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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I have a solution for the following problem, but it isn't a great one. Perhaps someone could come up with something better. But either way, I found the problem to be pretty interesting, so hopefully others will as well. The problem is as follows, from an actual RPG game:

You have a game where you have a set number of attribute points, p. The max p can be is 280. You can put points into either weapon skills (WS) or critical hit skills (CS). Putting points into WS will increase the amount of damage the weapon does per strike by 1. If a critical hit strikes (as it can on any attack), it will double the damage done by a normal hit. The chance for a critical hit is given by: 1.5/(3 + 100/CS).

Weapons do a random amount of damage over the range [a, b] at a normal distribution.

Given the amount of base damage done by a weapon and how many attribute points you have, find a way to spend your attribute points to get the maximum amount of average damage per strike.

NO PROGRAMS ALLOWED!

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**henryzz****Member**- Registered: 2007-06-03
- Posts: 14

what game is this

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I want to make sure I understand this. Is the range [a,b] defined by the weapon, and are we given both of those values?

Also, I don't see how the damage can be distributed normally, but also bounded. A rectangular distribution seems more likely.

Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Yes, you are given a and b.

Also, I don't see how the damage can be distributed normally, but also bounded. A rectangular distribution seems more likely.

Huh? All it means is that there is an equal chance for the damage to be any number in [a, b].

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Maybe we're confusing terminologies then. I take normal distribution to mean the 'bell-curve' thing.

I think I get it now. In that case, without looking at it that much, I think the hardest part will be the fact that p needs to be split into integers.

Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Maybe we're confusing terminologies then. I take normal distribution to mean the 'bell-curve' thing.

Whoops, I meant uniform distribution. Thanks. I hate statistics

I think the hardest part will be the fact that p needs to be split into integers.

You don't necessarily have to do that, but I'd be really interested in a solution with it. I couldn't come up with one myself.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Does the critical double the damage before or after WS is added?

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

After.

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