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		<title>Way Too Much Math</title>
		<link>http://madscientist.net/2008/02/15/way-too-much-math/</link>
		<comments>http://madscientist.net/2008/02/15/way-too-much-math/#comments</comments>
		<pubDate>Fri, 15 Feb 2008 20:41:09 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Stupid Geek Tricks]]></category>

		<guid isPermaLink="false">http://madscientist.net/2008/02/15/way-too-much-math/</guid>
		<description><![CDATA[I&#8217;ve lately started playing Warhammer after a pretty prolonged absence. To get back into it and to get use to the new rules I played a couple of small skirmishes, orcs against high elves, and I noticed something odd. Very often when my block of orc spearmen would come up against a smaller block of [...]]]></description>
			<content:encoded><![CDATA[<p>I&#8217;ve lately started playing Warhammer after a pretty prolonged absence. To get back into it and to get use to the new rules I played a couple of small skirmishes, orcs against high elves, and I noticed something odd. Very often when my block of orc spearmen would come up against a smaller block of high elf spearmen it was the elves who would break.<span id="more-60"></span></p>
<p>This seemed a bit odd to me since it seemed as though the odds should all be in favor of the elves. With smaller bases they could have 6 elves come into contact with 5 orcs. Secondly their spearmen have a big advantage in that they are allowed an extra row of attacks, meaning that they would get 18 attacks to my 10. Lastly the high elves had a better leadership score.</p>
<p>At first I wrote off the success of the orcs to a combination of lucky rolls and to getting my opponent to charge, reducing the number of attacks the elves could make. That only got me so far, though. I couldn&#8217;t recall making any really spectacular rolls and as I thought about it I realized that more than a few of those breaks occurred when I charged, reducing my number of attacks, or in the second round of combat when three rows of spearmen were able to fight.</p>
<p>I thought maybe the orcs just had a significantly higher probability of wounding the elves. Their high toughness meant the elves needed to roll a 5 to wound and even though they needed only a 3 to hit I knew that their odds were worse than the 4 to hit and 4 to wound the orcs needed. However after I thought about it a little longer I realized the odds weren&#8217;t really that different. For the orcs the odds of getting a hit and wounding were 1 in 4. For the elves the odds were 2 in 9. A little in favor of the orcs until you give the elves nearly twice as many attacks. Armor saves for the two units was identical so that was no help.</p>
<p>Time to start digging down into the exact probabilities and to stop guessing.</p>
<p>The first thing I had to do was to calculate the odds of each race causing a casualty. To cause a casualty there are three successive rolls involved. First the roll to hit. Next the roll to wound. Finally the armor save. If any one of those rolls fails (or succeeds in the case of armor) then the attack fails to cause a casualty. This makes the odds of causing a casualty fairly easy to calculate. For the orcs the odds are 1 in 2 times 1 in 2 times 2 in 3, or 1 in 6. For the elves the odds of causing a wound are 2 in 3 time 1 in 3 time 2 in 3 or 4 in 27.</p>
<p>Now that I had the odds of a single attack causing a casualty I could work out the odds of all the casualties each unit could cause. For a specific number of casualties the odds would be the odds of success raised to the number of casualties time the odds of failure raised to the remaining units times the number of possible combinations that resulted in that exact number of casualties. Put into a formula this is S<SUP>c</SUP>*(1-S)<SUP>(t-c)</SUP>*C(t,c) where S was the chance of success, c was the number of casualties caused, t was the total number of attacks, and C() was the combination formula of t!/c!(t-c)!.</p>
<p>For the orcs this gave me the following table:</p>
<p><TABLE WIDTH=100% BORDER=1 BORDERCOLOR="#000000" CELLPADDING=2 CELLSPACING=0><TR><TD>0</TD><TD>1</TD><TD>2</TD><TD>3</TD><TD>4</TD><TD>5</TD><TD>6</TD><TD>7</TD><TD>8</TD><TD>9</TD><TD>10</TD></TR><TR><TD>.1615</TD><TD>.3230</TD><TD>.2907</TD><TD>.1550</TD><TD>.0543</TD><TD>.0130</TD><TD>.0022</TD><TD>.0002</TD><TD>.0000</TD><TD>.0000</TD><TD>.0000</TD></TR></TABLE></p>
<p>For the elves this gave me this table:</p>
<p><TABLE WIDTH=100% BORDER=1 BORDERCOLOR="#000000" CELLPADDING=2 CELLSPACING=0><TR><TD>0</TD><TD>1</TD><TD>2</TD><TD>3</TD><TD>4</TD><TD>5</TD><TD>6</TD><TD>7</TD><TD>8</TD><TD>9</TD><TD>10</TD><TD>11</TD><TD>12</TD><TD>13</TD><TD>14</TD><TD>15</TD><TD>16</TD><TD>17</TD><TD>18</TD></TR><TR><TD>.0558</TD><TD>.1746</TD><TD>.2582</TD><TD>.2395</TD><TD>.1562</TD><TD>.0760</TD><TD>.0287</TD><TD>.0085</TD><TD>.0020</TD><TD>.0004</TD><TD>.0001</TD><TD>.0000</TD><TD>.0000</TD><TD>.0000</TD><TD>.0000</TD><TD>.0000</TD><TD>.0000</TD><TD>.0000</TD><TD>.0000</TD></TR></TABLE></p>
<p>Crossing the two tables together gave me the chance of each combination occurring. As an example since there is a 32.30% chance of the orcs inflicting one casualty and a 25.82% chance of the elves inflicting 2 there is an 8.34% (.3230*.2582) chance that the orcs will inflict 1 casualty while the elves will inflict 2.</p>
<p><TABLE WIDTH=100% BORDER=1 BORDERCOLOR="#000000" CELLPADDING=2 CELLSPACING=0><TR><TD WIDTH=8%><BR></TD><TD WIDTH=8%>0</TD><TD WIDTH=8%>1</TD><TD WIDTH=8%>2</TD><TD WIDTH=8%>3</TD><TD WIDTH=8%>4</TD><TD WIDTH=8%>5</TD><TD WIDTH=8%>6</TD><TD WIDTH=8%>7</TD><TD WIDTH=8%>8</TD><TD WIDTH=8%>9</TD><TD WIDTH=8%>10</TD></TR><TR><TD WIDTH=8%>0</TD><TD WIDTH=8%>.0090</TD><TD WIDTH=8%>.0180</TD><TD WIDTH=8%>.0162</TD><TD WIDTH=8%>.0086</TD><TD WIDTH=8%>.0030</TD><TD WIDTH=8%>.0007</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>1</TD><TD WIDTH=8%>.0282</TD><TD WIDTH=8%>.0564</TD><TD WIDTH=8%>.0508</TD><TD WIDTH=8%>.0271</TD><TD WIDTH=8%>.0095</TD><TD WIDTH=8%>.0023</TD><TD WIDTH=8%>.0004</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>2</TD><TD WIDTH=8%>.0417</TD><TD WIDTH=8%>.0834</TD><TD WIDTH=8%>.0751</TD><TD WIDTH=8%>.0400</TD><TD WIDTH=8%>.0140</TD><TD WIDTH=8%>.0034</TD><TD WIDTH=8%>.0006</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>3</TD><TD WIDTH=8%>.0387</TD><TD WIDTH=8%>.0773</TD><TD WIDTH=8%>.0696</TD><TD WIDTH=8%>.0371</TD><TD WIDTH=8%>.0130</TD><TD WIDTH=8%>.0031</TD><TD WIDTH=8%>.0005</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>4</TD><TD WIDTH=8%>.0252</TD><TD WIDTH=8%>.0504</TD><TD WIDTH=8%>.0454</TD><TD WIDTH=8%>.0242</TD><TD WIDTH=8%>.0085</TD><TD WIDTH=8%>.0020</TD><TD WIDTH=8%>.0003</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>5</TD><TD WIDTH=8%>.0123</TD><TD WIDTH=8%>.0246</TD><TD WIDTH=8%>.0221</TD><TD WIDTH=8%>.0118</TD><TD WIDTH=8%>.0041</TD><TD WIDTH=8%>.0010</TD><TD WIDTH=8%>.0002</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>6</TD><TD WIDTH=8%>.0046</TD><TD WIDTH=8%>.0093</TD><TD WIDTH=8%>.0083</TD><TD WIDTH=8%>.0044</TD><TD WIDTH=8%>.0016</TD><TD WIDTH=8%>.0004</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>7</TD><TD WIDTH=8%>.0014</TD><TD WIDTH=8%>.0028</TD><TD WIDTH=8%>.0025</TD><TD WIDTH=8%>.0013</TD><TD WIDTH=8%>.0005</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>8</TD><TD WIDTH=8%>.0003</TD><TD WIDTH=8%>.0007</TD><TD WIDTH=8%>.0006</TD><TD WIDTH=8%>.0003</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>9</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>10</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>11</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>12</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>13</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>14</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>15</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>16</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8%>17</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=8% HEIGHT=12>18</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR></TABLE></p>
<p>I also constructed two more tables. Each table lists the chance of either the orcs or elves failing a leadership roll under a specific set of circumstances.</p>
<p><TABLE WIDTH=100% BORDER=1 BORDERCOLOR="#000000" CELLPADDING=2 CELLSPACING=0><TR><TD WIDTH=9%><BR></TD><TD WIDTH=8%>0</TD><TD WIDTH=8%>1</TD><TD WIDTH=8%>2</TD><TD WIDTH=8%>3</TD><TD WIDTH=8%>4</TD><TD WIDTH=8%>5</TD><TD WIDTH=8%>6</TD><TD WIDTH=8%>7</TD><TD WIDTH=8%>8</TD><TD WIDTH=8%>9</TD><TD WIDTH=8%>10</TD></TR><TR><TD WIDTH=9%>0</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>1</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>2</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>3</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>4</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>5</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>6</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>7</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>8</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>9</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>10</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>11</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>12</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>13</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.4167</TD></TR><TR><TD WIDTH=9%>14</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.5833</TD></TR><TR><TD WIDTH=9%>15</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.7222</TD></TR><TR><TD WIDTH=9%>16</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.8333</TD></TR><TR><TD WIDTH=9%>17</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9167</TD></TR><TR><TD WIDTH=9% HEIGHT=12>18</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD></TR></TABLE></p>
<p><TABLE WIDTH=100% BORDER=1 BORDERCOLOR="#000000" CELLPADDING=2 CELLSPACING=0><TR><TD WIDTH=9%><BR></TD><TD WIDTH=8%>0</TD><TD WIDTH=8%>1</TD><TD WIDTH=8%>2</TD><TD WIDTH=8%>3</TD><TD WIDTH=8%>4</TD><TD WIDTH=8%>5</TD><TD WIDTH=8%>6</TD><TD WIDTH=8%>7</TD><TD WIDTH=8%>8</TD><TD WIDTH=8%>9</TD><TD WIDTH=8%>10</TD></TR><TR><TD WIDTH=9%>0</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD></TR><TR><TD WIDTH=9%>1</TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD></TR><TR><TD WIDTH=9%>2</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD></TR><TR><TD WIDTH=9%>3</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD></TR><TR><TD WIDTH=9%>4</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.9722</TD><TD WIDTH=8%>.9722</TD></TR><TR><TD WIDTH=9%>5</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.9167</TD><TD WIDTH=8%>.9722</TD></TR><TR><TD WIDTH=9%>6</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD><TD WIDTH=8%>.9167</TD></TR><TR><TD WIDTH=9%>7</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD><TD WIDTH=8%>.8333</TD></TR><TR><TD WIDTH=9%>8</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD><TD WIDTH=8%>.7222</TD></TR><TR><TD WIDTH=9%>9</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD><TD WIDTH=8%>.5833</TD></TR><TR><TD WIDTH=9%>10</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD><TD WIDTH=8%>.4167</TD></TR><TR><TD WIDTH=9%>11</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%>.2778</TD></TR><TR><TD WIDTH=9%>12</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>13</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>14</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>15</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>16</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>17</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9% HEIGHT=12>18</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR></TABLE></p>
<p>The first table is for the orcs and the second is for the elves. These tables were built with the assumption that the general (a hero in this case) is close enough to allow the unit to use his leadership skill. It also assumes a 2 point advantage in the combat results for the orcs for extra ranks (4 ranks instead of 3) and superior numbers (these are conditions under which the combats were occurring). Because orcs cost so much less than high elves they will probably almost always have superior numbers, though the elves can certainly field a fourth rank.</p>
<p>An example of the tables in action is if the orcs inflict 1 casualties and the elves inflict 2 the elves need an 8 (9 for their leadership-1 for the combat results) for their leadership roll, which is a 27.78% chance to break.</p>
<p>Multiplying these two tables with the probability table for a given combination gave me my last two tables. Again the first table is for orcs and the second table is for elves. They show the odds that in a combat a given combination of wounds will occur and that the loosing side (if there is one) will fail to make its leadership roll. As a final example since there is an 8.34% chance of the orcs inflicting 1 casualty and the elves inflicting 2 in a combat and this will result in a break for the elves 27.78% of the time there is a 2.32% (.0834*.2778) chance that in a combat the orcs will inflict 1 casualty, the elves will inflict 2, and the elves will break.</p>
<p><TABLE WIDTH=100% BORDER=1 BORDERCOLOR="#000000" CELLPADDING=2 CELLSPACING=0><TR><TD WIDTH=9%><BR></TD><TD WIDTH=8%>0</TD><TD WIDTH=8%>1</TD><TD WIDTH=8%>2</TD><TD WIDTH=8%>3</TD><TD WIDTH=8%>4</TD><TD WIDTH=8%>5</TD><TD WIDTH=8%>6</TD><TD WIDTH=8%>7</TD><TD WIDTH=8%>8</TD><TD WIDTH=8%>9</TD><TD WIDTH=8%>10</TD></TR><TR><TD WIDTH=9%>0</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>1</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>2</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>3</TD><TD WIDTH=8%>.0161</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>4</TD><TD WIDTH=8%>.0147</TD><TD WIDTH=8%>.0210</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>5</TD><TD WIDTH=8%>.0089</TD><TD WIDTH=8%>.0143</TD><TD WIDTH=8%>.0092</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>6</TD><TD WIDTH=8%>.0039</TD><TD WIDTH=8%>.0067</TD><TD WIDTH=8%>.0049</TD><TD WIDTH=8%>.0019</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>7</TD><TD WIDTH=8%>.0013</TD><TD WIDTH=8%>.0023</TD><TD WIDTH=8%>.0018</TD><TD WIDTH=8%>.0008</TD><TD WIDTH=8%>.0002</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>8</TD><TD WIDTH=8%>.0003</TD><TD WIDTH=8%>.0006</TD><TD WIDTH=8%>.0005</TD><TD WIDTH=8%>.0002</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>9</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0001</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>10</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>11</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%><BR></TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>12</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%><BR></TD></TR><TR><TD WIDTH=9%>13</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=9%>14</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=9%>15</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=9%>16</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=9%>17</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR><TR><TD WIDTH=9%>18</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD><TD WIDTH=8%>.0000</TD></TR></TABLE></p>
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<p>Totaling the contents of each table then tells me exactly what the odds are that in a given combat the side will break. In the case of the orcs it winds up being an 11.00% chance they will break while in the case of the high elves if winds up being a much higher 27.77% chance they will break.</p>
<p>Since I was pulling most of this math out of my butt (surprisingly there&#8217;s a lack of books on calculating break odds for WFB) I was a bit suspicious of these numbers. I never took a class in statistics or probability though I knew I had a pretty good grasp of the concepts and I haven&#8217;t taken a math class in over 20 years. So I sat down and wrote a little program for my calculator that would run a number of battles and give me the results. After simulating 30,000 combats I came up with 3,324 breaks for the orcs, 8,287 breaks for the elves, and 18,389 combats where neither side broke. This was against a projected result of 3,300 breaks for the orcs, 8,330 breaks for the elves, and 18,370 combats with no breaks occurring. That looked pretty good to me and after a quick spot of research and feeding it through a chi<SUP>2</SUP> goodness of fit test I came up with a 81.21% confidence. Research said that was to be considered extremely high confidence but since I don&#8217;t do chi<SUP>2</SUP> tests that often I wanted a little more data. I left the results as they were but changed the predicted values to 3,300/8,180/18,520. This was the predicted result if the predicted odds for the high elves, who already had scored fewer breaks than predicted, was half a percent lower (27.27% instead of 27.77%). Confidence dropped to 28.64%. Seeing the predicted results coming out so close to the observed results made me very confident that the theories I was using were correct.</p>
<p>Of course back when I made the combinations table I already knew I didn&#8217;t want to sit down with a calculator and calculate the contents of all 180 combinations so I set up a spreadsheet to do it, and the following steps, for me. The totals surprised me so I decided to change a couple of values and see what that did to the results. After about the third time of editing some of the tables I decided it would be better to just put the values where I could easily change them and to upgrade the code to make building the tables more automatic. With that done I could quickly and easily change values and see the odds of breaking for each side if the orcs charged, if the elves charged, if the elves had another rank, etc. and I found my answer; the single biggest factor in the odds of who broke was the combat result bonus. Add a fourth row of elves and reduce the orc bonus from +2 to +1 and now there was a 21.52% chance of the orcs breaking and only a 16.12% chance of the elves breaking. Nothing else had as profound an effect. If the orc spearmen charged then the odds would swing to be very slightly in the elves favor (17.83% to 16.79% orcs to elves), if the orcs gave up spears and shields for two choppas the odds shifted only a little in the first round and more in the second but the elves were still at a disadvantage (and now the orcs could charge so it was a trade off of risking breaking on the first round for charging spearmen or breaking in the second round for choppas) but really nothing had the impact of that extra rank.</p>
<p>So I guess the moral is &ldquo;Rank up. It has a bigger effect than you probably realize.&rdquo;And just in case you want to play around with the numbers yourself <a href="http://madscientist.net/Warhammer.ods">here is a link to the spreadsheet</a>. So that it is accessible to as many people as possible without having to use pirated software it is in an OpenDocument Spreadsheet (.ods) format which can be read with OpenOffice and a variety of other spreadsheet programs.</p>
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		<title>Not Dead Yet</title>
		<link>http://madscientist.net/2007/01/02/not-dead-yet/</link>
		<comments>http://madscientist.net/2007/01/02/not-dead-yet/#comments</comments>
		<pubDate>Tue, 02 Jan 2007 19:05:11 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Ramblings]]></category>

		<guid isPermaLink="false">http://madscientist.net/2007/01/02/not-dead-yet/</guid>
		<description><![CDATA[So obviously I haven&#8217;t been doing a great deal of posting any posting the past couple of months. This isn&#8217;t because I haven&#8217;t wanted to. I&#8217;ve just been kind of busy. With the release of Echoes of Faydwer a lot of my time was taken up with final polish on the horse animations. Frankly I [...]]]></description>
			<content:encoded><![CDATA[<p>So obviously I haven&#8217;t been doing <strike>a great deal of posting</strike> any posting the past couple of months. This isn&#8217;t because I haven&#8217;t wanted to. I&#8217;ve just been kind of busy.<span id="more-58"></span></p>
<p>With the release of Echoes of Faydwer a lot of my time was taken up with final polish on the horse animations. Frankly I think horses are one of the most difficult things to animate. They&#8217;re creatures that we see an awful lot of, so if there&#8217;s anything off on their animations people pick up on it fairly quickly. Humans are a similar story, of course, but as animators we tend to animate them an awful lot so we get fairly practiced with them. Real horses (as opposed to centaurs, hippogriffs, or other mythical horse-like creatures) are something that we tend to animate pretty infrequently.</p>
<p>Compounding the problem is that, like people, horses come in different builds and will move in different ways. A thick, heavy horse like a Clydesdale is going to move differently than a Shetland pony. Trying to find some sort of happy medium between all the variations was a bit maddening.</p>
<p>But enough rambling about animations. For Christmas I received a great book, Massive Multiplayer Game Development 2. Reading through it has sparked a lot of new thoughts that I want to talk about. I just hope there&#8217;s still enough of you out there to get a good dialogue going.<!--953b6309b06273cbd15fcd37c716e11e--><!--5ea6ee9c8013ba6140e3b7f94437cb1b--><!--6e3802fce5d5127801b85b759c09637d--><!--5c6ad28dc0aee3be4336790161f2d1c4--><!--bdbdcdccdde3264133dec6c6ce945a98--></p>
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		<title>Same Ship, Different Day</title>
		<link>http://madscientist.net/2006/08/22/same-ship-different-day/</link>
		<comments>http://madscientist.net/2006/08/22/same-ship-different-day/#comments</comments>
		<pubDate>Wed, 23 Aug 2006 01:34:16 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/08/22/same-ship-different-day/</guid>
		<description><![CDATA[So I&#8217;ve been playing a fair bit of Eve Online lately. I tried it out because people have told me what a great crafting system it has. Unfortunately I find the system a little flat myself. It doesn&#8217;t really feel like I have much control over customizing what I create. Certainly I can choose which [...]]]></description>
			<content:encoded><![CDATA[<p>So I&#8217;ve been playing a fair bit of Eve Online lately. I tried it out because people have told me what a great crafting system it has. Unfortunately I find the system a little flat myself. It doesn&#8217;t really feel like I have much control over customizing what I create. Certainly I can choose which modules I want to load into my ship, but there&#8217;s nothing particularly interesting about it. Either I have the skills to install a module, at which point it drops right in, or I don&#8217;t. There&#8217;s no elements of attempting something challenging that has a high potential for failure but which also has a chance of success. There&#8217;s no tension in the act since the success or failure is completely preordained and known to the player.<span id="more-57"></span></p>
<p>Working with blueprints to try and decrease time or increase material efficiency is a bit more in line with what I want from crafting but it still doesn&#8217;t really do it for me. The blueprint for my frigate will always produce the same frigate over and over again. I&#8217;ve got no way as a crafter to try and produce a better frigate. The most I can hope for is to produce my frigates a little faster or cheaper than someone else.</p>
<p>I still think it&#8217;s a fun game. I just don&#8217;t see what has people so excited about its crafting.</p>
<p>One thing it has made me think about, however, is the idea of crews. In Eve every ship only has a single player. Pirates of the Burning Sea looks to be the same. Why is this? Am I the only person who thinks it might be interesting to have a group of players controlling a single ship?</p>
<p>There&#8217;s two problems that I can foresee with having multiple people running a ship, of course, but I don&#8217;t think either is insurmountable. The first problem is simply one of making sure that it&#8217;s interesting for everyone. For people who are piloting or working as gunners there&#8217;s not too much that needs to be done but as an engineer there would probably need to be some kind of mini-game in place to let such a player have a more active role assisting in combat.</p>
<p>The other problem I see is that more casual players probably wouldn&#8217;t want to have to go out and round up a crew of others (forced grouping) every time they wanted to do something. That could probably be fixed by allowing NPCs to be hired to fill out empty spots. If the NPCs only had an average level of skill it would still be better to place a PC in those slots if one were available but it would hardly ground a ship if one weren&#8217;t.</p>
<p>Of course such things take time to program and if a lot of people didn&#8217;t want such a feature it would be a waste of resources, so I am stuck wondering if other people would be interested in such an aspect of game play or if I&#8217;m the only one.<!--4c94f47d80e8a7e513051ca336307e1f--><!--64c422cf3d72f5f3b1b089c897490286--><!--8b15296183074e2dd7610a5179b8a815--></p>
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		<title>Stay Tuned.</title>
		<link>http://madscientist.net/2006/07/25/stay-tuned/</link>
		<comments>http://madscientist.net/2006/07/25/stay-tuned/#comments</comments>
		<pubDate>Tue, 25 Jul 2006 19:46:07 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/07/25/stay-tuned/</guid>
		<description><![CDATA[I admit, I suck. It&#8217;s been nearly a week since I published anything. Reality 1.0 has been consuming a lot of my attention lately as I&#8217;ve been trying to complete a &#8216;Work&#8217; quest before the timer runs out. As a result I haven&#8217;t had time to write a post concerning the Mark Rein&#8217;s comments about [...]]]></description>
			<content:encoded><![CDATA[<p>I admit, I suck. It&#8217;s been nearly a week since I published anything. Reality 1.0 has been consuming a lot of my attention lately as I&#8217;ve been trying to complete a &#8216;Work&#8217; quest before the timer runs out. As a result I haven&#8217;t had time to write a post concerning the <a href="http://www.next-gen.biz/index.php?option=com_content&#038;task=view&#038;id=3396&#038;Itemid=2">Mark Rein&#8217;s comments</a> about episodic game content until now, which means that the topic is slightly dated.<span id="more-50"></span></p>
<p>After reading Mark&#8217;s comments the first thing I thought was &#8220;How odd. I&#8217;ve been doing something for the past five and a half years that&#8217;s a broken model and which can&#8217;t possibly work. I suppose that like the bumblebee which has been informed that it violates the rules of aerodynamics and which can&#8217;t possibly fly I should now plummet earthwards.&#8221;</p>
<p>Of course when Mark Rein is speaking of &#8216;Episodic Content&#8217; he isn&#8217;t thinking about MMO&#8217;s at all, but rather than weakening my position I think that strengthens it. Mark Rein isn&#8217;t thinking about anything at all other than publishing &#8216;Episodic Content&#8217; in the exact same fashion that stand-alone content has been published for years. This is sort of like assuming that &#8216;Episodic Television&#8217; can&#8217;t succeed because you can&#8217;t produce and market it the same way you produce and market a feature film. Yes, it is true that you can&#8217;t do that but that hardly means the product concept is doomed. &#8216;Episodic Content&#8217; is similar to the big stand-alone games that are produced but isn&#8217;t identical. Likewise its market is similar (game players) but isn&#8217;t identical. It just means that since you are bringing a different but similar product to a different but similar market you have to use different but similar techniques (as opposed to simply using identical techniques).</p>
<p>So why is this such a big deal to me? Because about a year or two ago I started thinking about the feasibility of producing an MMO that had a lot more episodic content than what traditional MMO&#8217;s have done. Such an MMO would still have lots of static quests, mob spawns, dungeons, and all the typical accoutrement that are associated with an MMO so players wouldn&#8217;t be giving up anything but in addition it would have evolving story-lines that were updated on a weekly basis.</p>
<p>Just as a quick example in EQ2 there could be a large area that is contested between Qeynos and Freeport. Each city has built settlements upon the area. At the outset characters could be given missions to spy upon the other settlements. The Freeport settlement could begin the construction of war machines to attack the Qeynos settlement. Freeport characters could be given quests related to the building of the war machines while Qeynos characters are given quests related to stopping the construction. Once the machines are built and ready the Qeynos characters would have quests to find items to assist in defending against the war machines while the Freeport characters have quests to try and stop such attempts. As conflict looms nearer an underground movement is discovered in the Freeport settlement. Freeport characters will receive quests to try to root out the underground while Qeynos character will receive quests to aid them. Frustrated by the lack of progress in taking over the Qeynos settlement through military means Lucan devises a plan to infiltrate the settlement and poison the food stores.</p>
<p>Rather than releasing the content all at once as is typically done for an expansion the storyline unwraps a bit at a time. During the first week there are only quests to develop the settlements. The next week more buildings are added to the settlement through an update and quests to find out what the other side is up to become available. The week after that a few more buildings are added and construction of the war machines begins while at the same time the quests to develop the settlements go away since there is a shift in effort.</p>
<p>While all of this is going on there is an orc settlement out in the hills and an ancient tower. Some story-lines may bring activity to them but there are plenty of self-contained quests for these zones similar to the quests in Runnyeye or Stormhold.</p>
<p>By doing this an environment could be created where players would &#8216;tune in&#8217; just to see the latest developments, just as people watch television series week after week to see what new things happen. It would create a world that felt much less static and if the story-lines were written in certain ways it would even become possible for characters to see the effects of their actions echoed in the world. What if the Qeynosians aren&#8217;t able to destroy the war machines before they are completed? What if the Freeportians succeed in poisoning the food supply?</p>
<p>Such a tactic would have a lot of difficulties. Story-lines and alternate story-lines would need to be worked out weeks in advance. The constant creation of new quests and art assets would require extra personnel. It would not be possible to fully test the quests  on a test server so the quest engine would need to be rock solid and there would need to be better tools for testing the quests before they went live.</p>
<p>On the other hand the benefits could be immense. If the story-lines were well executed it could strengthen customer retention as well as draw in new customers so that they could watch as the story-lines unfold, as opposed to hearing about them second hand.<!--4d4266e811948c88a9dc72f71304078b--><!--d180da6559e69f51cad0ad2a6a91e7fc--></p>
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		<title>The Rules.</title>
		<link>http://madscientist.net/2006/07/25/the-rules/</link>
		<comments>http://madscientist.net/2006/07/25/the-rules/#comments</comments>
		<pubDate>Tue, 25 Jul 2006 18:53:09 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/07/25/the-rules/</guid>
		<description><![CDATA[As I try to solve game design problems I try to make sure that I adhere to certain rules. This isn&#8217;t a list fixed in stone as every now and then I will think of a new rule that really needs to be inserted, but overall they shouldn&#8217;t change too much. The Game has to [...]]]></description>
			<content:encoded><![CDATA[<p>As I try to solve game design problems I try to make sure that I adhere to certain rules. This isn&#8217;t a list fixed in stone as every now and then I will think of a new rule that really needs to be inserted, but overall they shouldn&#8217;t change too much.</p>
<ol>
<li>The Game has to be fun. This is the most important rule of all. What I&#8217;m working on is a form of entertainment. People don&#8217;t have to play what I design and if what I design isn&#8217;t fun for them then they will stop playing.</li>
<li>Don&#8217;t assume because I enjoy something that other people will enjoy it. Don&#8217;t force them to do activities because I assume everyone will find them fun.</li>
<li>Give people choices. Don&#8217;t leave out activities that other people may enjoy just because I don&#8217;t find them fun. Remember something for everyone.</li>
<li>Keep a clear eye on balance. Make sure one play style doesn&#8217;t get favored over another. Do this by analyzing Risk verses Reward when there are different paths characters may take.</li>
</ol>
<p><!--57c38f6f23cfec72c5050d9c6dff2579--></p>
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		<title>Use and Abuse.</title>
		<link>http://madscientist.net/2006/07/19/use-and-abuse/</link>
		<comments>http://madscientist.net/2006/07/19/use-and-abuse/#comments</comments>
		<pubDate>Wed, 19 Jul 2006 19:39:51 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/07/19/use-and-abuse/</guid>
		<description><![CDATA[Raph Koster wrote an article talking about use-based skill systems in MMO&#8217;s and about how they worked out in Ultima Online and StarWars Galaxies. Just another example of synchronicity since I planned on following up A Distinct Lack of Class with a post about skill systems. As I stated in my earlier post I&#8217;m really [...]]]></description>
			<content:encoded><![CDATA[<p>Raph Koster wrote an <a href="http://www.raphkoster.com/2006/07/18/use-based-systems/">article</a> talking about use-based skill systems in MMO&#8217;s and about how they worked out in Ultima Online and StarWars Galaxies. Just another example of synchronicity since I planned on following up <a href="http://madscientist.net/2006/07/18/a-distinct-lack-of-class/">A Distinct Lack of Class</a> with a post about skill systems.<span id="more-56"></span></p>
<p>As I stated in my earlier post I&#8217;m really not a fan of class based systems. I find them artificial and I feel that too often they lead to odd methods of skill progression (beating up orcs to increase your ability to pick locks, as an example). There are some good points to class based systems, as I stated earlier, but I would rather try to find some way to bring as many of those advantages over to a skill based system than remain in a class based system solely for those advantages.</p>
<p>As I see it there are three main ways of handling advancement in a skill based system. The first is to have players earn experience that they spend as they see fit to advance their skills. A fair amount of tabletop RPG&#8217;s use this method since it is simple and easy to keep a track of. The biggest problem I have with this method is that it still leads to odd methods of skill progression (beat up orcs to earn the experience points you use to increase your lock-picking skills). This can be avoided somewhat by breaking experience into categories instead of a general pool, so the experience you gain from beating up an orc can be used to increase combat skills but not crafting skills. With a large number of pools this can quickly become too cumbersome for a tabletop game but with servers keeping track of a character&#8217;s stats it isn&#8217;t as much of an issue.</p>
<p>The second method I can see, and one I wouldn&#8217;t have even thought of until I tried Eve Online, is time based. You select a skill to &#8216;practice&#8217; and after a fixed amount of time it improves. There&#8217;s no XP to earn, just time to spend. It&#8217;s an interesting approach, but I&#8217;m not 100% sold on it since a player who is highly active progresses at the same rate as someone who only logs in when they need to choose the next skill to train (an oversimplification, but you get the idea). Still, since the skill gain occurs in real time whether you are online or not it definitely reduces any feeling that you are obligated to grind in order to increase skills.</p>
<p>The last method I can see is, of course, the use-based method. Skills are increased as you use them. This, unfortunately, tends to lead to grinding, grinding leads to macroing, and macroing leads to the dark side.</p>
<p>Enter the law of diminishing returns. This isn&#8217;t something I&#8217;ve talked about yet but it&#8217;s something that I&#8217;ve started to consider as possibly being a very important item in design of an MMO. Yeah, &#8216;started to consider as possibly being&#8217; is a pretty weak statement, but I&#8217;m certain of the idea yet, so I&#8217;m not about to trumpet it as a golden rule. Given that it has the ability to prolong enjoyment of a game by removing the importance of grinding, as well as levelling the field a bit between casual and hardcore gamers I can see a lot of potential in it, but I still need some time before I convince myself.</p>
<p>The law of diminishing returns is something that occurs in real life all the time and what it basically means is that as more energy is put into something the lower the return on investment is. This doesn&#8217;t mean that the return is less than it was before, simply that the return doesn&#8217;t scale linearly with the energy expended. </p>
<p>This is pretty much a universal constant, at least once certain minimums of expenditure are met, and the clearest example I can think of is a car. In order for a car to travel twice as fast it has to spend more than twice as much energy. This is because as speed doubles wind resistance squares. This is just one example of course. The world is full of others.</p>
<p>Learning, likewise, suffers from the law of diminishing returns. The longer a person spends trying to learn something without a break the more fatigued they become and the slower they will learn. A person who spends fourteen hours in a single day trying to perfect a skill will learn less than a person who spends two hours a day for a week trying to learn the same skill. </p>
<p>How do we translate that into a game system? Well, for starters I would consider breaking skill levels into &#8216;long term&#8217; and &#8216;short term&#8217; levels, much as human being have long term and short term memory. As a skill is used any gains from it go immediately into the &#8216;short term&#8217; pool.  Points drain out from this short term pool and into the long term pool at a rate based on how high the short term pool is. A short term pool that is higher will transfer faster than a short term pool that is lower</p>
<p>The catch is that the transfer rate isn&#8217;t linear but is an inverse geometric function. A pool that is holding a hundred points might transfer points twice as fast as one holding twenty five points, three times faster than a pool holding eleven points, etc. In the mean time the short term pool will additionally &#8216;bleed&#8217; points faster depending upon how large it is. The points are simply lost and not converted to the long term pool. This rate however is linear, so a pool with a hundred points would drain away at a rate four times faster than a pool with twenty five points and nine times faster than a pool with eleven points. Thus, to continue progressing twice as fast as another player a person would have to spend four times as much energy.</p>
<p>Most of this would be kept hidden from the players for the sake of simplicity, but of course as Raph Koster points out, any system you create will eventually be analyzed and decoded by the player base. To help prevent or at least mitigate &#8216;min-maxing&#8217; on the part of players all individual pools could be combined together for the purposes of transference and loss. A character with two pools at twenty five and one pool at fifty would transfer just as many points as a character with a single pool at one hundred, though the points would be split with a quarter of them going to one skill, a quarter to another, and the remaining half going to the third. Likewise the character would &#8216;bleed&#8217; points at the same rate, again with the loss being divided between the three pools.</p>
<p>Obviously such a system would take some balancing to get the math right. Four times the work for twice the gain might be too much work or too little work, but the concept remains the same. As more energy is spent the character progresses faster, but the  rate of increase is slowed so that the law of diminishing returns applies.<!--b4867304c31527b8eff491b68fdb6ced--></p>
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		<title>A Distinct Lack of Class.</title>
		<link>http://madscientist.net/2006/07/18/a-distinct-lack-of-class/</link>
		<comments>http://madscientist.net/2006/07/18/a-distinct-lack-of-class/#comments</comments>
		<pubDate>Tue, 18 Jul 2006 18:00:57 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/07/18/a-distinct-lack-of-class/</guid>
		<description><![CDATA[I&#8217;m not a 23rd level Artist or an 18th level Geek. I&#8217;m not even multiclassed as an Artist/Designer, but I don&#8217;t feel bad about this. The fact is that people in the real world simply aren&#8217;t divided into classes that dictate what they can and cannot do. So why do games do this? Probably the [...]]]></description>
			<content:encoded><![CDATA[<p>I&#8217;m not a 23rd level Artist or an 18th level Geek. I&#8217;m not even multiclassed as an Artist/Designer, but I don&#8217;t feel bad about this. The fact is that people in the real world simply aren&#8217;t divided into classes that dictate what they can and cannot do. So why do games do this?<span id="more-49"></span></p>
<p>Probably the greatest reason is because this is how Dungeons and Dragons works. You could argue that classes are a connection to that ancestry, a sort of homage, or you could simply say that it&#8217;s because designers tend to work through evolution rather than innovation, but either way the idea of classes in MMO&#8217;s comes to us from classes in Dungeons and Dragons.</p>
<p>Personally I haven&#8217;t really liked the concept of character classes for years. I&#8217;ve got two big objections to them. The first is the limitations.</p>
<p>To me it seems wrong to say that a person can&#8217;t learn to pick up a sword simply because somewhere along the line he identified himself as a &#8216;mage&#8217;. Even stranger to me is the limitation that he can&#8217;t put on a simple chain-mail shirt because he went to the wrong school.  There are, of course, arguments that can be made for this. Armor is heavy and a mage does not devote enough of his attention to physical development to wear it. The metal of the armor interferes with the wizard&#8217;s ability to cast spells. Maneuvering in heavy armor is a skill and a wizard has no experience in how to do so. Well, since the physical power of a character is determined by an attribute rather than a class I don&#8217;t see why a mage with a higher strength than a fighter wouldn&#8217;t be able to wear the same armor. As for the spell casting, we aren&#8217;t talking about the wizard wearing armor and casting spells, we are just talking about the wearing of armor (and that doesn&#8217;t address leather armor, anyway). Finally, while an untrained wizard might not be able to maneuver as well in a chain-mail shirt as a highly trained fighter I have to remain dubious that a person with an IQ of 150 who spends his time unravelling the mysteries of the universe can&#8217;t figure out that his head goes through the big hole and his arms go through the two smaller ones.</p>
<p>The second objection I have to classes is almost the opposite of the first; the things a character can do simply because of their class. Actually I suppose I don&#8217;t object so much to the fact that a thief can sneak around simply because they are a thief. What I really object to is the fact that to get better at sneaking around a thief has to do things completely unassociated with sneaking around; namely killing monsters. Because skills for characters in most games are tied to levels and levels are tied to killing monsters characters improve in skills completely unrelated to what they are doing by beating up on orcs and kobolds.</p>
<p>So what&#8217;s the upside to classes? For one they give us defined roles. When a player is trying to form up a group they can search for a tank by looking for people who belong to a tanking class. When they need DPS they look for someone belonging to a DPS class.</p>
<p>Classes are also easier for inexperienced players to grasp. If you want to run around in heavy armor with a sword you chose a Fighter. You don&#8217;t select the sword skill, the shield skill, the light armor skill which you need to build the medium armor skill which you need for the heavy armor skill. The advantages of simplicity should never be underestimated.</p>
<p>Another thing that classes do is protect the value of certain skills. While it might be too expensive for a wizard to follow the entire skill path of a rogue it probably wouldn&#8217;t be that much to just pick up some skill at disarming traps or picking locks.</p>
<p>On the other hand classless systems give freedom. Properly designed they allow people to make whatever character they are interested in playing (within reason). This can give people a powerful ownership in their character.</p>
<p>So ultimately which one is better for the mass market? Is the more comfortable and established class system the way to go or would a well designed skills based system ultimately draw more players? Under the &#8216;something for everyone&#8217; philosophy that I like to try to hold to can we bring the two systems together? Is there a way to make a system where players can choose either skill based or class based progression? </p>
<p>These questions are what I am turning around and around in my head right now.<!--d07df29c4763455f5a2916179ff36dcf--></p>
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		<title>Speed Bumps or Turtles?</title>
		<link>http://madscientist.net/2006/07/11/speed-bumps-or-turtles/</link>
		<comments>http://madscientist.net/2006/07/11/speed-bumps-or-turtles/#comments</comments>
		<pubDate>Tue, 11 Jul 2006 21:11:02 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/07/11/speed-bumps-or-turtles/</guid>
		<description><![CDATA[Under a previous post Lost asked the question: The real question/debate could be in evaluating each system on their own merits for the entertainment value of the player (which I attempted to touch on in my â€œRMT and game designâ€). While there certainly does need to be a â€œspeed limitâ€ to protect parts aspects of [...]]]></description>
			<content:encoded><![CDATA[<p>Under a previous post Lost asked the question:</p>
<blockquote><p>The real question/debate could be in evaluating each system on their own merits for the entertainment value of the player (which I attempted to touch on in my â€œRMT and game designâ€). While there certainly does need to be a â€œspeed limitâ€ to protect parts aspects of the game, such as the economy, are we trying to build a road with speed bumps or a 50 degree incline mountain road to climb? What value does long crafting/item creation times add to the entertainment value of the player? While it could be debated that it adds realism value, but that is hard position to support when the time it would take to make a sword in the real world would be much longer (even when converted into accelerated game world time).</p></blockquote>
<p>This is a good question and I&#8217;ve had to spend some time thinking about it.<span id="more-55"></span></p>
<p>Now obviously it isn&#8217;t really a question of speed bumps or a 50 degree grade. In both instances the same goal is reached, so to me it seems to be an issue of speed bumps to slow down progress at specific points or a general lowering of the speed limit, hence the title, Speed Bumps or Turtles?.</p>
<p>To me long crafting seems to be the turtle. It moves along slowly and methodically, but it always moves. Instant, or quick, crafting on the other hand will zoom forward whenever the magic button is pushed, spitting out a new item or component, but what then? Since we&#8217;ve already determined that there needs to be an overall limit to how fast players can hurtle down this road players are now forced to sit and wait, doing nothing until the red light changes and they can leap forward again. Since they are bound by the same rules the &#8216;speed bump&#8217; method will actually have to wait until the turtle catches up before zipping ahead again. It&#8217;s true that the speed bump method may be able to leap ahead through several tasks until it&#8217;s finally forced to stop, but the further ahead it jumps the longer it will have to wait, and waiting isn&#8217;t fun at all.</p>
<p>Of course it is possible to make it so that so much time piles up that players will be able to go off to do something else while they are waiting, but doing this runs into the problem of balance between adventuring and crafting. If it takes an average of 10 minutes of work for an adventurer to loot an item how will they react if it only takes 2 minutes of work for a crafter to make one, followed by 8 minutes of hanging around talking with people at the local tavern before the item is complete?<!--67a807561f26df70f992fcee1649c60d--></p>
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		<title>You&#8217;ve Just Gotten Better in Friendliness (28).</title>
		<link>http://madscientist.net/2006/07/05/youve-just-gotten-better-in-friendliness-28/</link>
		<comments>http://madscientist.net/2006/07/05/youve-just-gotten-better-in-friendliness-28/#comments</comments>
		<pubDate>Wed, 05 Jul 2006 21:58:50 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/07/05/youve-just-gotten-better-in-friendliness-28/</guid>
		<description><![CDATA[Raph Koster posted a small snippet about a new beta service called Playerep. I like the effort and hope that links out in the Blogosphere will help to drive a decent number of people to use it. Of course I feel that the system as implemented has some problems (some of which playerep can&#8217;t resolve [...]]]></description>
			<content:encoded><![CDATA[<p>Raph Koster posted a small <a href="http://www.raphkoster.com/2006/07/05/playerep/">snippet</a> about a new beta service called <a href="https://www.playerep.com/">Playerep</a>.<span id="more-53"></span></p>
<p>I like the effort and hope that links out in the Blogosphere will help to drive a decent number of people to use it. Of course I feel that the system as implemented has some problems (some of which playerep can&#8217;t resolve by themselves) but hopefully if it should catch on it will help motivate game companies to come up with similar tools or to at at least provide some tools that will help with the resolution of some of the problems playerep can&#8217;t solve on their own.</p>
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		<title>But Wait, There&#8217;s More!</title>
		<link>http://madscientist.net/2006/07/03/but-wait-theres-more/</link>
		<comments>http://madscientist.net/2006/07/03/but-wait-theres-more/#comments</comments>
		<pubDate>Tue, 04 Jul 2006 03:52:30 +0000</pubDate>
		<dc:creator>Evan</dc:creator>
				<category><![CDATA[Games]]></category>

		<guid isPermaLink="false">http://madscientist.net/2006/07/03/but-wait-theres-more/</guid>
		<description><![CDATA[So as I sit here, struggling to work out a crafting system that allows people to be &#8216;hard core&#8217; crafters while still allowing solo crafters and balancing the whole thing against adventuring I run into a new snag; the concept of &#8216;social whittling&#8216;. Social whittling is a concept proposed by Scott Jennings. In a nutshell [...]]]></description>
			<content:encoded><![CDATA[<p>So as I sit here, struggling to work out a crafting system that allows people to be &#8216;hard core&#8217; crafters while still allowing solo crafters and balancing the whole thing against adventuring I run into a new snag; the concept of &#8216;<a href="http://www.brokentoys.org/2006/06/30/crafty-thoughts/">social whittling</a>&#8216;.<span id="more-52"></span></p>
<p>Social whittling is a concept proposed by Scott Jennings. In a nutshell the idea is that sometimes people want simple, mindless, low stress activities, and that crafting fulfills this need. Now I&#8217;m not sure I agree with that 100% but in keeping with the &#8216;something for everyone&#8217; approach that I want to try to hold to I have to consider it. Obviously there are those who look to use crafting to fill such a role and creating a complicated crafting system runs the danger of &#8216;forcing&#8217; players to do something they find unfun (violating another of my tenets).</p>
<p>Of course the simplest solution, and the one espoused by Scott Jennings, is to have crafting not have any form of mini-game. To attempt a task you simply make sure you have the appropriate materials, click whatever needs to be clicked to start the task, and then wait. After a time you get a message that tells you whether you succeeded or failed.</p>
<p>On one level that seems straight forward enough, but if we balance the time of adventuring against the time of crafting it looks to me to be problematic. Assume for a moment that a solo adventurer will get an item drop roughly once every five minutes. This is probably a bit rapid but it should work for giving us a quick Fermi estimate. That provides a minimum amount of time that a crafter has to spend to make a comparable item. Obviously clicking to start the process and then waiting for five minutes will be incredibly tedious and while it might relax the social whittlers it is sure to bore the more involved crafters to tears. Some of this can be reduced through sub-combines, but it seems unlikely that you can find a number of sub-combines that will keep the dedicated crafters interested without providing too many steps for the social whittlers.</p>
<p>The answer seems to me to be to have two different sorts of crafting activities. I&#8217;m still trying to work out terms and metaphors for these activities but for now let&#8217;s refer to them as Routine and Experimental.</p>
<p>Routine actions are a sort of work-a-day activity. It is a person smelting ore while wondering what&#8217;s for dinner or else pounding out a blade while wondering what the weather will be like tomorrow. It isn&#8217;t the action of a master craftsman paying attention to every detail as they push their skills to their limit. It&#8217;s the action of a person who&#8217;s producing &#8216;yet another&#8217; sword.</p>
<p>Experimental actions, on the other hand, are where a craftsman is trying something new. It&#8217;s a person smelting ore and paying absolute attention to the heat of the fire and the color of the ore or the craftsman who works more carbon into the edge of the blade than is standard to try to make a sharper weapon.</p>
<p>Any step a craftsman would undertake can be either a Routine or Experimental action. Overall the two actions would take close to the same time. Routine actions would have much lower chances of failure but would also produce very average results. Experimental actions on the other hand would have the possibility of producing better results but with an increased chance of failure and would be far more interactive.</p>
<p>This would create a system where you could have social whittlers and dedicated craftsman side by side, but would it work? Would social whittlers feel cheated because their products are typically of lower quality than the dedicated craftsmen? Would dedicated craftsmen feel cheated that social whittling is easier? How prevalent is social whittling, anyway? In a system where crafting is a full blown class would social whittlers make alts so they could craft? Would they find another activity to take the place of social whittling? These are all questions that really need to be answered.<!--bb4b28cccc6b714f56c370937aa00c2f--></p>
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