Guide Cauldrons 103

[Katwick]

Google Sheets Recipe Creation using a Solver

The Sorceress in my live world took a Sabbatical this week, so I'm using the Diamond Ingredients from the Beta World. I was going to get around to posting in the Beta Forum eventually, so here we go. There's a ton of discussion at US Forum - Cauldrons 103

You can always download a current copy of the Google Sheet from Katwick Cauldrons > Production. Each week, once the Diamond Ingredients are known, several relevant recipes are posted, plus anything else that's interesting.

Katwick Cauldrons runs on vanilla Google Sheets, as the front end for a Frontline Systems server farm, so you can run the Solver on a rather modest desktop computer. The spreadsheet itself is accessible from a Mobile, but it's pretty painful.

The important feature is WHAT we solve for, and how. This data set is a Low Cost, Modest Success, Military Series, with 50 Recipes. 1-25 of them are restricted to 8 Ingredient Types, no diamonds, while the other 1-25 Recipes use all 12 Ingredient Types, with diamonds as needed.

We're optimizing (Solving) using the following criteria:

1. The AVERAGE of the Check-Boxed Effects. Note that the Average, by itself, doesn't make the Effects the same size, it just tells the Solver which Effects should get some extra attention.
   • If you Check-Box a single ingredient, you're going to get an Expensive Recipe with a very high Success Rate for that particular effect.
   • If you check several Effects you'll get a spread that's USUALLY a lot cheaper, but with modest success rates.
   • In the following analysis we've selected all 5 Military Effects, plus Orcs, and all of them except 17_HM (Health Mercenaries), were actually at the top of the Success list somewhere along the way, and 17_HM was hanging in there at 2nd or 3rd.
   • 01_C_ coins was actually first at one point, because of spillover, although it was not selected.
2. The Factored Values are flattened if you check the optional "Low Cost, Modest Success" box, which we did for this analysis. We're using Square of the Sum / Sum of the Squares (a Spline Fit) to prevent any one Effect from hogging the Brew Pot.
3. The Ingredient Type Totals are always part of the solution criteria, Square of the Sum / Sum of the Squares again, so there's a rigorous methodology for how many of each Type of Ingredient will be allowed. You don't need to cap the Ingredient Types.
4. Witch Points are calculated after the Ingredient Mix is already established, because using the Total Number of Ingredients as a cost cap pretty much does the same thing as a Witch Point cap, and the Amounts are far more accessible for the differential equations that are used in the nonlinear analysis. The Solver usually takes less than 15 seconds.
5. To keep the formulas from erroring out (most of the time) there's a +1 in numerators that might otherwise be 0, and there's a +1E-15 (a very small fudge factor) in denominators that might otherwise be 0.

Along with being pretty, this chart and the associated Witch Points breakout quite clearly illustrate that using 12 Ingredient Types allows us to use fewer of each Ingredient Type, 12/8 is half again more Ingredient Types, which dramatically reduces how many Witch Points are required. The end game players may be able to throw Witch Points at the Brew Pot, but early and mid-game players have to be very careful. _____________________________	_______________________________________________________________________
When we're only using 8 Ingredient Types, 17_HM gets nothing at all.	When we're using 12 Ingredient Types, 17_HM is right up there with the Big Boys.
12,491 Witch Points if we only use 8 Ingredient Types.	2,276 Witch Points, plus 150 Diamonds, if we use all 12 Ingredient Types.

Let's do the math: (12,491 - 2,276 Witch Points) / (6 Diamond Ingredients) = 10,215 / 6 = 1702.5 Witch Points or else 25 Diamond. If you're a low to mid-level player, that's pretty attractive, as 1700 Witch Points per week is the approximate allotment for a player with only 10 Diplomas.

We've picked off a recipe for each of the Effects that we check-boxed. 17_HM never made it to the top of the list, but 01_C_ caught it on spillover. You can review all 50 Recipes by downloading the Spreadsheet, or by peeking at Every Military & Orcs Low Cost 21_23_31_34, which is a static webpage that Google Sheets allows us to publish.

Target	Actual	Rate	WPs	$$	Dpl	##	11	12	13	14	21	22	23	24	31	32	33	34	____Date____	Title_with_an_optional_screenshot_Link,_or_perhaps_a_HoneyDew_List.
Multiple	01_C_	5.51%	300	25	20	7	1	1	1	1	0	0	1	1	0	0	1	0	2023-05-15	Every Military & Orcs Low Cost 21_23_31_34 (Beta World) #07
Multiple	03_SB	6.07%	400	75	20	11	1	1	1	1	1	1	1	1	0	1	1	1	2023-05-15	Every Military & Orcs Low Cost 21_23_31_34 (Beta World) #11
Multiple	07_ST	5.18%	150	25	20	4	0	0	0	1	0	0	1	1	0	0	1	0	2023-05-15	Every Military & Orcs Low Cost 21_23_31_34 (Beta World) #04
Multiple	09_OR	5.00%	50	0	20	1	0	0	0	1	0	0	0	0	0	0	0	0	2023-05-15	Every Military & Orcs Low Cost 21_23_31_34 (Beta World) #01
Multiple	11_SM	6.67%	400	50	20	10	1	1	1	1	0	1	1	1	0	1	1	1	2023-05-15	Every Military & Orcs Low Cost 21_23_31_34 (Beta World) #10
Multiple	16_HT	5.70%	150	0	20	3	0	0	1	1	0	0	0	1	0	0	0	0	2023-05-15	Every Military & Orcs Low Cost 21_23_31_34 (Beta World) #03

 

[Dorfl the Clay]

I respect the effort, but... I thought we were playing a game... this looks more like advanced book keeping

 

[Katwick]

I respect the effort, but... I thought we were playing a game... this looks more like advanced book keeping

So you're suggesting that Football and Soccer are simple??

 

[manax]

Thank you @Katwick it is an incredible and gigantic "work"
you are completely crazy...
And that is the wonderful thing

 

[Dorfl the Clay]

So you're suggesting that Football and Soccer are simple??

Not just suggesting, stating! If you play them as game, they are just that. I'ts the professionals that have turned it into rocketscience.. because of the money involved!

 

[Brummbaer]

@Katwick , thanks a lot for the great works.
It is as always. Some like it and other do not.

Please continue to support others.
Greetings Brummi

 

[Katwick]

Not just suggesting, stating! If you play them as game, they are just that. I'ts the professionals that have turned it into rocketscience.. because of the money involved!

So High School Baseball is now played by professionals??

 

[Biloutte91]

For my part, I PLAY Elvenar. no need for these tables to play. Sorry.

 

[Dorfl the Clay]

So High School Baseball is now played by professionals??

In itself baseball (like foorball or soccer) is a fairly simple game.. the statistics you can develope around it doesn't change that. Also your argument doesn't have much baring on my original comment, in which I only tried to point out that working out what recipes are most interesting ad/or useful to make is quite complicated and the fact that you need complicated spread sheets to work it out is not really player friendly. I play Elvenar to enjoy myself... I also find your comments feel like you are looking to pick a fight and I won't oblige. I wish you well...

 

[Katwick]

A sweep of low cost, modest performance recipes is a technical tour de force, but I quite agree that it's not intended for everyday use.

But there are 500+ entries in the Recipe  Library tab, and once you downlaod the spreadsheet you'll have full access to the rather excellent Google provided tools for Sorting and Filtering. Those revipes ARE intended for everyday use, as you can readily find sometime useful.

Using a Solver ALLOWS you to explore some interesting approaches. I'm waiting for the next time that Barracks Strength (Mana Shell) requires Diamonds, whereupon I'll select 03_SB ANYWAY, shut off the Low Cost option, and not allow Mana Shell to be used. As a consequence the Solver will STILL get some pretty decent % Success Numbers for Barracks Strength, but it will have to scramble to get there with a mix of other ingredients, which is another way of keeping the costs down.

 

[Katwick]

Just 03_SB Strength Barracks

The RNG gods picked Mana Shell this week, which paves the way for WHY focusing on a single effect, if you're unwilling to use Diamonds, is a pretty bad idea.

There are 25 Recipes in the data set at Just 03_SB.

The first couple of trials address a suggested strategy of just using a couple of Ingredients, and always focusing on Strength Barracks. Bad idea. Using a variety of Ingredients is ALWAYS cheaper.

• 5, 10, 15, 20, 25 Total Ingredients for each set.
• 03_SB focus with 2 Ingredient Types (no Diamonds)
• 03_SB focus with 3 Ingredient Types (uses Diamonds)
• 03_SB focus with 8 Ingredient Types (no Diamonds)
• 03_SB focus with 8 Ingredient Types (no Diamonds, but also no constraint on "the best" Effect, and 03_SB fails badly)
• 03_SB focus with 12 Ingredient Types (uses Diamonds)

 

[Karvest]

Why you are trying to max overall success rate? If you need only few effects - other effects are just a garbage. It's way better to get some spell fragments and/or diamonds from critical boosting back due to failed brew than to get some trash effect.

List of recipes "without diamonds" which costs way more than anybody can use has no sense too.

Not sure why you are focusing on barracks strength this week for a player with 20 diplomas. This week tourney most used unit is Orc Strategist for humans, elves can use few "free" Golems as well. TG strength looks more promising and easily achievable for free with current setup of diamonds ingredients (up to 58% in my city). But let's take it as an experiment for bad setup. It's not as bad as it could be, though. Worst setup will block all the ways to get desired effect.

If we are talking about players with less diplomas - focusing on barracks can give much better results without diamonds (for 3 diplomas and 700 WP (something near orcs chapter) - 56%, for my city in ch15 with 11 diplomas - 29.1%)
Even ch20 with 20 diplomas can get 33.7% barracks strength without diamonds. None of your usable recipes give that high chance (even the ones which require diamonds are worse!). Seems your solver is far not as good as my.=)
BTW, ch20 with 11 diplomas can get 40.6% barracks strength without diamonds. And up to 98% with 3 diplomas. That's a perfect illustration of how bad is to get more diplomas than you actually need.

Spoiler: screenshots

early chapter with 3 diplomas and 700 WP

11 diplomas in ch15:

20 diplomas in ch20:

11 diplomas in ch20:

3 diplomas in ch20 (not sure if 6850 WP can be achieved with 3 diplomas, but even if not - there would be 95%, which is overkill too):

11 diplomas ch15 focus on TG strength:

 

[Katwick]

The first couple of trials address a suggested strategy of just using a couple of Ingredients, and always focusing on Strength Barracks. Bad idea. Using a variety of Ingredients is ALWAYS cheaper.

I quite agree that focusing on Barracks Strength, or any other single effect is a BAD idea, as I indicated.

One of the folks in the US Forum was promoting the use of ONLY three ingredients, and always going for 03_SB. See Cauldron 3 Ingredient Types, and Voila! the Beta World pops up with Mana Shell as a Diamond Ingredient. So the above post is really about why that's a BAD idea.

I'm very close to suggesting a Too Simple approach for using the Brewery.

• Take whatever you get, but no Diamonds:
  • 8 Total Ingredients, one each of the NON-Diamond Ingredients. There's a nearly 60% chance of getting a buff, and you can use the rest of the Witch Points for Studying PERMANENT Effect Boosts
  • 8 Ingredient Types, 1*4 + 7*3s = 25 for a 100% Success Rate, which is low cost, but not at all cheap
  • Or somewhere in between, depending on what you can afford
• If you're willing to spend a few Diamonds, push a few Effects that use a lot of just one particular Diamond Ingredient
  • 8*2s that are non-Diamond + 9 * ONLY ONE Diamond Ingredient Type = 25, and go for a few High Success Rate Effects
  • Because of the way the Brewery calculates Witch Points, you can put in 2 of each non-Diamond Ingredient, and then add and backout each of the Diamond Ingredients, to see which one gives you the highest Success Rate for a few desirable Effects.

In my mind the best strategy is to get past the TEMPORARY benefit from the Brewery, you may or may not get a good buff, and invest your Witch Points in the PERMANENT benefits from Studying the Effects, so that they're all good buffs.

I'll be running some solutions, Manual/Solver comparisons, to ensure that a Too Simple approach makes sense, but so far it's holding up.

 

[Karvest]

The amount of WP you can save on brewing stage is almost nothing comparing with donations on studying stage.
Most of effects are useless if you get them not at right point of time. If I want stronger army for tourney and get something like 15% boost for goods production - that's clear fail, the only usage of that effect I can invent - to collect prepared 2days T1 production for bracelets at FA start. (and to get that boost you need to spend a lot of WP on studying that effect).
Upgrading only 3 military effects to 80+level costs few millions of WP, doing that by saving some from brewing stage will take years. Years of wasting time and efforts (and even diamonds!) on getting 100% success rate of brewing something you don't really need is nonsense... If you can't get desired effect and want to save WP - use just one ingredient and save almost all WP.

 

[Katwick]

You and I, and a handful of other players, understand how to squeeze what we want out of the Cauldron. But I've yet to see a useful approach that ignores all of the spreadsheet stuff, but still yields something beneficial.

I'm trying to offer something simple and quick, that can be used in-game, regardless of Diploma level or weekly Diamonds, by the folks who are currently just kissing off the free Witch Points because the whole thing is just too fiddly.

 

[Karvest]

Using only one ingredient and leveling up whatever effect they like using rest of WP is the best strategy for such players. Getting few hours of random boosts won't be beneficial most of the time.

 

[Katwick]

And they'll still have a 20% chance of getting a buff. We both know that.

But I want to lead into a pattern of:

• Add one of each non-diamond ingredient
• Add, and then blackout each of the Diamond Ingredients to see if it's worth the bother.
• If there's nothing interesting, dump the pot and use 1 non-diamond ingredient.
• If there's something Interesting, use up the rest of your Witch Point by adding a second item to the non-diamond ingredients
• Add 9 of the interesting Ingredient for 225 Diamonds

The yield will be a 57% to 100% chance of getting something interesting at a cost that ranges from:

• 573 Witch Points to
• 2290 Witch Points + 225 Diamonds

JUST using the Brewery Widget.

 

[Karvest]

There won't be "something interesting", there would be some trash that leads only to disappointment about wasted time, witch points and/or diamonds. Something becomes interesting only after you level it up high enough, and only if you need it at the time you press brew button.

 

[Katwick]

But first you have to get there.

Not doing snything at all is what wastes Witch Points.

 

[Karvest]

yes, click anywhere, waste only 50 WP and use the rest. That's much better than wasting 400+WP and maybe diamonds for some random effect which you can hardly use.