# Hammer of Math: 40k Self-Immolation Appreciation Station

This week’s Hammer of Math takes a look at the wonderful world of [HAZARDOUS] weapons.

Plasma weapons are the epitome of 40k. Incredibly advanced and potent weaponry from the Dark Ages of Technology, they are so valuable that should they overheat it is better that the weapon kill the bearer than be destroyed. The bearer might object to this, but since they’re generally either a menial conscript or a psycho-conditioned warrior monk the protest usually falls on deaf ears. 10th Edition continues the tradition of self-immolation through the introduction of the [HAZARDOUS] trait, which states that every time a weapon with this trait is fired the bearer must roll a D6 for a Hazardous Test. On a 1 the bearer is either killed (in the case of a lowly INFANTRY model) or takes 3 mortal wounds for CHARACTERS, VEHICLES, or MONSTERS. This is a distinct advantage over previous editions, where in 9th Edition every unmodified Hit Roll result of 1 would hurt the bearer, or in 8th Edition where every modified Hit Roll of 1 would do the deed.

So how do we calculate the probability that at least a given number of failures will occur for a particular number of tests? We use our good friend binomial probability. For those who don’t obsessively read this column, binomial probability is the chance that a given number of successes will occur for a set number of trials assuming a set probability of success. Cumulative binomial probability allows us to establish that probability that up to a given number of successes will occur. Subtract that from unity and you get the probability that more than a target number of successes will occur. Rather than do math, you can consult the helpful chart below.

Using this chart it’s possible to examine a variety of conditions that would be of interest.

• The chance of a squad of 5 Hellblasters firing out of an Impulsor and failing enough Hazardous Tests to blow up their ride is roughly 1 in 300.
• The chance of all 5 Hellblasters dying when they subsequently fire again is 1 in 7776, which means probability of 5 Hellblasters killing their Impulsor and then dying is 1 in 2.3 million.
• A Forgefiend can kill itself if it’s very unlucky. First it has to make a Dark Pact, fail the Leadership check, and then roll a 3 on the ensuing D3 (9% chance). Then it has to activate Daemonic Ordnance and fail all three Hazardous Tests (0.5% chance). Take it together and the chances of a Forgefiend killing itself at full health is roughly 1 in 2222.
• Chances are pretty good (roughly 1 in 8) that a Crisis Suit armed with four cyclic ion blasters will blow itself up after shooting.

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