Gears of War: Chainsaw probabilities

In the Gears of War board game, the main gun has a chainsaw attached. You can use this as an alternative attack, for example if you run out of ammo.

This works differently from regular attacks. You roll four attack dice and score an immediate kill if at least one comes up with an omen symbol.

So what are the chances of this succeeding?


The attack dice have funny symbols instead of numbers

There is one omen symbol on each attack die, so that is 1 in 6 (one sixth). You need to figure the chance of getting at least one omen in four rolls.

This is the opposite of getting no omens in four rolls, which is easier to calculate.

If the chance of getting an omen on one roll is 1 in 6 then the chance of not getting an omen is 5 in 6.

If you roll four times, you need to get no omen on the first roll, which is 5 in 6. Then get no omen on the second roll, which is another 5 in 6. And so on. You can see it gets less and less likely the more rolls you make.

Basically you multiply together the chances for each roll, so the chance of getting no omens in four rolls is (5/6) * (5/6) * (5/6) * (5/6).  This is 0.48, which is 48%, or just less than half the time.

But this is the chance of getting no omens. We want the chance of getting at least one omen, which is the opposite of this, i.e. 52%, or just over half the time. So using the chainsaw is roughly a 50/50 bet.

The fact that you have to multiply the probabilities when figuring out this stuff is why Sex Panther is not actually a sure thing. (“They’ve done studies, you know. 60% of the time, it works every time.”)