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<p>Further issues with the Bar at the 3 Peaks...</p>
<p><b>Background</b></p>
<p>The 3 peaks is a 5 round tournament. The entry was 5d 5d 2d 1d 1d
1k 1k 1k 2k.... and Bob Bagot wanted to put the bar at 1 kyu.
However, the software (Go Draw) put it at 5 dan, so in the first
round the 2 5 dans played each other (and the 2d played a 1 d).
With advice from Geoff - for which many thanks - the bar was
restrospectively changed to 1 kyu for rounds 2-5.</p>
<p>Incidentally one of the 5 dans lost to a 1 dan - it can happen.<br>
</p>
<p> <b>Analysis</b></p>
<p>The BGA Tournament Handbook
(<a class="moz-txt-link-freetext" href="http://www.britgo.org/organisers/handbook/tournament4">http://www.britgo.org/organisers/handbook/tournament4</a>) states (my
added emphasis):<br>
</p>
<h2 style="margin: 0px; padding: 0px; font-weight: bold;
font-family: Helvetica, Arial, sans-serif; clear: both; font-size:
19.2px; line-height: 34.56px; color: rgb(18, 18, 18); font-style:
normal; font-variant-ligatures: normal; font-variant-caps: normal;
letter-spacing: normal; orphans: 2; text-align: start;
text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><i>4.2</i><i><span> </span></i><i>The
Bar</i></h2>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><i>Because a player's
starting score is determined by their grade, a player who was 7
dan would have a massive advantage and the best chance to win
the tournament, as such a player would start with a very high
MMS. To counteract this, and to give as many people as possible
a reasonable chance of winning the tournament, players at or
above a certain rank all begin at the same MMS. This rank is
called the McMahon bar. For example, if the bar is set at 3 dan
(which is an MMS of 2) then no player can start at an MMS of
more than 2, no matter what his or her grade: 3-dans, and all
players stronger than 3-dan, also start with an MMS of 2, and
are said to start "above the bar". The position for the bar
depends on the number of rounds to be played and also the entry
at each of the higher grades. BGA recommended guidelines are as
follows:</i></p>
<table style="border-collapse: collapse; margin: 1em 0px; width:
800px; color: rgb(18, 18, 18); font-family: Verdana, sans-serif;
font-size: 12px; font-style: normal; font-variant-ligatures:
normal; font-variant-caps: normal; font-weight: 400;
letter-spacing: normal; orphans: 2; text-align: start;
text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;" border="0">
<tbody style="border-top: 1px solid rgb(204, 204, 204);">
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>3 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>4-8 players</i></td>
</tr>
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>4 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>5-10 players</i></td>
</tr>
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>5 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>6-12 players</i></td>
</tr>
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>6 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>7-15 players</i></td>
</tr>
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>7 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>8-18 players</i></td>
</tr>
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>8 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>9-22 players</i></td>
</tr>
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>9 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>10-26 players</i></td>
</tr>
<tr>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>10 rounds</i></td>
<td style="padding: 0.3em 0.5em; border-bottom: 1px solid
rgb(233, 214, 186);"><i>11-30 players</i></td>
</tr>
</tbody>
</table>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><i>These figures attempt
to meet the following conditions:</i></p>
<ul style="margin: 0.5em 0px 1em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;">
<li style="margin: 0.4em 0px 0.4em 0.5em; padding: 0px 0px 0.2em
1.5em; list-style-type: none; list-style-image: none;
background:
url("/sites/all/themes/garlandbga/images/menu-leaf.gif")
1px 0.35em no-repeat transparent;"><i>There must be a unique
winner. This sets an absolute upper limit, of 2</i><i><sup>r</sup></i><i><span> </span></i><i>players
above the bar, where r is the number of rounds.</i></li>
<li style="margin: 0.4em 0px 0.4em 0.5em; padding: 0px 0px 0.2em
1.5em; list-style-type: none; list-style-image: none;
background:
url("/sites/all/themes/garlandbga/images/menu-leaf.gif")
1px 0.35em no-repeat transparent;"><i>If there are too many
above the bar, the tournament will end without all of the top
players having played each other.</i></li>
<li style="margin: 0.4em 0px 0.4em 0.5em; padding: 0px 0px 0.2em
1.5em; list-style-type: none; list-style-image: none;
background:
url("/sites/all/themes/garlandbga/images/menu-leaf.gif")
1px 0.35em no-repeat transparent;"><i>If there are too few above
the bar, these receive an unfair (and unnecessary)
disadvantage.</i></li>
<li style="margin: 0.4em 0px 0.4em 0.5em; padding: 0px 0px 0.2em
1.5em; list-style-type: none; list-style-image: none;
background:
url("/sites/all/themes/garlandbga/images/menu-leaf.gif")
1px 0.35em no-repeat transparent;"><i>Higher graded players
should not run out of even game opponents.</i></li>
</ul>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><i>The McMahon System
imposes two quite severe constraints on the pairing of players
at each round. The first is the rule that there are no repeat
games. This increasingly restricts the opponents of the stronger
players in the later rounds. The second is the aim of pairing
players on the same MMS, which provides the main pairing
diversity in the early rounds.</i><i><span> </span></i><i><br>
</i><i><br>
</i><i>These two pairing rules, together with the nature of the
winning probability between players of different grades,
provides quite an important ingredient in determining the
position of the bar. </i><i><b>It turns out that players in the
bar group have at least some chance of winning the tournament
if the difference between the maximum grade and the bar grade
(the bar-depth) is less than 3</b></i><i>, whatever the number
of rounds [See BGJ 173 Finding The Bar].</i></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><i>If you are using
Geoff Kaniuk's GoDraw to create the draw,</i><i><b> it will
automatically set the bar according to the above table taking
into acount the restriction on the bar depth</b></i><i>. This
is particularly effective in tournaments where the dan entry is
very fragmented with possible gaps in the higher grades.</i></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><br>
<font face="Arial">Of course, the statement on bar depth being
less than 3 assumes that the grades are "correct" in some
ill-defined way. <br>
</font></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-size: 12px; font-style: normal; font-variant-ligatures:
normal; font-variant-caps: normal; font-weight: 400;
letter-spacing: normal; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; background-color: rgb(255, 255,
255); text-decoration-style: initial; text-decoration-color:
initial;"><font face="Arial">It is clear that what is happening is
the restriction on bar depth is over-riding the recommended
nuimbers in the Table. I believe that this is wrong, and that
the Table should have supremacy.</font></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-size: 12px; font-style: normal; font-variant-ligatures:
normal; font-variant-caps: normal; font-weight: 400;
letter-spacing: normal; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; background-color: rgb(255, 255,
255); text-decoration-style: initial; text-decoration-color:
initial;"><font face="Arial">The Table is constructed on 2 simple
principles:-</font></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-size: 12px; font-style: normal; font-variant-ligatures:
normal; font-variant-caps: normal; font-weight: 400;
letter-spacing: normal; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; background-color: rgb(255, 255,
255); text-decoration-style: initial; text-decoration-color:
initial;"><font face="Arial">a) The total should be less than 2**n
(where n is the number of rounds - this ensures a unique winner</font></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><font face="Arial">b)
The Tournament winner's opponents should all have started above
the Bar (although one appreciates that this may not have been
the case if the number above the bar is odd and the eventual
winner is drawn down in their first game).</font></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><font face="Arial">In
the 3 Peaks example,each 5 dan will play 5 opponents, of
strength (probably) 5d 2d 1d 1d 1k, and if (for example) one of
the 1 dans wins all 5 games, including beating both 5 dans, they
shdol win the Tournament.</font></p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;"><font face="Arial">Of
course one can always play handicap games at the top end.... but
that is a different debate.</font><br>
</p>
<p style="margin: 0.6em 0px 1.2em; padding: 0px; color: rgb(18, 18,
18); font-family: Verdana, sans-serif; font-size: 12px;
font-style: normal; font-variant-ligatures: normal;
font-variant-caps: normal; font-weight: 400; letter-spacing:
normal; orphans: 2; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; widows: 2;
word-spacing: 0px; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255); text-decoration-style:
initial; text-decoration-color: initial;">Toby</p>
<pre class="moz-signature" cols="72">--
Toby Manning
26 Groby Lane
Newtown Linford
LE6 0HH
01530 245298</pre>
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