General / Off-Topic I have a mathematical problem with probabilities.

So this is from a shooter game.

  • A weapon does a random number from 122 to 150 damage for each shot.
  • The weapon has 10 rounds of ammunition in a magazine.
  • The damage it needs to do to destroy a target is 1500.

In my mind this goes as follows:

The potential states of damage each shot can do is is 150-122 = 28 different damage values (122, 123, 124, 125 and so forth up to 150).

In order to do 1500 damage in total each shot needs to do 150 damage, which is 1 out of the 28 states.

Looking at this like rolling a 28 sided dice for each shot and needing to get the full 28 on each roll consecutively the probability is:

  • x = number of states we allow
  • y = amount of possible states
  • n = amount of rolls we will do (in this case 10 because of 10 shots in a magazine)

(x / y)^n ... therefore (1 / 28)^10 = 0,000000000000003376~

Am I doing this right so far?

Here is what I don't get though.

Looking at this in a more simplified way you could reason that in a single magazine the weapon can do a minimum of 1220 damage (10 x 122) up to a maximum of 1500 damage (10 x 150).

From 1500 to 1220 there are 280 different possibilities in terms of how much damage the weapon does when adding together the outcome of all 10 individual shots fired. It could do 1221 damage, or 1222, or 1223 and so on up until 1500.

However, to destroy the target we need to do 1500 damage and there is only 1 out of those 280 possibilities that allow this.

In other words there is 1 in 280 chance doing 1500 damage when firing a single magazine with 10 shots.

Now... 1 / 280 is A LOT more likely than the previous probability as seen above which is microscopic with it's 0,000000000000003376 chance (which is 211 / 62 500 000 000 000 000 with a bit of rounding off numbers).

So which one is correct?

Is the probability of doing 1500 damage in 10 shots 1/280 or 211/62 500 000 000 000 000 ?
 
Last edited:
I'll come back to this because I have to skim read this, but I believe the answer you are looking for is the lower probability; the 1/280 method suggests that the probability of getting each number is equal, but it is not...you would be talking about a gun with a single shot that can deal from 1220 to 1500 damage in that shot, which is effectively what you've produced by simplifying the concept.

Use a pair of dice to visualise this. You roll two, and have a maximum roll of 12. But the probability of getting two sixes is NOT one in twelve; this is because the numbers in between - say, 7 - have more than one way of appearing. So you can roll a 6 and 1, which is a total of 7, or roll a 5 and a 2, also 7, or 4 and 3...

There's only one way of getting 12. The probability is therefore actually 1/36. If it's easier to conceptualise, you have 36 possible rolls, but several of those rolls would produce the same number.

I'll check the figures on your less probable calculation when I get a moment.


EDIT: without actually running the calculation, looks sound to me.

Note - this is why you use an indice and not multiplication when working out probability here, multiplication being what you used in your latter attempt (I mean come on, I have to give you props for using indices first, your understanding is clearly at least above par). You'll notice that if using multiplication you'd effectively get 10 * 28 = 280, which is "the other" figure you worked out. And that's a true probability if you have a single 280 sided die - but you don't.

You have 10 dice (bullets) with 28 sides (possible damage range), and the probability that the result is somewhere in the middle is much higher than the probability of an extreme number such as your maximum possible damage, because there are increasing number of ways to roll a number towards the middle of your range of values.
 
Last edited:
Thanks for the explanation!

I think I understand better. Looking at it with simple 6 sided dice the chance of getting 7 is greater than getting 12 cause getting 12 means you must roll 2 x 6, no other way to get 12. But to get 7 you can roll 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2 and 6 and 1... so you have 6 ways to get to 7.
 
Thanks for the explanation!

I think I understand better. Looking at it with simple 6 sided dice the chance of getting 7 is greater than getting 12 cause getting 12 means you must roll 2 x 6, no other way to get 12. But to get 7 you can roll 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2 and 6 and 1... so you have 6 ways to get to 7.

Correct. Its related to the normal distribution
labeledChart2.jpg


In such a dice-rolling scenario (and many, many, many other scenarios) 'average' values are very common, and the more distant from average the less common. Another example would be body height: while genetically speaking there is a certain range, the outer values are increasingly rare. Which is why more people have approximately an average height than there are people with the height to be an NBA star. Even though both are 'just one possibility within a range of possibilities'.
 
Last edited:
Correct. Its related to the normal distribution
http://mathbits.com/MathBits/TISection/Statistics2/labeledChart2.jpg

In such a dice-rolling scenario (and many, many, many other scenarios) 'average' values are very common, and the more distant from average the less common. Another example would be body height: while genetically speaking there is a certain range, the outer values are increasingly rare. Which is why more people have approximately an average height than there are people with the height to be an NBA star. Even though both are 'just one possibility within a range of possibilities'.

Bah, bloody bell curves. I see them in my sleep even years after studying them.
 
Last edited:
Back
Top Bottom