Chaos Tool by Zenoooo

I released a few scrolling guides before
Scrolling Guide (SCRL 101) 30%, 70%, 60%, WS, CSS
Chaosing Value and Pricing of ATT Capes and Shoes
(Out of maintenance) Scrolling Cost and Market Price Fitting

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I received good responses as well as hate comments.
Also found people who well understand and actually implement the methods I shared (shout out to Star and Fuhuo!). There was one time I ran out of return scrolls and asked a stranger for some, and he/she gave me scrolls and said the guides are awesome. From time to time, people tell me they benefit from the methods. Thank you all and I appreciate the feedback.
Apart from the Chaos Tool I am introducing here, I also recommend players to save half (or 1/3 to 2/3) of the profit from chaosing equipment, and reinvest the rest until you have decent CGS and weapons. My personal standard is perfect +7 weapons + 60 CGS. You may adjust accordingly!

Basically, chaos is a random walk problem. If we use ws and allow the ATT to go negative it will look very much like this:

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Obvious, this is not the case with chaos, because ATT stops at 0, and rational players would choose not to CS some equipment (for example, 3/3 cape), and not to use WS on certain equipment.
Earlier on the Chaosing Value thread, I showed readers some simulation results.

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VL boots with random att (godly included), certain abandon rules, and ws rules.

You could code yourself or ask AI to code for you, and run on you computer.

I would introduce a more accessible tool for most players: Excel/Numbers.
Take shoes for example, we need 6/7 slots. Start with an input 1 on around line 46:

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Sum up 11 entries:

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And apply it up and down:

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Obviously, there would be 0 chance to get +6 with 1 chaos scroll.

Now you do it with the 2nd slot:

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And extend to the 7th slot:

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And it's a nice looking random walk distribution:

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Now we add some realistic cutoffs:
For a 8/6 boots, stop chaosing at 2/4, 3/3, 4/2, and 5/1. Also remove the 7th slot:

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Now the distribution looks like this.

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Now compare with the simulation figure.
1. The jump at ATT = 11 is the result of not using WS at around att+slot = 10.
2. The scattered dots at low ATT are the result of abandoning low att shoes (for example, 1/4). And the code treat 1/0 and 1/4 as the same output.

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VL boots with random att (godly included), certain abandon rules, and ws rules.

Note that here we are still working on ws+cs only. To touch the realistic cases where we don't use ws on low att shoes, we need to modify the formula at low ATT. Unfortunately I personally am not interested in low ATT, and I would prefer to run simulations. I haven't found the substitute formula yet.
I may update this part in the future.

How to use it:

Example 1:
1 in how many 8/6 would be at certain ATT?

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For example, 1 in 1,171,561 8/6 would be 38 ATT.

Example 2:
On average, how many 8/6 VL boots do you need to scroll to have at least one that's above the value of 8/6 boots + 6 successful attempts (about 22b in total, or say 15 ATT)?

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Sum up the number of 15 ~ 38 shoes:

One in 4.9 8/6 VL boots would be at least 15 ATT.
Note: At low ATT, people don't use WS. Actually less than one in 4.9. But ~20% is what we are looking for!

To be continued

 

Nice guide, impressive research.

now you can write the thesis and @Tim will award the diploma soon

 

Impressive math's behind

 

Love reading your posts. Keep up the good work!