How often do you hear that in a game?  I don't think I can go a whole club session without hearing it, often with a dissatisfied tone.  Of course, they are wrong.  They are saying "I threw enough fire-power at that unit to ensure its destruction", when what they mean is "I threw enough fire-power at that unit to kill it, on average".  These two events are not the same.

Example:  How many bolter shots to kill a Marine, on average?

We hit two thirds of the time, so that's 1x0.66 = 0.66
We wound him half of the times we hit him, so 0.66x0.5 = 0.33
He saves two thirds of the time, so 0.33x0.33 = 0.11

1 Marine / 0.11 chance of a shot wounding him = ~9 shots, on average to kill him.

What most players don't grasp is that this is on average.  It does not mean nine shots kills a marine.  In fact, we can work out how likely he is to still be alive:

One shot has a 0.89 chance to be survived.
Two shots has a 0.79 chance to be survived.
Three shots has a 0.7 chance to be survived.
...
Nine shots has a 0.35 chance to be survived.

You can shoot him nine times, and over a third of the time he will walk away.

So, let's change our definition.  How much fire-power do we need to ensure his destruction?  We will assume that any event with a probability greater than 90% is a certainty for our purposes, after all you can't remove the dice from the game.

Example:  How many bolter shots to kill a marine, with better than 90% certainty?

We can work this out by continuing the maths from above.

Nine shots has a 0.35 chance to be survived.
... (0.89*0.89*0.89......*0.89)...
Twenty shots has a 0.097 chance to be survived.

Twenty shots!  Over twice as many as our "on average" set of shots.  See why nine shots isn't a "He should be dead" situation now?

What's the lesson here?  If you need a unit to die, assign at least twice as much fire power as necessary to kill it on average, and always be prepared for it to walk away.  Always anticipate failure and always have a plan B.

The dice can, and will, betray you. Related Posts Plugin for WordPress, Blogger...