Brewing (or not)

The Cauldron allows folks to create custom buffs, rather than always being at the mercy of the RNG gods. The Cauldron is MUCH too complex for casual use, but it’s interesting for those of us with an engineering background, who are comfortable with spline fitting techniques, such as:
(Square of the Sum / Sum of the Squares)
and other computer based mathematical techniques for solving quadratic multivariable optimization problems.

We've tried to offer a simple technique for getting worthwhile benefits when you use the Cauldron, but it's like putting lipstick on a pig.

The Frontline non-linear solver extension for Google Sheets, that we’ve been using for a couple of years, has been moved behind a paywall, and we don’t intend to rehabilitate the Cauldron Spreadsheet.

If you do want to understand the intricacies of how the Cauldron works, the spreadsheet is available online (view only), or you can download a copy for your own use.

The fundamental problem is that the math is ugly.

If you look at the first column of the snapshot that we’ve included on this page, you’ll note a +3 to -2 range for 7 possible ingredients. One attribute from each of the relevant ingredients that you select will be added together as the base Value of that effect. Note that the attributes can cancel each other.

The next 5 possible ingredients are likewise added together, but as an exponential Factor. The formula is Weight = v * 1.1^f.

Worse yet, the value attributes for effects 13-24 are interleaved while the factor attributes are both interleaved and reversed. And there’s a data error that favors the Orcs a bit, at the expense of the Tier_1 Precious Goods. And then the whole Meshuggah is staggered so that there are 24 different contributions for each of the 12 ingredients, 4 of which will cost you diamonds if you insist on using your favorite recipe each week.

But that’s not all, folks! The weights are then scaled against the Sqrt(Total Ingredients / 25). To have a 100% chance of getting a successful brew, for each potion, you’ll have to use 25 ingredients or dump in some Shards.

The actual Witch Point cost of the ingredients is also pretty goofy. The first ingredient in each row increases all of the next prices by 1.1^n, while subsequent ingredients in each row increase all of the next prices by 1.4^n. So sequence matters (a lot) and you’ll want to make your ingredient jumps while the prices are as low as possible. The cheapest sequence is a multi-pass layer cake.

• 428 + 6873 Witch Points
  using the best ingredient 4 times
  using the other ingredients 3 times
  1+1+1+1+1+1+1+2 = 9 Buy the best first
  2+2+2+2+2+2+2+3 = 17
  3+3+3+3+3+3+3+4 = 25

• 1,582,950 if you were to use just 1 ingredient

Backing out the most recent ingredient a bit more expensive, but it’s a lot simplier, so you can easily skip the ingredients that you don’t like. A vague understanding of the math will help you avoid worthless recipes.

Then, to top it all off, only integer input values are allowed, which makes the whole thing a LOT more complicated by compromising many of the calculus techniques that are so effective when spline fitting polynomial data points.

Don’t bother with the spreadsheet or canned recipes. Just add one of each non-diamond ingredient, on each pass, and if you don’t like the results just back the ingredient out and skip it this week. Or maybe sneak in a Diamond ingredient.

The more Diplomas that you have, from completing chapter researches, the more the effects that will be competing for a piece of the potion. Scroll the widget to see all of the effects after you’ve added a couple of ingredients. It’s not pretty, and it’s very difficult to weed out the effects that you don’t want.