{"id":377,"date":"2006-05-12T15:08:38","date_gmt":"2006-05-12T20:08:38","guid":{"rendered":"http:\/\/www.shamusyoung.com\/twentysidedtale\/?p=377"},"modified":"2017-12-04T11:59:24","modified_gmt":"2017-12-04T16:59:24","slug":"one-hundred-million-characters-part-1","status":"publish","type":"post","link":"https:\/\/www.shamusyoung.com\/twentysidedtale\/?p=377","title":{"rendered":"One Hundred Million Characters, Part 1"},"content":{"rendered":"<p>A newbie D&#038;D player will usually generate their first character and be disappointed.  They roll the dice, add them up, and realize they have a perfectly run-of-the-mill character.  They were hoping to get a few lucky rolls and come up with someone <em>really<\/em> special.  Then they get an idea: <em>Maybe I&#8217;ll just toss this character and roll up a new one.  Maybe <strong>this time<\/strong> I&#8217;ll get lucky.<\/em><\/p>\n<table align=right>\n<tr>\n<td><img decoding=\"async\" src=\"images\/die6.jpg\"\/><\/td>\n<\/tr>\n<\/table>\n<p>There are six attributes that define a character: Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma. You start by rolling four six-sided dice.  Discard the lowest die. Add the other three together for a number from 3 (feeble) to 18 (magnificent). Do this once for each of your six attributes, and then you have your character.  An attribute of ten is &#8220;average&#8221; for a human being.  However, your character is (hopefully) better than the average human, which is one of the reasons they are a hero in the game world and not milking cows and shoveling dung like everyone else.  The rulebooks claim that 12 is the average value of an attribute for a player character, although below I&#8217;ll show that it&#8217;s actually slightly higher than this.<\/p>\n<p>An attribute of eighteen is hard to come by, since three of the four dice have to come up sixes.  But it&#8217;s even harder to throw a three, since <em>all four<\/em> dice would need to come up as ones. <em>(Note that you have to roll up all six stats one after another. Rolling one stat over and over until you get a number you like is cheating.  This is important.)<\/em><\/p>\n<p>But back to our newbie.  They look at the attributes they rolled:<\/p>\n<table>\n<tr>\n<th colspan=2>The Newbie<\/th>\n<\/tr>\n<tr>\n<th>STR<\/th>\n<td>13<\/td>\n<\/tr>\n<tr>\n<th>DEX<\/th>\n<td>17<\/td>\n<\/tr>\n<tr>\n<th>CON<\/th>\n<td>9<\/td>\n<\/tr>\n<tr>\n<th>INT<\/th>\n<td>14<\/td>\n<\/tr>\n<tr>\n<th>WIS<\/th>\n<td>12<\/td>\n<\/tr>\n<tr>\n<th>CHA<\/th>\n<td>13<\/td>\n<\/tr>\n<tr>\n<td colspan=2 align=right>(Average 13)<\/td>\n<\/tr>\n<\/table>\n<p>They see that their character has an average attribute of 13.  With a score of 13, they are going to actually be a point stronger than the typical character.  But still.  That 9 is disappointing. If only they had thrown something higher there!  They note that only one number is over 16, which is where the really &#8220;good&#8221; values are. The newbie looks at the score and starts wondering how much better they could do.  How hard could it be, anyway?<\/p>\n<p>I wrote a little program to demonstrate exactly this.  I had it roll up 100 million characters and tally the results.  It keeps track of how common the various scores are, and how likely it is that you can score at or above a given number. It will also record the best and worst characters. Note that I doubt there have been 100 million characters in the history of Dungeons &#038; Dragons.  That&#8217;s a third of the population of the U.S.  Well under 10% of the population plays D&#038;D, and many that do use prefab stats or point-buy instead of rolling the dice.  So even in it&#8217;s 30 year history, and even allowing for that fact that some players have several characters, I think the number of legitimate (rolled) characters falls well short of 100 million. <\/p>\n<p>I&#8217;m sure most of what I&#8217;m doing here is probably available online if I were to google around for it, but it&#8217;s far more interesting to go through the steps and see the results myself.<\/p>\n<h3>100,000,000 Characters<\/h3>\n<p>It turns out that rolling the dice this way produces a bell curve with astoundingly steep sides.  An average score of 3 is <em>possible<\/em>, but to get it, you would need a six-sided die come up with a 1, over and over again, for a total of 24 times times in a row.  Over the course of 100 million characters this never happened, which shouldn&#8217;t be a surprise.  The odds of 24 consecutive 1&#8217;s is 1 in 6<sup>24<\/sup>.  More exactly: 1 in 4,738,381,338,321,616,896. I&#8217;m <em>sure<\/em> it&#8217;s never been done. <\/p>\n<p>So at least we don&#8217;t have to worry about that happening.<\/p>\n<p>All 18&#8217;s is a little more likely (1 in 101,559,956,668,416) but that never happened either.  <\/p>\n<p>From the list below, we see that 12.3 is the most common score. If our newbie hopes to re-roll his character and get an average score of 14, the odds are against him.  29% of the characters created have a score of 13 or better, but only 7% have 14 or better.  If he&#8217;s shooting for 15, his chances drop all the way to 0.7%.  He&#8217;ll probably roll over a hundred characters before he sees one with a score of 15.  The odds of throwing a character with a score of 16 or better are an astounding 1 in 4,065.  If 16 still isn&#8217;t good enough and he wants to hold out for a 16.3, his odds shoot up to 1 in 18,867.  Assuming he rolls up a character every minute, he will be at it for over 13 days non-stop to generate 18,867 characters.<\/p>\n<p>Ten might be the normal score for Stableboys and Milk Maids, but only 3.5% of the characters he rolls will be that weak.  Note that the rules suggest that you should discard anything with a score of eleven or less, which will happen 16% of the time.  <\/p>\n<p>To get these stats the program had to roll the dice 2.4 billion times.  Read on to see all the stats and charts in detail&#8230;<\/p>\n<p><!--more--><\/p>\n<table>\n<tr>\n<th>Average<br \/>Attribute<\/th>\n<\/tr>\n<tr>\n<th>17.5:<\/th>\n<td> 2 characters have this score, which is the highest recorded.<\/td>\n<\/tr>\n<tr>\n<th>17.3:<\/th>\n<td>5 characters (0.0000%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>17.2:<\/th>\n<td>28 characters (0.0000%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>17.0:<\/th>\n<td>107 characters (0.0001%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>16.8:<\/th>\n<td>323 characters (0.0003%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>16.7:<\/th>\n<td>911 characters (0.0009%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>16.5:<\/th>\n<td>2,280 characters (0.0023%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>16.3:<\/th>\n<td>5,304 characters (0.0053%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>16.2:<\/th>\n<td>11,817 characters (0.0118%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>16.0:<\/th>\n<td>24,646 characters (0.0246%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>15.8:<\/th>\n<td>48,754 characters (0.0488%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>15.7:<\/th>\n<td>92,280 characters (0.0923%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>15.5:<\/th>\n<td>166,445 characters (0.1664%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>15.3:<\/th>\n<td>287,950 characters (0.2880%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>15.2:<\/th>\n<td>481,556 characters (0.48%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>15.0:<\/th>\n<td>774,993 characters (0.77%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>14.8:<\/th>\n<td>1,208,712 characters (1.2%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>14.7:<\/th>\n<td>1,827,761 characters (1.8%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>14.5:<\/th>\n<td>2,683,623 characters (2.7%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>14.3:<\/th>\n<td>3,833,524 characters (3.8%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>14.2:<\/th>\n<td>5,332,638 characters (5.3%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>14.0:<\/th>\n<td>7,235,428 characters (7.2%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>13.8:<\/th>\n<td>9,592,418 characters (9.6%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>13.7:<\/th>\n<td>12,437,427 characters (12.4%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>13.5:<\/th>\n<td>15,787,558 characters (15.8%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>13.3:<\/th>\n<td>19,642,719 characters (19.6%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>13.2:<\/th>\n<td>23,985,642 characters (24.0%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>13.0:<\/th>\n<td>28,760,117 characters (28.8%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>12.8:<\/th>\n<td>33,903,832 characters (33.9%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>12.7:<\/th>\n<td>39,328,882 characters (39.3%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>12.5:<\/th>\n<td>44,932,945 characters (44.9%) have this score or higher.<\/td>\n<\/tr>\n<tr>\n<th>12.3:<\/th>\n<td> 5,671,712 characters. This is the most common score.<\/td>\n<\/tr>\n<tr>\n<th>12.2:<\/th>\n<td>49,395,343 characters (49.4%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>12.0:<\/th>\n<td>43,763,388 characters (43.8%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>11.8:<\/th>\n<td>38,286,261 characters (38.3%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>11.7:<\/th>\n<td>33,056,293 characters (33.1%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>11.5:<\/th>\n<td>28,160,847 characters (28.2%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>11.3:<\/th>\n<td>23,659,255 characters (23.7%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>11.2:<\/th>\n<td>19,594,392 characters (19.6%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>11.0:<\/th>\n<td>16,000,469 characters (16.0%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>10.8:<\/th>\n<td>12,876,774 characters (12.9%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>10.7:<\/th>\n<td>10,206,824 characters (10.2%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>10.5:<\/th>\n<td>7,966,908 characters (8.0%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>10.3:<\/th>\n<td>6,124,240 characters (6.1%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>10.2:<\/th>\n<td>4,634,361 characters (4.6%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>10.0:<\/th>\n<td>3,450,479 characters (3.5%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>9.8:<\/th>\n<td>2,527,944 characters (2.5%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>9.7:<\/th>\n<td>1,822,878 characters (1.8%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>9.5:<\/th>\n<td>1,292,898 characters (1.3%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>9.3:<\/th>\n<td>901,008 characters (0.90%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>9.2:<\/th>\n<td>617,002 characters (0.62%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>9.0:<\/th>\n<td>415,925 characters (0.42%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>8.8:<\/th>\n<td>275,355 characters (0.2754%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>8.7:<\/th>\n<td>178,455 characters (0.1785%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>8.5:<\/th>\n<td>113,296 characters (0.1133%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>8.3:<\/th>\n<td>70,787 characters (0.0708%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>8.2:<\/th>\n<td>43,324 characters (0.0433%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>8.0:<\/th>\n<td>25,948 characters (0.0259%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>7.8:<\/th>\n<td>15,246 characters (0.0152%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>7.7:<\/th>\n<td>8,847 characters (0.0088%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>7.5:<\/th>\n<td>4,923 characters (0.0049%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>7.3:<\/th>\n<td>2,682 characters (0.0027%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>7.2:<\/th>\n<td>1,416 characters (0.0014%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>7.0:<\/th>\n<td>752 characters (0.0008%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>6.8:<\/th>\n<td>349 characters (0.0003%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>6.7:<\/th>\n<td>162 characters (0.0002%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>6.5:<\/th>\n<td>70 characters (0.0001%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>6.3:<\/th>\n<td>32 characters (0.0000%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>6.2:<\/th>\n<td>12 characters (0.0000%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>6.0:<\/th>\n<td>5 characters (0.0000%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>5.8:<\/th>\n<td>4 characters (0.0000%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>5.7:<\/th>\n<td>3 characters (0.0000%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>5.5:<\/th>\n<td>2 characters (0.0000%) have this score or lower.<\/td>\n<\/tr>\n<tr>\n<th>5.3:<\/th>\n<td> 1 characters have this score, which is the lowest recorded.<\/td>\n<\/tr>\n<\/table>\n<p>Maybe the list above doesn&#8217;t truly convey just how hard it is to get an unusual character. If that doesn&#8217;t pursuade the newbie that sitting around throwing new chars is a waste of time, maybe this will. <\/p>\n<table cellpadding=1 cellspacing=0 width=720>\n<tr>\n<th colspan=90>\n<h3>Average stat scores for 100,000,000 characters<\/h3>\n<\/th>\n<\/tr>\n<tr>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 3.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 3.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 3.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 3.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 3.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 3.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 4.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 4.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 4.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 4.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 4.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 4.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 5.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 5.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='1 characters with an average score of 5.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='1 characters with an average score of 5.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='1 characters with an average score of 5.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='1 characters with an average score of 5.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='1 characters with an average score of 6.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='7 characters with an average score of 6.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='20 characters with an average score of 6.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='38 characters with an average score of 6.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='92 characters with an average score of 6.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='187 characters with an average score of 6.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='403 characters with an average score of 7.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='664 characters with an average score of 7.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='1,266 characters with an average score of 7.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='2,241 characters with an average score of 7.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='3,924 characters with an average score of 7.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='6,399 characters with an average score of 7.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='10,702 characters with an average score of 8.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='2' width=8 alt='17,376 characters with an average score of 8.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='3' width=8 alt='27,463 characters with an average score of 8.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='4' width=8 alt='42,509 characters with an average score of 8.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='6' width=8 alt='65,159 characters with an average score of 8.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='9' width=8 alt='96,900 characters with an average score of 8.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='13' width=8 alt='140,570 characters with an average score of 9.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='19' width=8 alt='201,077 characters with an average score of 9.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='26' width=8 alt='284,006 characters with an average score of 9.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='36' width=8 alt='391,890 characters with an average score of 9.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='48' width=8 alt='529,980 characters with an average score of 9.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='64' width=8 alt='705,066 characters with an average score of 9.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='84' width=8 alt='922,535 characters with an average score of 10.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='107' width=8 alt='1,183,882 characters with an average score of 10.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='135' width=8 alt='1,489,879 characters with an average score of 10.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='167' width=8 alt='1,842,668 characters with an average score of 10.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='203' width=8 alt='2,239,916 characters with an average score of 10.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='242' width=8 alt='2,669,950 characters with an average score of 10.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='282' width=8 alt='3,123,695 characters with an average score of 11.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='325' width=8 alt='3,593,923 characters with an average score of 11.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='367' width=8 alt='4,064,863 characters with an average score of 11.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='407' width=8 alt='4,501,592 characters with an average score of 11.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='442' width=8 alt='4,895,446 characters with an average score of 11.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='473' width=8 alt='5,229,968 characters with an average score of 11.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='495' width=8 alt='5,477,127 characters with an average score of 12.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='509' width=8 alt='5,631,955 characters with an average score of 12.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='513' width=8 alt='5,671,712 characters with an average score of 12.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='506' width=8 alt='5,604,063 characters with an average score of 12.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='490' width=8 alt='5,425,050 characters with an average score of 12.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='465' width=8 alt='5,143,715 characters with an average score of 12.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='432' width=8 alt='4,774,475 characters with an average score of 13.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='393' width=8 alt='4,342,923 characters with an average score of 13.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='349' width=8 alt='3,855,161 characters with an average score of 13.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='303' width=8 alt='3,350,131 characters with an average score of 13.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='257' width=8 alt='2,845,009 characters with an average score of 13.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='213' width=8 alt='2,356,990 characters with an average score of 13.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='172' width=8 alt='1,902,790 characters with an average score of 14.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='136' width=8 alt='1,499,114 characters with an average score of 14.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='104' width=8 alt='1,149,901 characters with an average score of 14.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='78' width=8 alt='855,862 characters with an average score of 14.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='56' width=8 alt='619,049 characters with an average score of 14.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='40' width=8 alt='433,719 characters with an average score of 14.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='27' width=8 alt='293,437 characters with an average score of 15.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='18' width=8 alt='193,606 characters with an average score of 15.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='11' width=8 alt='121,505 characters with an average score of 15.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='7' width=8 alt='74,165 characters with an average score of 15.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='4' width=8 alt='43,526 characters with an average score of 15.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='3' width=8 alt='24,108 characters with an average score of 15.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='2' width=8 alt='12,829 characters with an average score of 16.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='6,513 characters with an average score of 16.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='3,024 characters with an average score of 16.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='1,369 characters with an average score of 16.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='588 characters with an average score of 16.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='216 characters with an average score of 16.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='79 characters with an average score of 17.0'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='23 characters with an average score of 17.2'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='3 characters with an average score of 17.3'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='2 characters with an average score of 17.5'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 17.7'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 17.8'\/><\/td>\n<td width=8 valign=bottom align=center><img src='images\/vbar1.gif' height='1' width=8 alt='0 characters with an average score of 18.0'\/><\/td>\n<\/tr>\n<tr>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>3.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>3.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>3.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>3.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>3.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>3.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>4.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>4.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>4.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>4.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>4.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>4.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>5.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>5.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>5.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>5.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>5.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>5.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>6.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>6.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>6.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>6.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>6.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>6.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>7.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>7.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>7.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>7.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>7.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>7.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>8.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>8.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>8.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>8.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>8.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>8.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>9.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>9.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>9.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>9.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>9.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>9.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>10.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>10.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>10.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>10.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>10.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>10.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>11.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>11.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>11.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>11.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>11.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>11.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>12.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>12.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>12.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>12.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>12.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>12.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>13.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>13.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>13.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>13.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>13.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>13.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>14.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>14.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>14.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>14.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>14.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>14.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>15.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>15.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>15.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>15.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>15.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>15.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>16.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>16.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>16.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>16.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>16.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>16.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>17.0<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>17.2<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>17.3<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>17.5<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>17.7<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>17.8<\/td>\n<td width=8 valign=top align=center STYLE='writing-mode: tb-rl; font-size: 6pt; line-height:0;'>18.0<\/td>\n<\/tr>\n<\/table>\n<p>Mouse over the individual bars in the table above to see the character counts.<\/p>\n<p>Note that every bar is (in theory) possible, but also note how very unlikely it is to have anything out of the mid range.  <\/p>\n<p>If the newbie has a lot of time on his hands (a little over a hundred years) he might someday come up with a truly remarkable character.  While rolling up our 100 million characters, my program came up with this one on the 54,746,934<sup>th<\/sup> attempt.  <\/p>\n<p><center><\/p>\n<table>\n<tr>\n<th colspan=2>Best Character: #54,746,934<\/th>\n<\/tr>\n<tr>\n<th>STR<\/th>\n<td>17<\/td>\n<\/tr>\n<tr>\n<th>DEX<\/th>\n<td>18<\/td>\n<\/tr>\n<tr>\n<th>CON<\/th>\n<td>17<\/td>\n<\/tr>\n<tr>\n<th>INT<\/th>\n<td>17<\/td>\n<\/tr>\n<tr>\n<th>WIS<\/th>\n<td>18<\/td>\n<\/tr>\n<tr>\n<th>CHA<\/th>\n<td>18<\/td>\n<\/tr>\n<tr>\n<td colspan=2 align=right>(Average 17.5)<\/td>\n<\/tr>\n<\/table>\n<p><\/center><\/p>\n<p>Actually, it looks like it came up with that score twice during the run.  Here is the worst one it managed to come up with:<\/p>\n<p><center><\/p>\n<table>\n<tr>\n<th colspan=2>Worst Character: #96,057,386<\/th>\n<\/tr>\n<tr>\n<th>STR<\/th>\n<td>5<\/td>\n<\/tr>\n<tr>\n<th>DEX<\/th>\n<td>7<\/td>\n<\/tr>\n<tr>\n<th>CON<\/th>\n<td>3<\/td>\n<\/tr>\n<tr>\n<th>INT<\/th>\n<td>8<\/td>\n<\/tr>\n<tr>\n<th>WIS<\/th>\n<td>4<\/td>\n<\/tr>\n<tr>\n<th>CHA<\/th>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td colspan=2 align=right>(Average 5.3)<\/td>\n<\/tr>\n<\/table>\n<p><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A newbie D&#038;D player will usually generate their first character and be disappointed. They roll the dice, add them up, and realize they have a perfectly run-of-the-mill character. They were hoping to get a few lucky rolls and come up with someone really special. Then they get an idea: Maybe I&#8217;ll just toss this character [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"class_list":["post-377","post","type-post","status-publish","format-standard","hentry","category-tabletop-games"],"_links":{"self":[{"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=\/wp\/v2\/posts\/377","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=377"}],"version-history":[{"count":0,"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=\/wp\/v2\/posts\/377\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shamusyoung.com\/twentysidedtale\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}