Thread: What are the odds? View Single Post 25 Jun 2006, 17:30   #4 (permalink)
Abanim
Shas'Ui   Join Date: Nov 2005
Posts: 903 Re: What are the odds?

Quote:
 Originally Posted by Pollo
That&#39;s a good article, but it doesn&#39;t address the problem of re-rolls, which was the subject of 77&#39;s query. I&#39;ll have a go at writing a quick explanation.

Okay, let&#39;s suppose that a broadside suit is firing its missiles, at BS3. You have the following possibilities:

Probability of a hit: [sup]3[/sup]/[sub]6[/sub] = 0.5
Probability of a miss: [sup]3[/sup]/[sub]6[/sub] = 0.5

Notice that the two probabilities sum to 1, like this: 0.5 + 0.5 = 1. This is important - it applies whenever you have two possibilities such that at least one of them must occur, but they can&#39;t both occur.

Now, let&#39;s say that broadside fires its twin-linked railgun instead. Rather than looking at the chance for it to hit, I&#39;ll try to work out the chance for it to miss, because that&#39;s easier to figure out. Now, for a twin-linked weapon to miss, you have to miss with your first roll to hit, then miss again on the re-roll.

Probability of a miss with the first roll: [sup]3[/sup]/[sub]6[/sub] = 0.5
Probability of a miss with the second roll: [sup]3[/sup]/[sub]6[/sub] = 0.5
Probability of missing with both rolls: 0.5 * 0.5 = 0.25

To get the probability that both events occurred (ie, that both rolls missed), I just multiply the probabilities together. So, the chance of missing with a twin-linked weapon at BS3 is 0.25. Now, remember what I said earlier about probabilities summing to 1? The chance to miss plus the chance to hit must always equal 1, like so:

(chance to hit) + (chance to miss) = 1

Therefore:

(chance to hit) = 1 - (chance to miss)

Since I&#39;ve already calculated the chance to miss, I can work it out:

(chance to hit) = 1 - 0.25 = 0.75

So the probability of hitting with a twin-linked weapon at BS3 is 0.75, or 75%. Is that clear enough? If you&#39;re not sure, try working it out for BS2 or BS4, and post your working so you can get some feedback. 