*Many thanks to Kingsley & Riggins, the finalists in the inaugural Invader League, for helping me see the light and inspiring me to write this article for others.*

I don’t have much of a mind for strategy.

I wish I did, but I don’t. And that’s why I’m most comfortable writing a blog about the basics of Legion – because if you asked me to do deep dives into statistics, tactics, and minute decision-making, I’d be worthless at it.

There is, however, one thing that I learned that I think is extremely helpful for beginner players to practice from the get-go: mental math.

Coming from X-Wing, I knew this to a small degree. I knew my attack die had a 50% chance of hitting a hit or crit, and my defense die a roughly 37% chance of hitting an evade. I never bothered with the in-depth statistics of when to focus or when to evade based on the numbers; I just went with my gut and that generally worked.

Fortunately for me, once someone showed me how simple the Legion numbers are, it was a much easier sell to memorize.

Because here’s the secret: it’s quite a pleasant pattern.

## Attack Dice

### Hit/Crit Probability

White | No Surge: |
2/8 | .250 |
---|---|---|---|

Surge: |
3/8 | .375 | |

Black | No Surge: |
4/8 | .500 |

Surge: |
5/8 | .625 | |

Red | No Surge: |
6/8 | .750 |

Surge: |
7/8 | .875 |

## Defense Dice

### Block Probability

White | No Surge: |
1/6 | .166 |
---|---|---|---|

Surge: |
2/6 | .333 | |

Red | No Surge: |
3/6 | .500 |

Surge: |
4/6 | .666 |

Hopefully seeing it laid out like this helps you in the same way it helped me. It’s nice, isn’t it? How cleanly the numbers line up.

Now, yes, this probably seems painfully obvious to some of you, if not many of you (right after I finished the first draft, I found at least one post that also goes into rerolls). It’s a dice game. It’s basic probability. But for those of you who are maybe more inclined to the crafty hobby aspect of Legion, this might be a revelation. Either way, it’s an important basic skill.

Once you think of the odds in this linear fashion, it’s simple arithmetic: lay out the dice in your head, and picture each probability. Then, add the numerators (the top number) together and divide by the denominator.

Alternatively, if you’re using the decimal version, just add it all up. One probably works better for you, and it’s ultimately inconsequential which one you use. You should get to the same end result either way.

But what does this actually look like in a game setting?

## Two Quick Examples

### Example 1

We want to compare the efficacy of two fictional weapons we can attach to our vehicle. **Weapon 1 **adds 6 white attack dice, and **Weapon 2 **adds 3 red attack dice. The vehicle does not have a surge.

Which weapon adds the higher number of expected hits? Let’s take a look at the numbers.

Weapon 1 | 2/8 + 2/8 + 2/8+ 2/8 + 2/8 + 2/8 = 12/8 = 3/2 |
1.5 Expected Hits |
---|---|---|

.250 + .250 + .250 + .250 + .250 + .250 = 1.5 |

Weapon 2 | 6/8 + 6/8 + 6/8 = 18/8 = 9/4 |
2.25 Expected Hits |
---|---|---|

.750 + .750 + .750 = 2.25 |

**So in this case, Weapon 2 comes out .75 expected hits ahead due to the higher chance of hitting paint on the red dice.** All other things equal, we should go with that one.

Seen another way, Weapon 1 would need three times the dice as Weapon 2 to come out even. Similarly, if Weapon 1 used black dice it would need 1.5 times the dice to come out even.

### Example 2

Now, a more complicated one.

Our trooper unit is ready to attack, and has caught two enemy trooper units without cover. One has white defense dice and 6 remaining units, while the other had red defense dice but only 2 remaining units. Neither has surge.

Our unit attacks with a total of 4 black dice (let’s say it’s impact grenades, range 1), without surges. So first, we calculate our expected number of hits:

Our Unit | 4/8 + 4/8 + 4/8 + 4/8 = 16/8 = 2 |
2 Expected Hits |
---|---|---|

.500 + .500 + .500 + .500 = 2 |

Now, we look at their units, rolling against 2 expected hits with their D6s:

Enemy Unit 1 | 1/6 + 1/6 = 2/6 = 1/3 |
.333 Expected Covers |
---|---|---|

.166 + .166 = .333 |

Enemy Unit 2 | 3/6 + 3/6 = 6/6 = 1 |
1 Expected Cover |
---|---|---|

.500 + .500 = 1 |

Given the scenario above, we have a decision to make.

**Enemy Unit 1** is not expected to roll a block result in this situation, bringing their total from 6 units down to 4.

**Enemy Unit 2 **is expected to roll 1 block, bringing their total from 2 units down to 1.

Depending on the scenario, it may be more favorable to choose Unit 1 over Unit 2, or vice versa. Perhaps attacking Unit 2 allows you to get rid of a particularly nasty heavy weapon, but attacking Unit 1 allows you to reduce their numbers, place a suppression, and hamper their upcoming activation.

It’s here that some level of tactics and game sense come into play. And maybe you, like me, know that it’s not your strongest suit. **But at least you’ll be making an informed decision based on probability. **Even a little bit of that, with practice, can go a long way.

You also have to be comfortable with chance: that’s what makes dice games fun and dramatic. Sometimes, everything goes as expected. Sometimes you blank out. Sometimes you roll 6 natural crits on 6 white dice. Statistically it’s bound to happen to someone.

Obviously we haven’t addressed aim or dodge tokens, crits and armor, cover, or abilities. I’ll leave that to another, smarter blog to handle. For now, use the easy math to influence your gameplay where you can fit it in.

Best of luck, you mathematical Commanders!

## 0 comments on “No Such Thing as Luck: On Mental Math in Legion”