Mining hat

[GM-Ayu]

Fishing/Mining generally looks like this in script

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set x, rand(1,y)
[where y is total number of possibilities]
if x = 1 to 3, then goto A
if x = 4 to 6, then goto B
{and so on}
if x = 100 to 300, then get 'junk'
if 300 < x < y, stone/pick break [note: again I don't know if pick break is a subset of stone, or is it a totally different category, but it should be the last few numbers either way]

What's A, B and so on? They maybe...
1) getting an item directly (simplest case)
2) enter another round of random number generator, which for simplicity's sake, we'll call it a subset.

Eg.
If A, then set z, rand (1,10)
if z = 1, then A1
if z = 2, then A2
etc etc

And you may get items now, or enter even more subsets within the subset.

now if you have fishing/mining hat, then y = y - c (where c is some constant, for fishing hat it's 40. For mining hat, don't know what the value is... but probably something similiar)

So you see equipping the hat is just lowering the denominator.

The "3%" is a decrease in chance of pick/bait disappearing (or getting stone, again depends if breaking is a subset or not). The chance of any other event therefore increases to fill up the gap of this 3%. However, this doesn't mean that every other event increases in chance by 3% either.

Since the denominator changed, then all the other cases get an indirect increase again. However, because it's a subtraction in the denominator value, it will not result in linear change for all other events... Hopefully showing the super-simplified-psuedo-code can briefly explain mathematically why the rate of increase for any particular item is by no way linear. It's pretty complicated without the real script, which I haven't seen either (so I don't know the exact numbers) but I know that this is how fishing/mining works in theory.