Weighted Outcomes are Heavy Stuff

This is foundation article and I’m going to start it off on a bit of a tangent.

I love to talk trash.

I try to keep my abuse restricted to friends and those who can handle it, but in general, boy-oh-boy do I love smack talk.  I don’t know why.  Does it heighten the intensity of the game?  Is it an outlet for my superhero/supervillian witticisms?  Who knows?

Thankfully I play with a good group of guys that like to reciprocate.  The newest arrow in their quiver is “I’m not sure if that’s technically the most sound mathematical decision.  If you read the article on MoM by Tmage, you’d know better.”

Yea.  Thanks buddy.  I know Tmage.  I know the math.  I’m just not Rain Man.:)

No one in their right mind does THIS much math in their head during a game.  Maybe someone does.  I don’t.  I can tell you ALOTof the top players do not.  They know their fundamentals and use their cognitive power on positioning and competitive interaction. (or flirting in PhatAsian’s case)

You can’t keep it all in your mind but I want to reinforce the three magical facts highlighted in Episode 10.  These are great shortcuts to guide your reasoning.

1. The average on 1d6 is 3.5.

This is an easy calculation and a powerful fact.  You add up the faces of the die (21) and divide by the number of faces.(6)  Now you can set a personal expectation for the variability of the game and if the dice are REALLY boning you or if you’re just a whiney Nancy.

2. The odds of rolling a 7 is 58%.

Now we’re digging a bit deeper.  There are 36 potential rolls on 2d6.  They range from snake eyes (1,1) to box cars (6,6).  If you sit and write out all the combinations and you’ll find 21 of the 36 are 7 or higher.  As a result, 21/36 = 58% is your probability of rolling a 7 or better.

The last point is counter-intuitive but absolutely true.

3. Average damage on 2d6 at dice -7 is one.

The first time I heard this I thought it was crazy garbage, but it’s true.  There are two ways to calculate an average.  One assumes equal probability distribution (the method I used for proving #1) the other does not.  That other method is called a weighted average.

A weighted average takes into account the magnitude of the outcome (how much damage) with the likelihood that it will happen.  So take a look at this;

WHAT!?!  The weighted average of a 2d6 roll at dice minus 7 is just about one.  Fancy that.  I usually run all my assassination calculations without this component.  I think of it as a little fuzzy mathematical factor in my favor so my estimates are conservative.  It’s definitely food for thought though.

I hope this hasn’t been too boring/painful for you.  This is a small step in the right direction about knowing the core mechanics of the game.  While these types of rules don’t exist in Prime or Primal, they’re certainly helpful to have in the back of your mind.

The more you know… (hum the little diddy in your head when you read this last part)

Author: Tmage

I'm a gaming and math enthusiast. I find games that balance strategic interaction with economic principles (delayed option, resource control, etc.) are some of the most rewarding for me as a player. I concentrated in Finance, Analytic Consulting, Decision Sciences and Management Strategy while getting my MBA at Kellogg (Northwestern University) and majored in Chemical Engineering during my undergrad at University of Illinois. I view gaming through this lens and share my perspective via periodic articles. Thanks for reading!

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