# Game math problem **URL:** \ **Category:** The Game Room\ **Created:** [September 9, 2009, 10:54pm UTC](https://boards.straightdope.com/t/game-math-problem/509487 "2009-09-09T22:54:09Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![YogSothoth](https://avatars.discourse-cdn.com/v4/letter/y/8edcca/32.png) [@YogSothoth](https://boards.straightdope.com/u/YogSothoth)\ **Post date:** [September 9, 2009, 10:54pm UTC](https://boards.straightdope.com/t/game-math-problem/509487/1 "2009-09-09T22:54:09Z")
I’m trying to figure out the rate of magic point (MP) savings for spells and how it is affected by an ability. The ability in question activates on 25% of spells cast, and when it activates, the saves an amount of MP based on the following formula: (n/16) \* (spell MP cost), rounded down n= integers 8-15. All occurences of n has an equal chance of appearing The faq for the ability then says that “…thus, each activation of the ability saves 28.125% of MP cost on average.” I admit it, I’m bad at math. I skated through pre-calc in high school and took more than one try in college calculus. Plus, its been like a decade since I took any math class. I can’t seem to figure out how they got from “all occurences of n has an equal chance of appearing” to “28.125%”. Can anyone help? :smack: ---
**Author:** ![Hoopy\_Frood](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hoopy_frood/32/8452_2.png) [@Hoopy\_Frood](https://boards.straightdope.com/u/Hoopy_Frood)\ **Post date:** [September 9, 2009, 11:13pm UTC](https://boards.straightdope.com/t/game-math-problem/509487/2 "2009-09-09T23:13:52Z")
With an equal chance of all numbers 8-15 coming up, that means on average you’ll have a value of 11.5 for n. 16 - 11.5 = 4.5. So on average you’ll save 4.5 which is 28.125% of 16. ---
**Author:** ![YogSothoth](https://avatars.discourse-cdn.com/v4/letter/y/8edcca/32.png) [@YogSothoth](https://boards.straightdope.com/u/YogSothoth)\ **Post date:** [September 9, 2009, 11:23pm UTC](https://boards.straightdope.com/t/game-math-problem/509487/3 "2009-09-09T23:23:12Z")
Why do you minus 11.5 from 16? Why isn’t it 11.5/16 average savings? ---
**Author:** ![Hoopy\_Frood](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hoopy_frood/32/8452_2.png) [@Hoopy\_Frood](https://boards.straightdope.com/u/Hoopy_Frood)\ **Post date:** [September 9, 2009, 11:25pm UTC](https://boards.straightdope.com/t/game-math-problem/509487/4 "2009-09-09T23:25:26Z")
11.5/16 is average cost. Full cost - average cost = average savings. ---
**Author:** ![YogSothoth](https://avatars.discourse-cdn.com/v4/letter/y/8edcca/32.png) [@YogSothoth](https://boards.straightdope.com/u/YogSothoth)\ **Post date:** [September 9, 2009, 11:30pm UTC](https://boards.straightdope.com/t/game-math-problem/509487/5 "2009-09-09T23:30:21Z")
Thanks! I really need a refresher math course… ---
**Author:** ![Bosstone](https://avatars.discourse-cdn.com/v4/letter/b/22d042/32.png) [@Bosstone](https://boards.straightdope.com/u/Bosstone)\ **Post date:** [September 10, 2009, 12:29am UTC](https://boards.straightdope.com/t/game-math-problem/509487/6 "2009-09-10T00:29:56Z")
It’s been answered, but I thought I’d present it another way. Assume you cast a spell that costs 100 mana and this kicks in. n/16 \* MP average n = 11.5 11.5/16 \*100 .71875 \* 100 71.875 That’s how much MP the spell costs. Well, 71 since it rounds down, but we’re talking math here, not reality. You save: 100 - 71.875 = 28.125, or 28.125%. Of course, it only occurs every 1 in 4 spells, which means you’re really only saving about 7% overall. ---
**Author:** ![Mosier](https://avatars.discourse-cdn.com/v4/letter/m/7ea924/32.png) [@Mosier](https://boards.straightdope.com/u/Mosier)\ **Post date:** [September 10, 2009, 2:53pm UTC](https://boards.straightdope.com/t/game-math-problem/509487/7 "2009-09-10T14:53:38Z")
> [@Bosstone](#): > > Of course, it only occurs every 1 in 4 spells, which means you’re really only saving about 7% overall. This is the important part to remember. The ability saves a little more than 7% of your mana, overall.