#game math

Puzzle Quest Math

On Reddit, somebody's mathifying my timewaster game, Marvel Puzzle Quest.

I play it free, being an old cheapskate. There are two main currencies in the game, Hero Points and Command Points. The main thing you want, after playing awhile, are the 5 star characters. It takes 13 covers to champ a character, and 113 to maximize a 5 star. I'm just maximizing my first ones...

There are two ways in the store to get a chance at 5 star characters, the Latest Legends and the Classic Legends. The Latest Legends are the three latest, released once/month. Classic Legends are all the rest, with three at elevated 18x odds. Latest Legends cost 25 CP and Classics 20 CP. There's a chance at bonus shards (fractions of a cover) which is also marginally different. Typically players hoard LL tokens until there are 3 good ones in the store. (I like having everyone champed, so I spend from the hoard enough to get characters champed. Just recently spent 750 covers on a good store with Namor, Agatha Harkness and Mephisto, though.) Currently there are 104 5 star characters.

For every 1000 HP spent (50 covers), in Classic Legends you should expect 8 five star characters, .99 of each featured character [(1/6)*18*50*(1/152)], and about 2% chance at any non-featured character. As well as 2 occurrences of 5 star bonus shards and 150 shards (30% of a cover) guaranteed. About .1% chance on a single pull of a given non-featured character, so about 5.5% chance at a given cover you want. This is decreasing a little bit each month as the roster of 5 star characters grows.

180 armor

20 Thick Cloth

25 Rope

25 Leather

3 Copper

For : Kettle Hat, Gabeson, Quilted Trousers, Leather Gloves, High Boots

Healing

40 Raw Meat

80 Leek Seeds

520 Flaw Fiber

For: Jerky, Leek Soup, and Bandages

Now for the total raw materials I need because typically I can't find shit the level I need:

690 Flax Fiber

25 Pelts

40 Raw Meat

80 Leek Seeds

20 Glass Vials

100 Edible Red Berried

200 Not Edible Berries

300 Wood

9 Copper Ore

So I am also aiming for 20 Bitter Tinctures, which good fucking luck finding glass vials, and a relative good amount of health.

This doesn't include weapons, or what I need for building the altar so I can have more abilities. Or feeding my direwolf and my character. Constantlty needing armor and weapons, and tools to gather the supplies.

On average I can find 20-40 flax fiber in one go if I can run to the good raid spots.

Cylinders! Yes, of course, cylinders! I was hoping no one would mention those, as each alchemy skill has different variables, which calculates slightly differently depending on how many charges you have, which requires me to calculate everything out. I'm looking at you, Zurrkitty.

Still, I can't ignore the Alchemists that make up a good amount of the Mabinogi population, and for good reason.

I'll only be calculating the simplified formulas for three skills, Water Cannon, Flame Burst and Heat Buster. The other skills are affected through non-damage attributes or the affects on increase damage are minor or negligible.

And, once again, we will be looking at the life of Milletian. In addition to his other traits, through years of alchemical training, he has gained the ability to always be in prime range for Water Cannon. Good job, Milletian!

Except this time, we will be doing something different. We will be assuming the wiki's formula is wrong. And the reason is that, through initial testing and application of common sense, it's been discovered that, despite what the wiki's formula may show, charging up multiple charges of Water Cannon does, indeed, increase its damage.

The error is most likely a failure to use parentheses. With that out of the way, let's get started.

The formula for the skills we are using is:

Damage = (Base + ResourceMultiplier * RemainingResource) * ChargeMultiplier + (FlatAlchemyBonuses * Charges)

Next, we calculate the average damage for both:

0.7 * ((145 + 0.3 * x) * 1 + (31 * 1)) + 0.3 * (((145 + 0.3 * x) * 1 + (31 * 1)) + 1.5 * ((150 + 0.3 * x) * 1 + (31 * 1))) = 0.7 * ((145 + 0.3 * x) * 1 + (0 * 1)) + 0.3 * (((145 + 0.3 * x) * 1 + (0 * 1)) + 2.12 * ((150 + 0.3 * x) * 1 + (0 * 1)))

As long as you have over 305 mana, your Water Cannon will benefit more from red than blue. Next, we'll have to use the same type of calculation for the other skills and situations.

Water Cannon, 1 Charge: 305 Mana Water Cannon, 5 Charge: 119 Mana Flame Burst, 1 Charge: 1326 Health Flame Burst, 5 Charge: 1326 Health Heat Buster: Blue is never better

Technically, that last line is false. Even so, good luck getting -2281 Stamina

More Follow-Up: As you get greater Fire Alchemy Damage enchants, you need less and less health to make Flame Burst worthwhile. The formula is 

y = -12.5 * x + 1326

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Math Car