\documentclass[a4paper]{article}
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\usepackage{grbbridge}
\begin{document}

\title{Strong NoTrump for mathematicians}
\author{Georgi Georgiev (Skeleta)}
\maketitle

%\vspace{5pt}

The short name of the system is \textbf{sNT}. 

It is a relay-based \textbf{Acol}-style natural system. 

Unlimited opening bid 1NT promises 21+ points or $\leq$5 losers (see \ref{1NT}).

\textbf{sNT} uses the compression scheme for distributions, described in 
\href{http://skelet.ludost.net/bidding/distribution_codes.pdf}
{Coding the distributions in contract bridge}, please read it first!

If not specified, we assume that N opens the bidding.

%\textbf{Компресираме} 4 разпределения към 1 \textbf{фиктивно} така: \\
%ако има една нечетна дължина, вадим от нея единица; \\
%ако има една четна дължина, прибавяме към нея единица.

%\vspace{5pt}

\paragraph{}\mbox{}
\textbf{Correct your points} -- reduce one point for 4-3-3-3, 
add one point for double, two points for singleton and 3 points for a void.
Reduce a point for singleton K, D or J.  

\emph{Exceptions:} 
With distributions 4-4-3-2 and 5-3-3-2 do nothing, for 5-4-2-2 add one point.


\section{One-level openings}
\paragraph{}\mbox{}
\cl{1}/\di{}/\he{}/\sp{} promises a 4+ card suit and 11-20 corrected points. 

Divide the strength to min/max -- 11-14/15-20 points ($^-$ and $^+$ in table 1).\\
With minimum open without 6+ color. With skew bicolor 6-4-x-x open in 6-th color.
With flat bicolor (4-4-x-x, 6-6-0-0) open in lower color, if the colors are not glued, % noncontiguous, 
and in higher, if they are glued. 
With 4-4-4-0 open in the color, preceding shortness (with short \cl{} open \sp{1}).

%Делим на минимум и максимум -- 11-14/15-20 точки ($^-$ и $^+$ в таблица 1).\\
%С минимум откриваме без 6+ цвят. С неравен бикульор откриваме в 6-тия цвят.
%С равен бикульор (4-4-x-x, 6-6-0-0) откриваме в по-ниския цвят, ако не са съседни
%и в по-високия, ако са съседни.

\emph{Exceptions:} 

With min and 6-4-x-x open 1$\clubsuit$.

With min and x-6-4-x open 1$\diamondsuit$.

With min and x-x-6-4 open 1$\heartsuit$.

\paragraph{}\mbox{}
S decreases his points, if misfit is probable.

With provided 8, 9 or 10-card fit, he adds 1, 2 or 3 points respectively.

\paragraph{Responses to 1 of a suit:}\mbox{}

pass -- 0-5 points

glued bid -- 10+ points, forcing for one round, N becomes a teller and uses

$\quad$ table 1 to describe his shape. New glued bid from S is relay and game

$\quad$ forcing, any other rebid is natural and contract offer.

all other bids -- 6-9 points, natural and limited.

\paragraph{Short color of N:}\mbox{}

In the majority of cases the glued color of the opening bid is short color of N (0-3 cards). 
This is the reason why the forcing bid of S starts here.
After \cl{1}/\di{}/\he{}/\sp{} short color is \di{}/\he{}/\sp{}/\cl{} respectively.

%\newpage

\input{table_sNT_a.tex}

After the second, forcing bid from S, he becomes an Asker.
%This forcing is glued bid again, if there is no special arrangement.
N divides the maximum (15-20 points) into two intervals -- m=15-17p. and M=18-20p.
He describes his group and strength, using levels.
A list of options is explained as in the examples:

4-x-4-x, 4-0-4-4 $\to$ (4-x-4-x$^-$, 4-0-4-4$^-$, 4-x-4-x$^+$, 4-0-4-4$^+$)

4-x-x-4 $\to$ (4-x-x-4$^-$, 4-x-x-4$^+$) $\to$ (4-x-x-4$^-$, 4-2-2-4$^+$, 5-3-1-5$^+$, 5-1-3-5$^+$)

6-x-x-x$^+$ $\to$ (6-x-x-x$^M$, 6-x-x-x$^m$) %$\to$

$\quad$ $\quad$ $\quad$ $\to$ (6-x-x-x$^M$, 6-2-2-2$^m$, 7-3-3-1$^m$, 7-3-1-3$^m$, 7-1-3-3$^m$)

%\vspace{5pt}

\section{Weak openings}
\paragraph{}\mbox{}
Openings from \cl{2} up to \sp{4} promises a 6+ card suit and 11-14 corrected points:

\vspace{5pt}
%\paragraph{}\mbox{}

2 $\clubsuit , \diamondsuit , \heartsuit$ % $ , \spadesuit$
-- 6+ suit, 0-3 cards in next color (see Table 2)

2 $\spadesuit$
-- 6+ spade: groups 4-x-x-6, x-4-x-6, x-x-x-6

2 $NT$ -- 6+ spade: groups x-x-4-6, 0-0-6-6

3 $\clubsuit , \diamondsuit , \heartsuit , \spadesuit$ -- 8-x-x-x into the suit.

4 $\clubsuit , \diamondsuit , \heartsuit , \spadesuit$  -- 10-x-x-x into the suit. 

\vspace{5pt}
%\paragraph{}\mbox{}

Glued bid from S is forcing with 13+ points, all other responses are natural.% and limited.

\input{table_sNT_b.tex}

%Допълнителни фиктивни разпределения:\\
%3-3-3-3=(4-3-3-3, 3-4-3-3, 3-3-4-3, 3-3-3-4)\\
%5$^=$-3-3-3=(5-2-3-3, 5-3-2-3, 5-3-3-2)
%\vspace{5pt}

\section{Additional tables}

\vspace{5pt}

\input{table_sNT_c.tex}

\vspace{2pt}

\input{table_sNT_d.tex}

\vspace{5pt}

%\textbf{Намеси след откриване на противника:}
\textbf{Overcalls:}

\vspace{4pt}

After opponents 1$\clubsuit$ opening:

$\quad$ double -- same as opening 1$\clubsuit$ 

$\quad$ all other bids are same as the openings. 

\vspace{4pt}

After 1$\diamondsuit$ or higher opponents opening use the standard overcalls.

\newpage

\section{Opening 1NT}\label{1NT}

%\textbf{Силно откриване:} 1NT -- 21+ точки или до 5 губещи. Развитие:
\paragraph{}
\textbf{Unlimited} opening bid 1NT promises 21+ points or $\leq$5 losers.
This is the most complex part of the system.
The player, who first make a bid in range \he{2}$\ldots$\sp{4} 
describes his distribution and becomes a teller.

\paragraph{}
Bids from \he{2} to \cl{3} promises 4+ cards in \he{}/\sp{}/\di{}/\cl{} 
and 0-3 cards in \sp{}/\di{}/\cl{}/\he{} respectively. 
Exact groups for bids  \he{2}$\ldots$\di{3} are defined in table 1NT. 
Meaning of the higher bids:

3$\heartsuit$ -- groups x-x-6-4, 0-0-6-6 (after relay, expand x-x-6-4 first)

3$\spadesuit$ -- group x-4-x-6

3NT -- group 6-x-x-4 (relay is 4$\diamondsuit$)

4 $\clubsuit , \diamondsuit , \heartsuit , \spadesuit$ -- 10-x-x-x.


\paragraph{Responses from S:}\mbox{}

2$\clubsuit$ -- 0-5 points, at most one control (K or singleton)

$\quad$ 2$\diamondsuit$ -- forcing, S describes his shape with a bid in range \he{2}$\ldots$\sp{4}.

$\quad$ 2$\heartsuit\ldots$3$\spadesuit$ -- proposal for a score, not forcing.

2$\diamondsuit$ -- 10+ points, N describes his shape with a bid in range \he{2}$\ldots$\sp{4}.

\he{2}$\ldots$\sp{4} -- 6-9 points and suitable distribution.

\vspace{4pt}

\input{table_sNT_e.tex}

\vspace{10pt}

\copyright\ by Skelet in terms of LGPL, mail:skeleta@gmail.com 
% (GNU Lesser General Public License).

\LaTeX\ and PDF files: % http://skelet.ludost.net/bidding/sNT\_en/
\href{http://skelet.ludost.net/bidding/sNT_en/}
{http://skelet.ludost.net/bidding/sNT\_en/}

%Мейлът ми за кореспонденция е skeleta@gmail.com

\end{document}