\chapter{Opening bid structure}
In \fs, all hands with 17\+ \hcp\ or decent 15\+ \hcp\ unbalanced open
1\c, \emph{except} 20--21 \bal\ hands, which open 2\nt. The exception
is to help us show balanced hands in competition, by passing with a
minimum hand and bidding cheaply in \nt\ with 22\+. We may rarely
open 1\c\ with 13 or 14 \hcp\ hands of unusual playing strength. In
\tf, all these ranges are 1 point higher.
We open most 11 \hcp\ and good unbalanced 10 (rarely 9) \hcp\ hands in
\fs. Hands with a five-card major open 1\h\ or 1\s\ (unless suitable
for 1\nt); hands with a six-card minor, but not five cards in the
other minor, open 2\c\ or 2\d; and the remaining unbalanced hands open
1\d. Balanced hands open 1\nt\ with 14--16, 1\d\ with 11--13. We
consider any 4333, 4432, 5332, 5m422, and some 6m322 (with many honors
in the short suits) to be balanced, although 1\d\ may never contain a
five-card major. We might treat a 4441 or 5431 with a stiff Ace or
King as balanced.
% XXX What do we do with a maximum 5M6m?
In \tf, our opening ranges are nominally all raised by 1 point. In
3rd however it is rare for responder to have an invite opposite 11--16
without a good fit, so we may feel free to open with 9 or 10 \hcp\ and
a reason to want to bid. (We are especially likely to stretch a 2m
opener; we would probably never stretch a 1\d\ opener.) Our
1\nt\ opening is 15--17 in \tf, 2\nt\ 21--22.
\chapter{The 1\c\ opening}
We first describe responses to a \fs\ 1\c\ opening. Responses to a
\tf\ 1\c\ opener are similar; in section \ref{tf1c} we describe the changes
when responder is a passed hand.
1\d\ is the negative response, normally 0--8 \hcp, but could contain a
stronger hand with fewer than 2 \ak. 1\h\+ is \gf, transfer-oriented
symmetric relay, promising 2 \ak.
\section{1\c--1\d}
1\h\ shows any 19\+ \hcp\ unbalanced, 21\+ \hcp\ balanced. 1\nt\ shows 16--18 \bal\ (including 5 card majors). Other rebids are artificial.
\begin{figure}[h]
\begin{tabular}{rll}
Opener's rebid & Description & Artificial inquiry\\
\hline
1\s & At least one long minor, with a 4-card major possible. & 1\nt\\
2\c & Both majors. & 2\d\\
2\d & One major, 6\+. & 2\nt\\
2\M & 5\+\ of the bid major and a 4\+-card minor. & 2\M+1\\
2\nt & 6m322 any quality, good for declaring \nt, almost worth 1\h. & 3\s\\
3\x & Natural, long good suit. & ---\\
3\nt & To play, long running suit with side stoppers. & ---\\
4\M & To play. & ---\\
\end{tabular}
\caption{1\c - 1\d}
\end{figure}
Even the artificial rebids are not forcing! Thus a ``raise'' of the
artificial bid is not needed as natural and is instead used to show a
semi-positive hand (a good 6 to 8) with specified shape. Other
semi-positive hands use an artificial inquiry listed above. All other
bids show less than semi-positive and are pass/correct or natural
(except for transfers to the majors over 2\nt, and a 2\nt\ response
which shows a weak known two-suiter).
\newpage
\subsection{1\c--1\d--1\h}
1\s\ is a second negative showing 0--4 \hcp; 1\nt\+ is \gf,
transfer-oriented symmetric relay shifted up two steps, not promising
any \ak.
We may eventually modify the two-up relay chart to change some optimizations, but for now it is just shifted up 2.
\subsubsection{1\c--1\d--1\h--1\s}
1\nt\ shows 21--23 \bal. It's sort of silly that we end up in
1\nt\ with 21 opposite 0 but 2\nt\ with 20 opposite 0, but oh well.
Strong notrump systems are on (responder can certainly have a
game-forcing hand).
2\c\ is an artificial \gf. Continuations are natural. (Maybe
responder should (nearly) always bid 2\d?)
2\nt\ shows 24--25 \bal. 3\nt\ is to play, likely a long running suit
and side stoppers.
Suit bids from 2\d\ to 3\c\ are natural.
\subsubsection{1\c--1\d--1\h--1\s--2\x}
% XXX this section made sense before but is way too complicated now--
% how can responder have a game force non-raise
In general, continuations are mostly natural, except that 2\nt\ by
either hand is artificial showing a minimum hand in the context of the
auction. It is a puppet to 3\c\ when it is responders first bid after 1\s, and
otherwise mostly forcing, but may be passed if a misfit seems likely.
With a bad hand, responder must either
\begin{itemize}
\item pass,
\item jump shift, or
\item bid 2\nt, and over the 3\c\ response, pass or correct to a suit
below 3\x.
\end{itemize}
An exactly invitational hand with a 6\+-card suit \y\ above \x\ may
bid 2\nt\dots3\y, and an invitational hand with a ``fit'' for \x\ may
bid 2\nt\dots3\x. The
invitational raise is really just suggesting to play 3\x\ when the
invite is rejected; since we cannot play 2\nt\ this may not be a real
fit and opener should probably bid 3\nt\ even holding hearts. That
covers the immediate 2\nt\ response by responder. (The sequence
2\nt\dots3\nt\ is undefined.)
If responder does not make an initial jump shift or 2\nt\ response,
the auction is forcing to 2\nt\ by either player. Bidding immediately above 2\nt,
or slowly bidding to a new suit above \x at the 3 level establishes a game force.
The artifical 2\nt\ is
not forcing; a minimum hand can pass but will more often pull to a
known fit or to 3\c\ to play in opener's second suit. A maximum hand
bids above 3\x\ to establish a game force (this is why a hand which is
only invitational must start with 2\nt).
An initial 2\y\ over 2\x\ only shows a 4-card suit. When we establish
a game force rather than bidding game directly, it tends to show doubt
over strain rather than level. So 2\x--2\y--3\y\ will usually be a
3-card (\gf) raise. Opener can make a minimum (3- or) 4-card raise
via 2\x--2\y--2\nt--3\c--3\y. A jump shift to a new suit after
2\x--2\y\ is a splinter raise.
\subsubsection{1\c--1\d--1\h--1\s--3\c}
If responder does not pass now, a game force is created.
\subsection{Opener's limited artificial rebids over 1\c - 1\d}
\begin{figure}[p]
\begin{tabular}{lllllll}
1\c & 1\d & 1\s &&&& At least one long minor, with a 4-card major possible.\\
&&& 1\nt &&& Semi-positive ask.\\
&&& &2m && Min, 5\+ m, 4 card M possible.\\
&&& & &2M & To play, but opener can raise.\\
&&& & &2\nt & Natural, invitational (near max).\\
&&& &2\h && 4\h, good 5\+ minor, non-min.\\
&&& & &2\s & Asks for minor. (2\nt = clubs, 3\c=diamonds).\\
&&& & &2\nt & 6\+ \s, forcing.\\
&&& & &3m & Pass or correct.\\
&&& & &3\h & Natural, invitational.\\
&&& &2\s && 4\s, good 5+ minor, non-min.\\
&&& & &2\nt & Asks for minor.\\
&&& & &3m & Pass or correct.\\
&&& & &3\h & 6+\h, forcging.\\
&&& & &3\s & Natural, invitational.\\
&&& &2\nt && 5\+ / 4\+ minors, non-min.\\
&&& & & 3m & To play.\\
&&& & & 3M & 6+M, non forcing but opener can raise.\\
&&& & & 3\nt & To play.\\
&&& & & 4m & Natural, invitational.\\
&&& &3m && Good 6\+m, non-min, no 4 card M.\\
&&& 2m &&& Pass or correct.\\
&&& 2\h &&& To play, weaker than semi-positive, but opener can raise.\\
&&& 2\s &&& Artificial semi-positive, 4-4 in majors (possibly 5-4).\\
&&& & 2\nt && Both minors, min.\\
&&& & 3m && No major, min.\\
&&& & 3M && Natural, min, 4 card suit.\\
&&& & 3\nt && Natural, max, no major.\\
&&& & higher && Natural, max.\\
&&& 2\nt &&& Weak, artificial, 5\+ / 5\+ in majors?\\
&&& 3\x &&& To play, weak, but opener can raise.\\
&&& 3\nt &&& To play.\\
1\c & 1\d & 1\nt &&&& 16-18 balanced (could have 5 card major). Strong systems on.
\end{tabular}
\caption{1\c--1\d--(1\s, 1\nt)}
\end{figure}
\begin{figure}[p]
\begin{tabular}{lllllll}
1\c & 1\d & 2\c &&&& Both majors.\\
&&& 2\d &&& Asks for better major. Semi-positive unless next bid passed.\\
&&& & 2M && Better major.\\
&&& & & 2\s & (over 2\h) Natural, invitational in spades.\\
&&& & & 2\nt-3M & Natural, invitational.\\
&&& & & 3\h & (over 2\s) Natural, invitational in hearts.\\
&&& & & 3\nt & ?\\
&&& & & 4M & To play.\\
&&& & & others & Splinters.\\
&&& 2M &&& To play.\\
&&& 2\nt &&& Weak, both minors, 5\+, 5\+.\\
&&& 3\c &&& Semi-positive, both minors, 5\+, 5\+.\\
&&& 3\d &&& Natural, weak.\\
&&& 3M &&& Natural, weak with 5 card suit; opener can raise.\\
&&& 3\nt &&& To play.\\
&&& 4m &&& Transfer to corresponding major.\\
&&& 4M &&& To play.\\
1\c & 1\d & 2\d &&&& One major 6\+.\\
&&& 2M &&& Pass or correct.\\
&&& 2\nt &&& Asks strength/suit, semi-positive.\\
&&& &3\c && Min, \h.\\
&&& & &3\d & Puppet to 3\h (after which 3\nt is choice of games).\\
&&& & &3\h & To play.\\
&&& & &3\s & Natural, 6\+ \s.\\
&&& & &3\nt & To play.\\
&&& &3\d && Min, \s.\\
&&& & &3\h & Puppet to 3\s (after which 3\nt is choice of games).\\
&&& & &3\s, 3\nt & To play.\\
&&& &3\h && Max, \h.\\
&&& & &3\s & Natural, 6\+ \s.\\
&&& & &3\nt & To play.\\
&&& & &4m & Natural, invitatinoal.\\
&&& &3\s && Max, \s.\\
&&& & &3\nt & To play.\\
&&& & &4m & Natural, invitational.\\
&&& & &4M & To play.\\
&&&3\c &&& Weak, long suit \\
&&&3\d &&& Semi-positive, 6\+ \h.\\
&&&3M &&& Weak, long suit.\\
&&&3\nt &&& To play.\\
&&&4m &&& Weak, natural, very long suit.\\
&&&4M &&& Natural, to play, very long suit.\\
\end{tabular}
\caption{1\c-1\d-(2\c,2\d)}
\end{figure}
\begin{figure}[h]
\begin{tabular}{lllllll}
1\c & 1\d & 2M &&&& 5\+ M, 4+ m.\\
&&& 2M+1 &&& Semi-positive ask.\\
&&& & 2M+2 && Min, \c.\\
&&& & 2M+3 && Min, \d.\\
&&& & 3M-1 && Max, \c.\\
&&& & 3M && Max, \d.\\
&&& & & 3\s & (over 2\h) 6\+ spades, forcing if opener max.\\
&&& 2\nt &&& (over 2\h) spades, weak.\\
&&& 3m &&& Pass correct.\\
&&& 3M &&& Natural, invitational.\\
&&& 3oM &&& Weak, long suit.\\
&&& 3\nt &&& To play.\\
1\c & 1\d & 2\nt &&&& 6m322 any quality, good for declaring \nt, almost worth 1\h.\\
&&& 3\c &&& Pass or correct.\\
&&& \hbox to 0 pt{3\d,3\h} &&& Transfer.\\
&&& 3\s &&& Asks for minor (3\nt = \c, 4\c = \d).\\
&&& 3\nt &&& To play.\\
1\c & 1\d & 3\x &&&& Natural, long good suit.\\
1\c & 1\d & 3\nt &&&& To play.\\
\end{tabular}
\caption{1\c-1\d-(2\h+)}
\end{figure}
\newpage
\section{Game forcing responses to 1\c}
\subsection{Basic idea}
A \gf\ response requires 2 \ak; see \ref{controls} Controls. The 1\c\ opener
is now the \emph{relayer} or \emph{asker} and will continue making the
cheapest available bid (with two exceptions, see below) until able to
place the contract. The other hand is called the \emph{relay
responder} and makes a sequence of descriptive bids (separated by
semicolons here). Ideally, the relayer will be the declarer and the
defenders will have no information about the closed hand; hence
``transfer-oriented.''
\subsection{Signoffs}
If the relayer bids 3\nt, that is always to play. A bid of 4\d\ by
the relayer is the \emph{end signal}: responder bids 4\h\ whereupon
the relayer places the contract. But with a very good hand responder
can bid over 3\nt\ or 4\d\ showing controls, starting with 4\c/4\s\ =
4 \ak. (See \ref{controls} Controls.) When the next step is 3\nt\ or 4\d,
relayer can continue relays by bidding one step higher instead.
\subsubsection{Slam Invites}
\subsubsection{Quantitative Invites}
\subsection{Responder's bids}
The responding hand is described in four stages: shape, range,
controls, and denial cuebidding (location of specific honors).
Sometimes a single bid belongs to two or more stages, thanks to a
technique called \emph{zooming}: when responder would make the highest
possible bid at the end of one stage, responder also begins the next
stage as though the relayer had made a relay ask one step below that
bid. For example, the sequence 1\s; 3\d\ just shows 3424 shape, but
1\s; 3\h\ shows 4243 shape and a minimum, 1\s; 3\s\ shows 4243 shape
and a maximum with 3 \ak, etc., because there is no shape assigned to
1\s; 3\s.
\subsection{Shape}
Hands are divided into one-suited, two-suited, three-suited and
balanced (for our purposes defined as 4432 or 4333) shapes. A
``suit'' is a suit of at least 4 cards, provided the hand is not
balanced. Every shape that does not have an 8-card suit or 12 cards
in two suits is shown exactly, except that the 2- and 3-card suits of
a 7321-type hand are not distinguished. With extreme shape, make the
smallest lie possible.
\subsubsection{One-suiters}
First bid your suit using the scheme 1\h\ = \s, 1\nt\ = \h, 2\c\ = \d,
2\d\ = \c. (This ensures that the relayer will play the hand if we
play in responder's long suit, provided it is not \h.) Your next bid
will be 2\s\ or higher. Look at your length in your other three suits
and see if you have a unique shortest suit. If so, bid 2\s\ if it is
the highest side suit, bid 2\nt\ if it is the middle side suit, and do
nothing for now (a kind of zoom) if it is the lowest side suit; then
show your shape: 3\d\ = 5332, 3\h\ = 6331, 3\s\ = 7330, \zoom{3\nt} =
7321. The underline is a reminder to zoom to range and controls,
since 7321 is the highest possible shape on this sequence. If you do
not have a unique shortest suit, your shape must be 6322 or 7222, and
the sequences are 2\s; 3\c; 3\h = 6223, 2\s; 3\c; \zoom{3\s} = 6232,
3\c; 3\h = 7222, 3\c; \zoom{3\s} = 6322. (How do you remember these
sequences? The general rule is increasing numeric order; the general
exception is that when the highest bid would then show a rarer shape
than the bid one lower, we switch them, because zooming saves
\emph{two} steps.)
\subsubsection{Two-suiters}
Generally begin by bidding both your suits according to the one-suited
scheme. However, partner's relay asks will prevent you from making
two consecutive bids! So, there are special sequences for showing
\d+\h\ or \c+\d: with \d+\h\ bid 1\s; 2\c, and with \c+\d\ do nothing
for now; your first bid will be 2\h\ or higher, showing a two-suiter
with the minors. There's one other slight adjustment: your next bid
might be 2\h, but you can't do that if you bid 2\d\ showing \c. So
showing a major and then bidding 2\h\ shows \c, also, as though it
were 1\h/1\nt; 2\d; 2\h. (We didn't use the 2\h\ rebid for
one-suiters, so this is OK.)
Suppose first that one of your suits is only 4 cards long. Bid
2\h\ now if it's the higher one. Next bidding 3\c\ shows 5422 and
\zoom{4\c} shows 7411. Otherwise, one of your short suits is shorter
than the other; bid 2\nt\ if it's the higher one. Then show your
shape: 3\d\ = 5431, 3\h\ = 6421, 3\s\ = 6430, 3\nt\ = 7420 (zoom from
3\nt\ only if you bid 2\nt\ first). (Generally when $x$ shows two
equal lengths, $x-1$ shows ``high shortage.'')
If instead both your suits have at least 5 cards, bid 2\s. Now
3\d\ shows singletons in both short suits, followed by 3\s\ = 5611,
\zoom{3\nt} = 6511. Otherwise, bid 3\c\ if your higher short suit is
shorter, then 3\h\ = 5521, 3\s\ = 5530, 3\nt\ = 5620, \zoom{4\c} =
6520. (The first two digits in these numbers are the lengths of your
long suits, with the higher one first; the second two are the lengths
of your short suits with the longer one first.)
\subsubsection{4432 and 4333 shapes}
With these balanced shapes, start with 1\s\ (so that relayer will
declare a notrump contract). Your next bid will be 2\d\ or higher.
With 4432, consider your two 4-card suits; bid 2\d\ if they are the
same color, 2\h\ if they are the same rank, and do nothing for now if
they are the same shape; then bid your doubleton: 2\nt\ = \s, 3\c\ =
\c, 3\d\ = \d, \zoom{3\h} = \h. With 4333, bid 2\d\ with a 4-card
major, then 2\s\ always, then 3\c\ with long \c\ or \h\ and \zoom{3\d}
with long \d\ or \s.
\subsubsection{Three-suiters}
These are last because they live in the gaps formed by the rest of the
system. The two unused sequences are 1\h; 1\nt; 2\d\ and 2\c; 2\h.
The first shows a three-suiter with both majors, the second a
three-suiter with both minors. After one of these starts, there are
only 8 possible shapes, so the follow-ups are simple and step-based:
bid the cheapest step first if you have a high short suit (\s\ or \d),
then bid in steps showing the lengths of your long suits in
\s\h\d\c\ order (444, 445, 454, 544---and zoom with 544).
\subsection{Range}
Bid the cheapest step with a minimum, otherwise zoom on to controls.
A minimum is a hand with fewer than 12 \hcp\ or fewer than 3 \ak. A
passed hand is always a minimum and skips this stage.
\subsection{Controls} \label{controls}
We define \ak\ as a measure of controls: an Ace is worth 2 \ak, a King
1 \ak. We don't count any \ak\ for shortness, since relayer already
knows responder's shape. \ak\ points are shown in steps, starting
with 2 (and zooming with 5) if responder has shown a minimum, 3 (never
zooming) if a maximum.
\subsection{Denial cuebidding}
Sort your suits by length with the longer suits first, breaking ties
by putting higher ranking suits before lower ones. You will cycle
through the suits in this order, looking at each suit a number of
times depending on its length: three times for suits of at least 4
cards, twice for 3-card suits, once for 2-card suits, and never for
singletons or voids. The first time you look at a suit, check whether
it contains exactly one of the Ace or King; the second time, check
whether it contains the Queen; the third time, check whether it
contains the Jack. (There is an exception for suits of 6 or more
cards described below.) So, once you have all these ``yes'' or ``no''
answers, what do you \emph{bid}? If the answer to the first question
is ``no,'' bid the cheapest step. In general, skip a number of steps
equal to the number of ``yes'' answers. If relayer continues, start
again where you left off, with the answer after the first ``no.'' In
these auctions, any non-relay bid by the relayer is to play, as is any
bid at the slam level; the highest relay ask is 5\nt.
\subsubsection{Long suit exception}
When checking a suit of 6 or more cards, replace the first two checks
with the following: first check whether it contains at least two of
the Ace, King and Queen, then check whether it contains an odd number
(the larger possibility given the answer to the first check).
\subsubsection{Josh's Law}
"JoshÕs Law: Whenever information regarding high cards or their location is absolutely known from previous bidding, then that information is skipped even if it hasnÕt been asked for yet. This can take many forms, such as knowing responder can have no more controls, or high card points, or can even pertain to distribution." \cite{TOSR}
We do not currently play Josh's Law, but may eventually.
\subsection{Examples} In each example North deals and opens 1\c.
\[
\begin{tabular}{ll|ll|lll|ll|l}
1.
&\s\ KQ73&1\c&2\c&\d& \qquad 2.&\s\ A9&1\c&1\s&balanced or \d+\h\\
&\h\ AKJ2&2\d&2\h&three-suited with \c+\d& &\h\ AQ1072&1\nt&2\h&same rank\\
&\d\ Q10&2\s&3\c&4144& &\d\ AQJ&2\s&2\nt&2344\\
&\c\ Q107&3\d&3\nt&maximum, 4 \ak& &\c\ AK9&3\c&3\d&minimum\\
&&4\d&4\h&end signal& &&3\h&3\s&2 \ak\\
&\s\ J654&4\s&---&9 \ak\ is not enough& &\s\ J2&4\c&4\h&\d K, no \c K\\
&\h\ 4&&& for slam without& &\h\ K98&4\s&5\c&\h K, no \s K\\
&\d\ K954&&& more distribution.& &\d\ K642&5\d&5\h&no \d Q\\
&\c\ AKJ6&&&& &\c\ J732&5\s&5\nt&no \c Q\\
\multicolumn{5}{}&& &&6\nt&---&7\nt\ is at best\\
\multicolumn{5}{}&& &&&& on a finesse.
\end{tabular}
\]
\subsection{Relay Breaks}
If opener makes a bid which is not the relay bid and is not a signoff bid, it is a relay break. The meaning is determined by the following list.
\begin{enumerate}
\item 10-shape reverse relay. If this is opener's first rebid above a 1\h, 1\s or 1\nt bid by responder, a relay break begins a 10-shape reverse relay sequence.
\item 4-shape reverse relay. If this is opener's first rebid above a 2\c or 2\d bid by responder, a relay break begins a 4-shape reverse relay sequence.
\item Stopper ask. If responder has $n$ known 2 or 3 card suits, the first $n$ relay breaks are stopper asks, if below 3\nt.
\item Exclusion. If responder has finished showing shape with 3\h or lower, then 4\c is the exclusion relay.
\item RKC ask. If none of the above relay breaks applies and the bid is not a signoff or a slam invite, then it is a Roman keycard ask.
\end{enumerate}
\subsubsection{10-shape Reverse Relay}
\subsubsection{4-shape Reverse Relay}
\subsubsection{Stopper Ask}
\subsubsection{Exclusion}
\subsubsection{RKC Ask}
\section{\tf\ seat 1\c\ openings} \label{tf1c}
As normal, an opening of 1\c\ in \tf\ seat promises 2\hcp\ more than in \fs. Thus all of responder's point ranges are shifted down by 2 points.
Responder now needs 1-4 \ak\ and 7-10 \hcp\ for a positive response.
There is no distinction between minimum and maximum for a responder's hand: after showing shape, the next question is number of \ak.
\section{Interference Over 1\c}
\subsection{Low-level auctions}
If they bid 1\h\ over our 1\c\ we ignore it---\p\ replaces 1\d\ and
\x\ replaces 1\h\ (by either player).
If they double or bid 1\d, responder may:
\begin{itemize}
\item Make the same relay response they would otherwise, game forcing
as usual. We ignore the \x/1\d.
\item Bid 1\d\ or double it, showing the weakest range (0--6). Even
though this is not the normal range for a 1\d\ bid, we pretend the
auction has gone 1\c--1\d\ as far as our systems are concerned.
1\h\ now shows 21\+, over which 1\s\ is 0--3. Other rebids show
16--20.
\item Pass (with \c\ length) or redouble (for takeout) over a double,
or pass 1\d. This shows a semi-positive. We bid as though they
opened 1\c/1\d: double/redouble by opener is takeout, the rest
natural.
\end{itemize}
\begin{figure}[p]
\begin{tabular}{cccl}
1\c & (x) & -- & 7-8\hcp, some \c\ length\\
1\c & (x) & xx & 7-8\hcp, takeout of \c\\
1\c & (x) & 1\d & 0-6\hcp\\
1\c & (x) & 1\h + & normal relays\\
1\c & (1\d) & -- & semi-positive, non-\gf\\
1\c & (1\d) & x & 0-6\hcp \\
1\c & (1\d) & 1\h + & normal relays\\
1\c & (1\h) & -- & Non-\gf\ (opener's \x\ = 1\h, strong; others as over 1\c--1\h)\\
1\c & (1\h) & x & Would have bid 1\h\ (normal relays)\\
1\c & (1\h) & 1\s + & normal relays\\
1\c & (1\s,2\c,2\d) & -- & 0-5\hcp\ or penalty pass or 6-8\hcp but not able to double.\\
1\c & (1\s,2\c,2\d) & x & 6-8 \hcp, 3-4 cards in opponents suit; flattish with penalty interest or \gf without stopper.\\
1\c & (1\s,2\c,2\d) & cue & \gf, takeout, decent support in unbid majors.\\
1\c & (1\s,2\c,2\d) & suit jump & 6-8\hcp\ with 6\+ (or good 5) in suit.\\
1\c & (1\s,2\c,2\d) & bid & Natural, \gf.\\
1\c & (2M) & -- & Nothing to say or penalty pass. \\
1\c & (2M) & x & 6-8\hcp, possibly more. \\
1\c & (2M) & cue & Looking for stopper for 3\nt. \\
1\c & (2\h) & 3\s & ? \\
1\c & (2M) & 4m & Leaping Michaels. \\
1\c & (2M) & 4M & Both minors. \\
1\c & (2M) & bid & Natural, \gf.\\
1\c & (3\x) & -- & Nothing to say or penalty pass.\\
1\c & (3\x) & x & Take-out oriented, \gf.\\
1\c & (3\x) & 4\x & Huge hand, takeout.\\
1\c & (3\x) & suit jump & \gf, playable opposite no support.\\
1\c & (3\x) & bid & Natural, \gf.\\
1\c & (4\c+) & -- & Nothing to say or penalty pass.\\
1\c & (4\c+) & x & Game values, cooperative.\\
1\c & (4\c+) & cue & Huge hand, takeout.\\
1\c & (4\c+) & \nt & Huge two suiter.\\
1\c & (4\c+) & bid & Natural.\\
\end{tabular}
\begin{tabular}{cccccl}
1\c & (--) & 1\d & (1M) & -- & forcing a double, could be penalty. \\
1\c & (--) & 1\d & (1M) & x & Takeout. (later jump cue asks for stopper)\\
1\c & (--) & 1\d & (1M) & 1\nt & 16-18\hcp, balanced. Stopper and a source of tricks. \\
1\c & (--) & 1\d & (1M) & 2\nt & 21-22\hcp, balanced. Stopper and a source of tricks. \\
1\c & (--) & 1\d & (1M) & jump shift & Natural, \gf \\
1\c & (--) & 1\d & (1M) & cue & Big 2/3 suit takeout. \\
1\c & (--) & 1\d & (1M) & jump cue & Natural (psych exposer). \\
1\c & (--) & 1\d & (x = \d) & xx & penalty (to play).\\
1\c & (--) & 1\d & (x = \d) & -- & strong, takeout-ish, relays on if passed to responder.\\
1\c & (--) & 1\d & (x = \art) & bid & Natural.\\
1\c & (--) & 1\d & (x = \art) & jump & Strong.\\
1\c & (--) & 1\d & (x = suits) & cue & Takeout.\\
1\c & (--) & 1\d & (x = suits) & jump cue & Psych-exposer.\\
\end{tabular}
\end{figure}
\begin{figure}[h]
\centering
\begin{minipage}{\textwidth}
\begin{tabular}{c}
\begin{tabular}{l|l|l|l|l|}
& 1-suiter & 2-suiter & 3-suiter & balanced \\
1\h & \s & \s & \s\hsmash{\footnote{With \s\d\c\ bid 2\c\ first}} & -- \\
1\s & -- & \h\d\ (2\c\ next) & -- & balanced \\
1\nt & \h & \h & \h\hsmash{\footnote{With \h\d\c\ bid 2\c\ first}} & -- \\
2\c & \d & \d\hsmash{\footnote{With \d\c\ bid 2\h\+ directly}} & \d & -- \\
2\d & \c & \c\ (non-reverse) & \h+\s+(\d\ or \c) & \textbf{BAL} \\
2\h & -- & reverse (45\+); \c & \c\+\d+(\s\ or \h) & \smash{\vdots} \\
2\s & high shortage & 5\+5\+ & \textbf{3-SUITER} & \\
2\nt & mid shortage & high shortage & \textbf{3-SUITER} & \\
3\c & equal shortage & 5422 / high shortage && \\
3\d & 5332 & 5431 / equal shortage &&\\
3\h & 6331 / 6223 / 7222\hsmash{\footnote{6223 is shown via 2\s\ and 3\c\ while 7222 is shown via 3\c\ only.}} & 6421 / 5521&& \\
3\s & 7330 / \zoom{6232} / \zoom{6322}\hsmash{\footnote{6232 is shown via 2\s\ and 3\c\ while 6322 is shown via 3\c\ only.}} & 6430 / 5530 / 5611&& \\
3\nt & \zoom{7(32)1} & 7420 / 5620 / \zoom{6511}&& \\
4\c & \smash{\vdots} & \zoom{7411} / \zoom{6520}&& \\
4\d & & \smash{\vdots}&&\\
\end{tabular} \\
\\
\hline
\begin{tabular}{c|c}
&\\
\textbf{3-SUITER} & \textbf{BALANCED}\\
\begin{tabular}{lll}
1&&high shortage (then start at 2)\\
2&&5440 (then ascending numeric)\\
&a&4450 \\
&b&4540 \\
&c&\zoom{5440}\\
3&&\zoom{4441}\\
4&&\smash{\vdots}\\
\\
\\
\end{tabular} &
\begin{tabular}{l|l|l|}
& 4432 & 4333 \\
2\d & color & 4-card major \\
2\h & rank & -- \\
2\s & -- & always \\
2\nt & 2\s & -- \\
3\c & 2\c & 3433 \\
3\d & 2\d & \zoom{4333} \\
3\h & \zoom{2\h} & \smash{\vdots} \\
3\s & \smash{\vdots} &
\end{tabular}\\
\\
\end{tabular} \\
\hline
\begin{tabular}{c|c}
\\
\textbf{10-SHAPE RR} / 1\h,1\s,1\nt & \textbf{4-SHAPE RR} / 2\c, 2\d \\
\begin{tabular}{lll}
1 && 4441 / 4450 / 4540 / 5440 (\textbf{4-SHAPE RR})\\
2 && 4531 / 3451 / 5341\\
&a& 4531\\
&b& 3451\\
&c& \zoom{5341}\\
3 && 4351\\
4 && 3541\\
5 && \zoom{5431}\\
6 && \smash{\vdots} \quad\quad \textbf{Hearts primary with known \h\ fit}
\end{tabular} &
\begin{tabular}{lll}
1&& 4450 / 4540 / 5440\\
&a& 4450\\
&b& 4540\\
&c& \zoom{5440}\\
2&& \zoom{4441}\\
3&& \smash{\vdots}\\
\\
\\
\multicolumn{3}{l}{\textbf{No zoom past} 3\nt\ \textbf{without known fit}}\\
\end{tabular}
\end{tabular}
\end{tabular}
\end{minipage}
\caption{Relay Summary}
\end{figure}
\chapter{The 1\d\ opening}
The 1\d\ opening, in \fs, shows one of
\begin{itemize}
\item 11--13 \bal,
\item good 10--bad 15 three-suited (4441, 5431, 5440), without a 5-card major,
\item 10--14 both minors (55 or longer).
\end{itemize}
The point ranges are 1 point higher in \tf.
Initial responses are natural.
\begin{itemize}
\item[\p] 0--5 \hcp\ or so, usually balanced or both minors or a long
minor not good enough for a weak jump shift to the three level. We
would respond 1\M\ on any hand which has somewhere to go if opener
rebids 1\nt.
\item[1\h/1\s] 4\+-card major, 0\+ \hcp, may have longer minor even if \gf\ strength.
\item[1\nt] about 6--11 \hcp, no 4-card major, no game interest opposite 11--13 \bal.
\item[2\c/2\d] 4\+-card minor, maybe \bal, 12\+ \hcp, no cheaper 4-card suit.
\item[2\h/2\s] weak jump shift, 6\+-card suit, 0--9 \hcp\ or so, no
game interest unless opener has a big fit. This bid is mandatory
since rebidding 2\M\ after 1\M\ would be invitational.
\item[2\nt] balanced \gf, 13--16 \hcp, asking for shortness.
\item[3\c/3\d] weak jump shift, 7\+-card suit, not invitational opposite 11--13 \bal.
\item[3\nt] to play (not interested in 4\M/5m).
\end{itemize}
Everything else is preemptive, as though responder was opening.
In Midchart events, we do not play weak jump shifts to 3\c/3\d\ but instead:
\begin{itemize}
\item[2\nt] balanced \gf, 13--16 \hcp, \OR\ weak jump shift in a minor
\item[3\c/3\d] 7-card suit to two of the top three honors or AJT or KJT; no side Ace or King
\end{itemize}
XXX Passed hand bidding?
\section{1\d--1\h/1\s}
Opener has many raises available. We raise on 3-card support when the
hand contains a singleton (or void) or small doubleton, except that
opener rebids 1\s\ in preference to raising 1\h\ with 3.
\subsection{Opener does not raise}
Over 1\h, opener's first priority is to show a 4-card spade suit by
bidding 1\s. We basically play our ordinary two-way new minor forcing
here.
\begin{figure}[h]
\begin{center}
\begin{tabular}{llllll}
1\d&1\h&1\s&1\nt&&\nf, 6--11 \hcp, 4--5 \h s, no game interest opposite 11--13 bal\\
&&&&2\c/2\d&\nf, \nat, 5-card suit\\
&&&&2\h&3-card support, does not promise extras XXX always minimum?\\
&&&&2\s&maximum, 4144/40(54)\\
&&&&2\nt&maximum, 43(15). 3\c\ = pass/correct, 3\d\ asks, 3\h\ to play.\\
&&&2\c&&puppet to 2\d\ to play or for invite (then 3\nt\ = choice of 3\nt/4\h)\\
&&&2\d&&artificial game force; opener rebids naturally\\
&&&2\h&&invite with 6 \h s\\
&&&2\s&&4 \s s, not invitational\\
&&&4\c&&splinter (\s\ agreed)\\
&&&4\d&&splinter (\s\ agreed)
\end{tabular}
\end{center}
\caption{1\d--1\h--1\s}
\end{figure}
Otherwise, opener rebids 1\nt\ with 11--13 balanced or a
three-suiter (5431 or 4441) of equivalent playing strength with a
singleton in responder's major. See below for transfers.
The remaining hands are either 55 in the minors or too strong to
respond 1\nt. They are handled as shown in Figure~\ref{fig:minors-or-max-misfit}.
\begin{figure}[h]
\begin{center}
\begin{tabular}{lllllll}
1\d&1\M&2\c&&&denies 3-card support; minimum 5\+5\+ minors \OR\\
& & &&&maximum three-suiter short in responder's major except 1453 (after 1\s)\\
& & &2\d&&\nf\ preference, not invitational\\
& & &2\M&&invitational with a 6-card suit\\
& & &2\OM&&fourth suit forcing to game, relays\\
& & &2\nt&&invitation, no fit\\
& & & &3\c/3\d&65 minimum\\
& & & &3\h&maximum with 4 \h s\\
& & & &3\nt&maximum\\
& & &3\c/3\d&&invitation, 3-card support\\
& & & &3\h&maximum with 4 \h s\\
& & & &3\M&stopper ask in \OM\\
& & & &3\nt&maximum\\
& & &3\M&&natural, \gf\\
& & &4\c/4\d&&natural slam try\\
& &3\c&&&maximum, 5\+5\+ minors XXX artificial follow-ups probably better\\
& & &3\d&&to play\\
& & &3\M&&asking for a raise on Hx support\\
& & &3\OM&&asking for a stopper or shortness in \OM\\
& & & &3\nt&stopper\\
& & & &4\c&shortness \\
& & & &5\c&no stopper or shortness, pass/correct\\
&1\s&2\d&&&maximum, 1453 exactly. 2\h\ through 3\c\ are signoffs, higher bids are \gf.
\end{tabular}
\end{center}
\caption{Opener's rebid with 5\+5\+ minors or a maximum misfit\label{fig:minors-or-max-misfit}}
\end{figure}
\subsection{Transfers after 1\d--1M--1\nt}
Responder's rebid of 2\M\ always shows an invite with 6 cards in \M.
2\c\ handles all other invites, plus some other hands; other bids
through 3\c\ are transfers, except 2\s\ is always natural; and higher
bids are \gf\ and mostly natural (except 3\OM\ is a splinter). The
meanings of SMM/LMM will be explained below.
After 1\d--1\M--1\nt:
\begin{enumerate}
\item[2\c] puppet to 2\d, for \d\ signoff, most invites, or simple 3\nt/4\M\ choice-of-games
\item[2\M-1] transfer to \M, \gf\ with 5 \M s (not 5 \s s 4\+ \h s)
\item[2\M] invite with 6 \M s
\item[2\d] if \M=\s, shows 5\+ \s s, 4\+ \h s, weak or \gf. Opener should
give preference, assuming a weak hand.
\item[2\s] if \M=\h, natural, showing exactly 44 in the majors, \gf
\item[2\nt] transfer to 3\c, for \c\ signoff or \gf\ with 5\+ \c s, usually exactly 4 \M s. Next 3\d\ LMM with 6\+ \c s, or 3\h\+ SMM.
\item[3\c] transfer to 3\d, for (longer) \d\ signoff or \gf\ with 5 \d s, usually exactly 4 \M s. Next 3\h\+ SMM.
\item[3\d] \gf\ with 6\+ \d s, LMM
\item[3\M] \nat\ \gf, single-suited, but not a solid suit. 3\nt, 4\M\ are to play, others cues showing Hx+ support.
\item[3\OM] (41)44 \gf
\item[3\nt] to play
\item[4m] natural, 6 \M s, 5 ms
\item[4\M] to play
\item[4\nt] quantitative invite (quite likely (43)33?)
\end{enumerate}
\subsubsection{1\d--1\M--1\nt--2\c}
After 1\d--1\M--1\nt--2\c--2\d\ (forced), jumps are choice-of-games and
other bids natural invites:
\begin{enumerate}
\item[\p] \d\ signoff
\item[2\M] invite with exactly 5 \M s
\item[2\h] if \M=\s, invite with 5 \s s 4\+ \h s
\item[2\s] if \M=\h, invite with exactly 44 in the majors\footnote{
Even in our style, we might prefer to play 2\s\ in the 4-3 fit to 2\nt.
}
\item[2\nt] natural invite (with exactly 4 \M s)
\item[3\c] natural invite (5\+ \c)
\item[3\d] natural invite (5\+ \d)
\item[3\h] if \M=\s, strong invite with 55 in the majors; if \M=\h, strong invite with 5 \s s 6 \h s
\item[3\s] XXX ???
\item[3\nt] choice of 3\nt\ or 4\M, with 5 \M s but leaving the decision up to opener (generally correct unless 4333)
\end{enumerate}
XXX There are a bunch of 4-level bids available, including 4\y
XXX Maybe the 3\s\ could also be a slammish checkback?
In the sequence 1\d--1\M--1\nt--2\c--2\d--2\M, it is almost mandatory
for opener to raise to at least 3\M\ with 3-card support, as responder
may have an invitational 55 which improves greatly with a known fit.
(With a maximum and a fit, opener of course bids 4\M.) If opener bids
anything else below game, rejecting the invite without a fit,
responder might then run to a second 5-card suit at the 3-level.
\subsubsection{Transfers}
The transfer 1\d--1\M--1\nt--2\M-1 is used with most \gf\ hands with a
5-card major. The exceptions are
\begin{itemize}
\item hands with a solid suit, which jump to 3\M;
\item hands which are willing to play 3\nt\ opposite some openers with
3-card support, which bid 2\c;
\item hands with at least 5 spades and at least 4 hearts, which
transfer to \h\ instead;
\item hands with at least 65 (either way) in a major and a minor,
which jump to 4m (with a 6-card major) or transfer to the minor
(with a 5-card major).
\end{itemize}
After 1\d--1\M--1\nt--2\M-1--2\M:
\begin{itemize}
\item[2\s] (\M=\h) natural \gf. Opener usually rebids 2\nt\ to hear
more about responder's hand (3m = fragment, typically 45(31); 3\h\ =
6 \h s; 3\s = 5 \s s 6 \h s; 3\nt = 4522, \nf\ but some slam
interest), or can rebid naturally (raise \h\ with 3-card support or
bid 3m with a hand which wants to play in the minor opposite the
right 45(31) shape).
\item[2\nt] \gf\ transfer, 4--5 \c. With 5 \c, 3\d\ LMM next, otherwise 3\h\+ SMM.
\item[3\c] \gf\ transfer, 4 \d, next 3\h\+ SMM.
\item[3\d] \gf, 5 \d, LMM.
\item[3\h] (\M=\s) XXX natural \gf\ probably, but what shape? 7411?
\item[3\M] \gf, sets trumps, but not a solid suit (some help needed in
trump for slam). Opener's first responsibility is to sign off in
4\M\ with bad trumps (worse than Qx). Frivolous 3\nt\ is on.
\item[3\nt] \nf, choice of games, but demanding that opener raise with
3-card support. Opener could cue with a great hand, I guess.
\item[Jumps] self-splinters.
\item[4\M] To play, wanted to check for at least two-card support (XXX ?)
\item[4\nt] Quantitative invite with 5\M, probably 5332 type. If you
just want to bid keycard for your major, go through 3\M (with or
without a transfer as seems appropriate).
\end{itemize}
After we show both majors, bidding is generally natural. For example
after 1\d--1\s--1\nt--2\d--2\h/2\s:
\begin{itemize}
\item[2\s] 64 majors
\item[2\nt] 5422, unsure of strain or level
\item[3\c] fragment, usually 5413
\item[3\d] fragment, usually 5431
\item[3\h] 55 majors
\item[3\s] 64 majors if opener rebid 2\s, otherwise XXX ???
\item[3\nt] 5422 \nf, no slam interest, probably something in each minor suit
\end{itemize}
Raising opener's preference shows extra length there, which is enough
to guarantee a fit, and sets trump, with the implication of at least
mild slam interest.
\subsubsection{1\h\dots2\s}
This slightly silly sequence promises exactly 44 in the majors. If
responder were balanced he would just bid some number of \nt\ instead,
so it also implies shortness in one of the minors. Opener can bid
3\nt\ with wasted stoppers in both minors, or 2\nt\ to hear more.
After 1\d--1\h--1\nt--2\s--2\nt:
\begin{itemize}
\item[3\c] 4414
\item[3\d] 4441
\item[3\h] 4405
\item[3\s] 4450
\end{itemize}
\subsubsection{SMM (short minor module)}
The ``short minor module'' applies in auctions where responder has
transfered to a minor and has not bid 3\d. These are effectively
relay auctions and we use a modification of the auction termination
structure from our relays after a strong club opening.
At this point in the auction, responder has shown either a 5-card
major and a 4-card minor, or vice versa. The continuations are
\begin{itemize}
\item[3\h] high shortage, then continue at 3\nt\+
\item[3\s] 5422 type
\item[3\nt] low shortage, 5431, \nf. Not a slam try opposite a misfitting hand.
\item[4\c] low shortage, 6421 (only possible with a long major)
\item[4\d] low shortage, 6430 (only possible with a long major)
\item[4\h] low shortage, 5431, slam try opposite 11--13 balanced (forcing)
\end{itemize}
Over 3\s\ or 3\nt, opener can bid 3\nt\ or pass as a signoff
(attempt), bid 4\d\ as an attempt to sign off with a bad hand, bid a
game contract with a medium hand, or bid 4\c\ as a transfer to
4\d\ with a great hand. When the final contract will be in a major,
responder can use kickback to check on opener's keycards. When it
will be in a minor, opener should bid 4\nt\ rather than 5m with the
larger number of keycards possible for the range shown (1 for ``bad'',
2 for ``medium'', 3 for ``good'').
Over 4\c, there are only two ranges available: 4\d\ shows the weaker
range and bidding game directly shows the stronger range. If agreeing
to a minor, the weaker range is defined as 0--1 keycards and the
stronger range as 2--3 keycards, with 4\nt\ used to show the larger
number.
Over 4\d\ and higher, good luck! I suggest bidding what you think you
can make.
\subsubsection{LMM (long minor module)}
The ``long minor module'' applies in auctions where responder has
shown a minor and bid 3\d. Opener can relay for the shape and short
suit, or just sign off somewhere, or bid 3\s\ as a 3-card raise of the
major, or 4\c\ as a raise of the minor.
The relay is simply
\begin{itemize}
\item[3\s] high shortage
\item[3\nt] low shortage, \nf
\end{itemize}
\section{1\d--1\nt}
\section{1\d--2\c/2\d}
\section{1\d--2\nt}
\chapter{The 1\h\ and 1\s\ openings}
We open 1\h\ or 1\s\ with a 5-card major and 10--14 \hcp\ in \fs,
12--16 \hcp\ in \tf\ (though we could occasionally have fewer than
12). We open 1\h\ or 1\s\ even with a 6-card minor if the hand is
minimum. We normally do not open 1\nt\ with a 5-card major, but may
if the hand is especially notrump-oriented, with a poor suit and
values in the side suits.
Our raises include
\begin{itemize}
\item 2\M, a ``very constructive'' raise: roughly 11--13 support
points and 3-card support (maybe 4-card support in a balanced hand);
\item 2\nt\ as a 4\+-card limit raise or a 3\+-card slammish raise
(though other sequences are available with the latter);
\item 3\M, a mixed raise: 4-card support (rarely 3 or 5) and
constructive but less than limit values;
\item 3\M+1, an undisclosed light splinter, enough to make slam
opposite a well-fitting maximum opener;
\item 3\nt\ (when \M=\h), 4\c\ and 4\d, strong splinters, enough to
make slam opposite a well-fitting minimum opener (when \M=\s, both
club and heart splinters go through 4\c);
\item 4\M, to play, but might be either a classic preemptive raise to
4 or a high-card raise without slam interest or anything in-between.
\end{itemize}
Hands with 3\+-card support unsuitable for the above raises go through
a forcing 1\nt\ and correct opener's rebid to 2\M. This includes
hands with 3-card support and less than invitational values or ugly
4-card raises that do not want to commit to the 3-level. Note that
1\s--4\h\ is to play (as is 1\h--4\s).
We play 2/1 \gf, with 2\c\ clubs or balanced (may have 3-card support,
or 4 \s s over 1\h) and 2\d\ and 2\h\ guaranteeing 5-card suits. For
continuations, see section \ref{2over1}. Game-forcing 1444 hands in
response to a 1\s\ opening go through a forcing 1\nt\ and bid game or
jump in a new suit on the next round.
1\s\ over 1\h\ is natural and forcing with 4\+\ spades, and 1\nt\ is a
forcing notrump. However, neither of these bids promises any values.
Moreover there are many hands with exactly 4 spades which start with a
bid other than 1\s\ (see section \ref{1h-1s} for details) so in fact
1\s\ is quite often a 5-card suit. As previously mentioned, the
forcing 1\nt\ contains weak raises and \gf\ 1444 hands over 1\s, as
well as nonfitting weak-to-invitational hands except for one-suited
invites. Single jump shifts to the 3-level are invitational while
1\h--2\s\ is weak; the sequence 1\h--1\s--2\x--2\s\ is invitational
with a 6-card suit.
XXX Passed hand bidding? Fit jumps?
\section{Artificial raise sequences}
We have two ranges of splinters, shown in Figure
\ref{fig:1M-splinters}. With an extremely strong hand, responder may
do better to eschew a splinter and instead start with 2\nt\ or 2\c.
\begin{figure}[ht]
\begin{center}