Today’s post will be a bit math heavy, but I promise to make it fun along the way!

Let’s say you and I decide to make an awesome new game.  We’ve decided to make “Fall of the 11th Age”, because 13 is too many ages for you.  A major part of the game is number 11.  We’re going to base the main dice mechanic on its so important.  You’ve had an awesome idea to make a cool new die called a d11 that will go from number 2 to 12, and you excitedly start making the game.  I say that we don’t have the kickstarter money to custom make d11s, so I start working on my version that uses 2 regular six-sided dice (2d6).  Since we both cover basically the same numbers (2 to 12), out systems look close enough to one another. So, we merge my and your ideas and start to really make some headway in the play testing.  But, some strange things begin to happen.  When we use my 2d6 system, things are pretty predictable.  The fighter almost always hits the goblins.   But, when we use the d11, the fighter misses the goblins ~50% of the time, and the wizard pulls of some hits that we didn’t think were possible.  What’s going on?

The answer lies in the math behind the game or, more specifically, the statistics of the dice.  Below I have two graphs.  The first is a graph showing how random each result is on the d11.  Statisticians love them some dice problems, so lots of work has gone into the dice.  On a fair die, every side has equal probability of occurring.  For our die d11, that means every side has a ~9% chance of being rolled.  This makes the behind-the-scenes math of “Fall of the 11th Age” pretty easy to figure out.  Here’s a quick example:  to hit the goblin, a fighter needs to roll a seven or better.  So the fighter can roll a 7, 8, 9, 10, 11, or 12.  That’s 6 numbers.  To find that probability of that occurring you multiply 6 by the probability of each event (6 x 1/11).  So the end result is 6/11 or ~55% chance of success on any roll.  I’ve put in a handy chart to show what I mean.

But things are not that simple when it comes to the 2d6 system.  Above, I mentioned how statisticians love them the dice, well a major part of that is how fair dice are and independent.  When you roll a d6, every die face has an equal probability of occurring.  When you roll two, each side has an equal probability of occurring AND what occurs on one die face does not affect the result of another.  There are a few assumptions that go with this and I don’t want to get crazy with physics of rolling dice together, so we’re going to keep this simple.  PLEASE!  It gets weird from here if we go deeper!  So dice are random and separate.  So when we want a result, to figure out the probability of that result we have to count the number of ways to make that result.  I’ve included a table to help with this.  A really important thing to note on this chart is how multiple dice roles make the same number.  For a simple example, look at the 3.  A 1 on the first die and a 2 on the second makes a 3 while a 2 on the first die and a 1 on the second also makes a three.  This is part of the independent results thing above.   So if we use the same “Fall of the 11th Age” math we used above with the d11 to hit the goblin, we need at least a 7 on 2d6.  There are multiple ways to make a seven.  For this, the best way to find the likely hood of this event is to ADD the percentage likelihood of each individual event.  So for a 7 to occur we add 16.67+13.89+11.11+8.33+5.56+2.78 which equals 58.34%.  This may not be a massive change from the d11 system, but it’s also not the whole story.

from http://www.wikihow.com/Sample/Dice-Probabilities

Besides just finding the likelihood of hitting the goblin, there is a few more statistics “things” at play.  These are the mean, median, mode, and standard deviation.  Let’s look at the first three.  A mean is the average that we all know and love.  For “Fall of the 11th Age,” we just add up the dice results of 2 to 12 and divide by the total number of events (11) which is 7.  The median is the middle value; think of the median as a balance on a teeter-totter on a play ground.  If we moved the middle of the wooden beam around a bit, where would both sides balance one another.  Again this is 7.  2 3 4 5 6-7-8 9 10 11 12  There are five numbers to 7’s left and five numbers to 7’s right.  Where things really get interesting is with the mode.  The mode is the most likely to occur event in our group of events, or another way to think about it is, the event with the most number of ways it can happen.  For “Fall of the 11th Age,” in the 2d6 approach 7 can occur the most often since six different dice rolls can make a seven.  But, in the d11 approach, there is NO MODE!  Every number can occur equally.  (Again, we can get all math argue-y with if there is no mode you take an average bla bla bla, but this is my article and I want to make a point, so NO MODE!).

Standard Deviation is a bit more complicated, and I won’t go into it all.  For a great summary, go to http://www.mathsisfun.com/data/standard-deviation.html.  But, a real simple definition of standard deviation is a measurement of how much things very.  You use standard deviation to find out how random your stuff really is.  Let’s look at the 2d6.  The average result is 7, but over 60% of the time, you will role between a 5 to a 9.  When you roll a d11, the results get a little more varied.  Using standard deviation, 60% of the time you will roll between 4 and 11.  (If you check my math, I’ve simplified down the actual results.  It makes life a bit easier).  What this really means is you are more likely to be closer to the average in 2d6 then with d11.

Why does this matter?  Well it matters for how random you want your random to be.  For 2d6 vs d11, the difference between 55% and 58% doesn’t matter much, but what if we only needed a 6 instead of a 7?  Using what we went through above, the d11 likelihood is now a 64% while the 2d6 likelihood is now a 71%.  The difference is getting pretty substantial at this point.  Also, how random you want extreme events to be?  For the 2d6 system, 12 or crit will only be 2.78% which is pretty low.  But, for the d11 system, it’s 9%.  The d11 dice don’t really care what side comes up (dice, they are a cruel mistress….).  And since the math works the same in reverse, critical fumbles work exactly the same way (2.78% cs. 9%).  If we graphed the d11 results we would see a flat curve of probabilities.  When multiple ways to achieve the same value occur, interesting new things occur in the data and your game.

The example above is a pretty simple.  Let’s look at something a bit more extreme.  Let’s use Dungeons and Dragons d20 vs. Hero System’s 3d6.  (Yes, I know 3-18 is a smaller range then 1-20, but I want to use some real world example for the gamers).  A d20 is a single die, every side is equally likely, so every side has a 5% likelihood.  For Hero System, I’ve put another chart below to show all the results and likelihoods to make life easier.  For this one the “%=” column give the probability of a dice roll, and “%>” is the likelihood of this and all higher number dice rolls.  Let’s say you have to roll a 9 to hit a monster.  For a d20, you have a 60% chance to get that event.  But, for the Hero System, its 74%.  Again, this major difference has to deal with the mode and likelihood difference between each number in the two dice pools.  A d20 doesn’t really have a mode (See rant on mode averaging above), while a 3d6 pool has a mode at 10 or 11 and each number has a different probability of being rolled.  What if we need to crit to hit?  In DnD with a d20, its only a 5% chance, but in Hero System’s 3d6 dice pool, I’m looking at a 10-fold lower difference with a meager 0.463%.  When you look at the standard deviation, you are most likely to get between 8 to 13 on 3d6, while on a d20, for the same probability, you will most likely get between a 5 and 15.

from seanswgcorner.blogspot.com

            What the crux of this argument boils down to is likelihood differences in getting different dice values.  How much random do you want in your games?  When I do something in the real world, is my life a full of extremes or is it pretty average?  How often do things get crazy vs. stay normal.  How often do the normal expected results occur when I do something?  On a d20, if a10 hits and a 14 hits, since each are equally likely, does a 14 really represent more skill or just another hit since both are equally likely?  For 3d6, I feel there is a palpable difference in likelihood and it affects the stories I tell.

What do you think?  Now, no system is “wrong”, but what does the math “say” to you?  What do you feel when you play these different games?  Do you feel a difference when a modes and different outcome likelihoods enter the game vs. when it’s just one die?  One of my favorite systems Arcanis uses 2d10 plus an attribute die for its d20 + attribute rolls.  I love that system because you get all the fun of a d20 game, but you also get the predictability of a smaller standard deviation.  While I enjoy the randomness, I feel that helps help keep the game from being overly swingy or random.  What do you want in a game?  How random do you want your random?

It’s the first Blurbs from the Booth and today I talk about why I love Living games!

I’ve stood at the invasion of Elturguard as the companion went dark.  I’m immortalized in a statue commemorating the defeat and sealing of an elemental in Mil Takarn.  I’ve thrown waves after waves of demons against intrepid heroes as they stood valiantly in Jappa.  I’ve hacked computers owned by Renraku and stolen a wizard only to sell him to a different corporation in Seattle.  I’ve single handedly destroyed skyships as during the invasion of the floating fortress.  And you may have too.

I love living games.  Living games are long running campaigns where a series of modules are put out by a company or group in a particular game system.  The living game will place rules on what can and can’t happen in character generation and each module so the story that every character experiences is somewhat standardized.  Games like the Living Forgotten Realms, Living Arcanis, Shadowrun missions, Living Divine, Pathfinder Society, Legends of the 13th Age, and others all fill me with only happiness.  Now I know many others out there poo-poo the idea of a “regulated” game, but I don’t mind slight changes to the rules.  Where they only see “limitations” because they can’t do everything they want, I see only opportunities and awesomeness.  Here are some of the high points I see to living games:

• Unity-Every week, I go to church.  I’m a Roman Catholic and at just past midway through, we all say the Our Father.  I get a feeling of unity with the larger group out there.  I’m not just one guy, I part of a larger whole.  I get that same feeling during a battle interactive (a large multi table game where parties can often interact with one another to help each other out).  I’m filled with a feeling that few can experience when I know several other people are all out there at the same time all fighting for a common goal.
• Shared Experience- I talked above about all the crazy things I’ve done in game as a GM and a player.  You may have done something similar, and that is AWESOME!  We might not have ever met, or ever will meet, but we have shared something that only a few other people can.  We can sit down at a bar or a con and talk about the crazy stuff that happened when I tried to steal the gem and what happened when you did it.  No two tables are the same, but the basics will be there and now we have some comradery that would never have existed if it weren’t for our shared passion for an RPG.
• Family/Friends-I’ve met friends at living games who I would have never, ever know existed.  These people came to my wedding, go with me to other cons, play other random games, and have become an important part of my life.  I look forward to hearing from them on a regular basis.  Living games give you an impressive opportunity to meet people you would otherwise not know existed.
• Personal Opportunities-Everybody has to start somewhere.  Monte Cook did not start writing 1000 page source books.  Neither will you.  But a great place to learn about the industry is to do the grunt work of it.  Cons and living games get your name out there.  I’ve ran games for Wizards of the Coast and got to have sit down chats with heavy hitters in the industry, and it was amazing!  Also, since living games are constantly looking for people to write, it’s a great place to make some in roads.  Now, I’m not saying this will the minor leagues compared to major league baseball, but it’s at least like playing in high school.  It will get your feet wet and get your name out there.  Have a favorite game and want to make a name for yourself?  Check their website.  Most have a proper procedure for you to try being a writer.
• Groups-Have a game you love, but can’t find a home group to do your crazy My Little Pony/Cthulhu version of it?  Go check out the living games.  Any company worth their salt will have an awesome website to support their living game.  These websites will help you find games or even give you Google groups to start playing in.  Then you find some friends, and eventually crazy Cthulhu Shuterfly with some equally crazy people.
• Achievement (Real)-Paizo does this amazingly well.  The more you GM for them, the higher your rank.  I was at the table where the first five star female Pathfinder GM earned her rank.  In addition to being with an awesome group of people, I got to witness something phenomenal.  Or, think of it this way, YOU GET TO LEVEL UP IN REAL LIFE!
• Achievement (Not as Real)- Every Living Forgotten Realms adventure ends with a reward sheet.  Every Pathfinder Society event ends with a chronicle.  You get a tangible reward for playing.  Now, I know it’s just paper, but you “earned” that.  There is a reason why so many companies are popping up selling game aids that represent in game achievement like gold and weapons.  It’s not much, but these represent some hard work by your character.  And, while not as great a say winning a football game, getting your sheet for winning the day does feel pretty good.
• Effects on the Game World- I’ve been part of a vote to turn the Companion of in Elturguard.  I’ve changed the world of the Forgotten Realms forever.  Can you say that? Often times in each living game, the people who run the campaign ask for feedback based on what the characters did.  This affects future mods and ultimately changes the world.  I want my character to be part of the world and to make a difference.  Do you?  While I know you’re home group now destroyed Cormyr, but did you change the larger world outside your home group?  This is an awesome aspect of Living game: real, tangible effects on the game you love.
• Company Opportunities-I honestly play more “living” games then I do home games.  I play a lot, but I prefer the play games where anybody can drop in and play and everybody gets a shot to have some fun.  These games give companies who might not otherwise get their game out there a shot to make some noise.  As a player, if I can’t find a group to play a game, then I won’t spend the $90+ to play Dungeons and Dragons (Players Handbook, Monster Manual, and Dungeon Masters Guide).  But if I know that I can easily just jump into a random group and play for free a bunch of times, I am much more likely to buy those three books and as many source books as I can get my hands on.
• Portability-Some people are locked in an area and can only play RPGs with one group of people.  In some of these groups, sometimes you have to deal with people you otherwise would not like, since it’s your only shot at playing a game.  Living games don’t have that problem.  Don’t like how I GM your game?  You can most likely find someone either online or close by who will run the game system you love for you.  Or you could start your own group and get other who loves your game to join you!  Its win-win!
• Spreading the Good Word- You have a system you love.  Whatever it is, you absolutely love it.  And I’m happy for you.  So you go to a con or two and run your intro game with pregens you personally created and a mod you wrote with love.  Your players all adore the game and say they will get every book then can!  And they don’t.  They look around, see no one else playing, and forget about that greatest game they ever played.  Living Games give you a bit of help with spreading your word.  Now, that group that loved your came know how to find others.  They know that others are playing.  They will (hopefully) join up with those others and now play your game.  And your game will spread.
• Adventures- We all love RPGs.  It’s why you’re reading a blog on a RPG website.  What’s harder is having that game ready when your friends show up.  Every week they’re going to show up and you have to spend the prep time to get the game ready, and they don’t care that game prep takes away from your spin class because in this example your friends are mean.  Any Living game worth its salt will have a giant back log of adventures and whole quests for you to work through.  And they are cheap, well put together, and right there!
• GAMES!-WHY ELSE ARE YOU PLAYING A RPG!  Here are some games that you don’t have to (usually) pay for!  Great living games give you a good taste of a game that a demo can’t.  You get to play a few sessions and maybe even gain a few levels.  Honestly, if you’re at a con and you see a new living game you’ve never heard of, give it a shot.  You’ll get your new pregen character and some fancy new adventure logs.  You have some tangible rewards and you got to play an awesome new game that you can show your friends back home with a ton of adventures for them to play and other new friends to show it too.

This is what I see when I see a living game.  Give them a try if you can.  You just might get more out of them then a simple game.  See if you feel what I feel when I step into a room with a couple hundred of my comrades at arms.