world_abstract_games/bulo.htm at main · jpneto/world_abstract_games · GitHub

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<title>Games of Soldiers - BULO</title>
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<blockquote>
<h1 align="center"><strong><font face="Arial Black">BULO</font></strong></h1>
<p align="center"><font size="3"><strong>Copyright (c) 1949 Piet Hein</strong></font></p>
<p align="left"><font size="3" face="Arial">This gam</font><font size="3" face="Arial">e
(aka TacTix) is played on the following 4x4 square board:</font></p>
    <center>
      <table border="1" width="186" cellspacing="1" bordercolorlight="#333366" bordercolordark="#000000">
        <tr>
          <td width="100%" background="back-board.jpg" align="center">
<script LANGUAGE="JavaScript">boardgv2diag("lurd,4,4,xxxx/xxxx/xxxx/xxxx");</script>
          </td>
        </tr>
      </table>
    </center>
&nbsp;
<table border="0" width="80%">
  <tr>
    <td width="100%">
      <ul>
		<li><font size="3" face="Arial"><b>TURNS</b>
            - At each turn, each player must remove a connected orthogonal line
          of stones.</font>
            </li>
		<li><font
        size="3" face="Arial"><strong>GOAL</strong> - The player that removes
          the last stones, loses.</font></li>
		</ul>
    </td>
  </tr>
</table>
&nbsp;
<table border="1" width="600" cellspacing="3" cellpadding="2" bordercolorlight="#333366" bordercolordark="#000000">
    <tr>
      <td align="center" width="110" bordercolor="#000000" background="back-board.jpg">
<script LANGUAGE="JavaScript"><!--
boardgv2diag("lurd,4,4,.xX./..Xx/xx../.xx.");
//--></script>
      </td>
      <td valign="top" width="414"><font face="Arial"><strong>An example</strong><p><font size="3" face="Arial">If
        the next player removes the marked stones, he wins the game. The
        adversary cannot avoid removing the last stone(s).</font></font>
      </td>
    </tr>
</table>
<p><font size="3" face="Arial">This is a CGT game, sort of 2D NIM. With perfect
play, the second player wins.</font></p>
<p><font size="3" face="Arial">This game can
be expanded to any board size (<b>TacTex</b> is one name used for hex boards), and also to allow different shapes to be removed
(like rectangles, pentominoes or diagonal crosses). </font></p>
<p><font size="3" face="Arial"><a name="eatcake"></a></a><b>Eatcake</b>
 <font SIZE="3">is a misère Bulo</font>: Given a NxM board full of pieces, the first player
must remove a </font><font size="3" face="Arial">connected horizontal line
          of stones, and second player a vertical line. The last player to move,
wins.</font></p>
<p><a name="bonusNim"></a><font size="3" face="Arial">Bill Taylor invented a variant, called <b>Bonus
NIM</b> played on a 7x7 board (which is expandable to any rectangular board). A player may remove an orthogonal connected line of stones
of any size. There is a restriction for the first move, where the move must take
less than half the maximum possible. Also, there is a bonus of four stones for
making the final capture. <u>Winner is whoever obtains most stones</u>.&nbsp;</font></p>
<table border="1" width="600" cellspacing="3" cellpadding="2" bordercolorlight="#333366" bordercolordark="#000000">
    <tr>
      <td align="center" width="168" bordercolor="#000000" background="back-board.jpg">
<script LANGUAGE="JavaScript"><!--
boardgv2diag("lurd,7,7,xx.x.../x..xXXx/xx.xxxx/7/7/7/7");
//--></script>
      </td>
      <td valign="top" width="414"><font face="Arial"><strong>An example</strong><p><font size="3" face="Arial">First
        player has 18 stones, second player has 17. Second player's turn.</font><p><font size="3">If
        Second removes the marked stones, First may reply by removing the two
        below (e5 and f5), creating a null position (i.e., a winning position)
        which provides him with 4 extra points.</font><p><font size="3">Even if
        Second tries to maximize each move, he will not gather enough stones to
        win (e.g., if Second replies by capturing three stones like d6,d7,d8,
        First just replies g2 and still have enough points to win).</font></font>
      </td>
    </tr>
</table>
<p><font size="3" face="Arial"> This bonus mechanism can be applied to many NIM
games, giving a new interest to these mathematical studied games. The bonus size
is critical to define the best strategy.</font></p>
<p><font size="3" face="Arial">Another NIM-like games: <a href="nineteen.htm">Nineteen</a>,
<a href="kinghorses.htm">King's Horses</a>.</font></p>
</blockquote>
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