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What are the odds?
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Old 25 Jun 2006, 06:33   #1 (permalink)
77
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Default What are the odds?

I'm trying to crunch numbers better and I am wondering what is the statistical (%'s) averages when you re-roll hits/wounds? Eg. I know that having BS3 means that you hit 50% of the time, but what about TL weapons? How does that number change.

I have tried this before in previous posts and have run into differing numbers.

Just seeing if there is someone there that can lend a hand.
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Old 25 Jun 2006, 07:37   #2 (permalink)
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Default Re: What are the odds?

Someone has a list of probabilities of rolls for a d6 and 2d6, I don't remember who, though.. might be on the main site.

-Nuke
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Old 25 Jun 2006, 09:51   #3 (permalink)
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Default Re: What are the odds?

Quote:
Originally Posted by Nuke
Someone has a list of probabilities of rolls for a d6 and 2d6, I don't remember who, though.. might be on the main site.

-Nuke
The article in question.
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Old 25 Jun 2006, 16:30   #4 (permalink)
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Default Re: What are the odds?

Quote:
Originally Posted by Pollo
That's a good article, but it doesn't address the problem of re-rolls, which was the subject of 77's query. I'll have a go at writing a quick explanation.

Okay, let'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't both occur.

Now, let's say that broadside fires its twin-linked railgun instead. Rather than looking at the chance for it to hit, I'll try to work out the chance for it to miss, because that'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'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're not sure, try working it out for BS2 or BS4, and post your working so you can get some feedback.
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Old 26 Jun 2006, 03:48   #5 (permalink)
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Default Re: What are the odds?

This looks good and is very helpful.

Here's what I came up with:

For Regular weapons:
BS2 = 33% chance to hit
BS3 = 50% chance to hit
BS4 = 66% chance to hit
BS5 = 83% chance to hit

For TL weapons:
BS2 = 55% chance to hit
BS3 = 75% chance to hit
BS4 = 88% chance to hit
BS5 = 97% chance to hit

[hr]

This really helps for testing. Correct any of the math if it wrong.
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Old 26 Jun 2006, 07:56   #6 (permalink)
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Default Re: What are the odds?

All correct! It looks like you've got the hang of it.
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Old 27 Jun 2006, 09:16   #7 (permalink)
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Default Re: What are the odds?

There is one I'd like to add... and that is Sharpshooters:

58.333% chance of hit.

For those who are interested, here's the "full" Bs table.

Bs 0 = 0.000%
Bs 1 = 16.666%
TL Bs 1 = 30.554%
Bs 2 = 33.333%
Bs 3 = 50%.
TL Bs 2 = 55.554%
Bs 3.1 = 58.333% [Sharpshooters]
Bs 4 = 66.666%
TL Bs 3 = 75%
Bs 5 = 83.333%
TL Bs 4 = 88.888%
TL Bs 5 = 97.222%
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Old 27 Jun 2006, 11:31   #8 (permalink)
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Default Re: What are the odds?

Excuse my ignorance, but I've never heard of a sharpshooter. What are they?
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Old 27 Jun 2006, 12:19   #9 (permalink)
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Default Re: What are the odds?

It's a Doctrine available to the Guard.
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