What’s Dice Got to Do With It?

To quote the great Sheldon Cooper, “The dice giveth and the dice taketh away”.  Over the course of our gaming career, each of us has heard or been witness to the infamous ‘I got diced’ excuse.  This article takes a quick walk through of averages and lesser known variance of dice outcomes involved in playing Warmachine and Hordes.  Think of it as a little guide on how to screw or be screwed by dice.

Games operate on components of luck and skill at their basest components.  Games of pure luck amount to flipping a coin and deciding a winner.  Games of pure skill tend to run dry as asymmetry in player ability makes itself clear.  By incorporating both elements, a game can be enjoyable in a competitive sense and accessible to a wider play group.  To embody luck (and keep it under reigns) Privateer Press employs a d6 system.  Two six sided dice yield and average outcome of 7 and a standard deviation of 2.45.  This means that 68.2% of your dice outcomes will fall between 7 plus or minus 2.45.  That’s not too bad.  You have a good guess at what you’ll roll (7) and an idea of when you’re lucky(>7) or not (<7).

Some powerful spells and effects in the game tinker with dice statistics.  The most notable examples include; Signs and Portents and Star Crossed.  These two not only change your average outcome, but also impact the standard deviation of the rolls.  Here’s a graph on the effect of Signs and Portents on a boosted to roll.

First off, the average has shifted from 10.5 to 12.24.  Yes.  Signs and Portents is an amazing spell!  The additional power of the effect is that it reduces the variability of your outcomes.  Look at how the red curve is narrower.  This means that dice results are clustered more toward the average result.  In addition to rolling a higher average, you’ll be more consistently rolling a 12.24.  When you’re making a strategically important move you need it to happen, consistency is a big deal.

 

I’ve focused in on these two spells, but there are similar consequences to just boosting a roll.  You are going to hit 10.5 more often then 7 when you boost a roll because the additional die lessens the variability of your outcomes.  I’ve included a little chart of common dice combinations, averages and standard deviations for your perusal.  Enjoy!

Dice Average Std Dev
1d6

3.5

1.87

2d6

7

2.45

3d6 drop lowest

8.46

2.22

3d6 drop highest

5.54

2.22

3d6

10.5

2.96

1d20

10.5

5.92

4d6 drop lowest

12.24

2.85

4d6 drop highest

8.76

2.85

4d6

14

3.34

 

Tmage

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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