Dice math 101

I started this blog by looking at maths, and I’ve written plenty of specific articles focussing on a character, but this is aimed at player with maybe a little less experience of the game to introduce them some overarching ideas in Marvel: Crisis Protocol.

Variance

The first key idea in the game is that variance is very high. To illustrate, let’s compare with some other miniatures games. In 40k, you might roll 18 dice needing 3+ on a d6 to hit. Your average result is going to be 12 hits, but you are very likely to get a result between 9-15. This is referred to as the standard deviation – the range in which 68% of results fall and double that (two standard deviations) in which 95% of results fall.

This allows you to make decisions based on expected results, with small tolerances for rolling higher or lower than average.

Equally in Warmachine, the core mechanic is based on a 2d6 system boosting to a 3d6 system. Again, this has an easy to internalise average with small standard deviation from the average.

By having as opposed system – both you and your opponent roll dice and compare – it generates a highly varying distribution of probabilities. Take for example, a 6 dice attack against a 3 defense character.

Damage Dealt

2 damage is the most likely outcome, but only just! Rather than being a curve like in other systems, this example is very flat. That can make it hard to be certain in the outcome of your attacks.

The effect of this on the game is making sure you have a plan for failure, as that is a very real possibility. Reacting to dice rolls is a key skill in the game and is greatly helped by planning your activations.

Rerolls vs extra dice

A common comparison is looking at an extra dice vs a reroll. Mathematically they are pretty similar, but they are different, largely due to the fact that a critical on a reroll doesn’t generate an extra dice. The fact you can’t reroll fails contributes too, but that effect is smaller. An extra dice is better than a reroll.

But if you get multiple rerolls, that has a bigger effect than one extra dice. You can see that in Spider-Man’s Spider Senses:

It’s almost as good as 5 dice, but not quite.

The main place this comes up is with Black Panther. I’ve dug in to his various options here. But the short version is his reroll any from Mantle of the Black Panther is better than rolling extra dice.

Choosing attacks

Another common situation can be embodied in Iron Man against Iron Man.

Which attack would do more damage? 4 str vs 3 def or 5 str vs 4 def?

It’s true for all attacks that one higher strength vs one higher defense will result in more damage. This ignores the other effects of the attacks though. Power generation especially is an important consideration.

But what about Venom? Venom has a much lower energy defense than physical. Iron man should target that low energy defense:

Rule of thumb: if they get more additional defense dice than you get additional attack dice, go for the less powerful attack on the much lower defense.

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