If you dont wanna read a lot, please go down to the highlighted lines and tell me if the final equation is correct.

Ok, so I am making a Fishing System which, when you fish, works like this:

• If [random chance] 22 + stats_FISHING [% of the time]
• • You catch a Roach!
• Else
• • If [random chance] 18 + stats_FISHING [% of the time]
• • • You catch a Carp!
• • Else
• • • If [random chance] 12 + stats_FISHING [% of the time]
• • • • You catch a Pike!
• • • Else
• • • • You fail to catch anything...

So, this all works fine. My question is about the math of the chances of the more rare fish.

I am making an XCell document to track my food items, and I am trying to build equations into it to show me the actual chance of either of 2 characters catching each fish, so I can adjust the base amount to find a good game balance.

So, we have Fish Base Chances:
R% = Roach at 22% base
C% = Carp at 18% base
P% = Pike at 12% base

We have Character Skills which are added:
H$ = Harumi, with a 12% bonus to Fish Base Chances
K$ = Kahko, with a 7% bonus to Fish Base Chances

So, on my XCell sheet I have Columns and Rows like so:

........... Base Chance ... Harumi Chance ...Kahko Chance
Roach |
..Carp |
...Pike |

So, here's how I calculated the Roach Rows, very simple

Harumi Roach Chance (HR!)

HR! = R% + H$ = 0.22 + 0.12

Kahko Roach Chance

KR! = R% + K$ = 0.22 + 0.07

But since the Carp can only be caught if the Roach is not, and the Pike can only be caught if both Roach and Carp are not, I am not confident that my Math is right on the following...

Harumi Carp Chance (HC!)

HC! = (C% + H$) * (1 - HR!) = (0.18 + 0.12) * (1 - 0.34)

Harumi Pike Chance (HP!)

HP! = (P% + H$) * (1 - HR!) * (1 - HC!) = (0.12 + 0.12) * (1 - 0.34) * (1 - 0.2)

I know this a lot of boring text, but I do not want to start working off a faulty foundation, so if a Math whiz could confirm that I have done this right, or tell me how I did it wrong, I would be very, very grateful!

I'm not used to seeing formulae in that notation; but I think the last formula is a bit off.

HP! = (P% + H$) * (1 - HR!) * (1 - HC!) = (0.12 + 0.12) * (1 - 0.34) * (1 - 0.2)

I think this would be correct if HC! was "chance of catching a carp given that you didn't catch a roach", or the base C% + H$.

Because your HC! has already been modified to be a base chance and the options are mutually exclusive, you want

HP! = (P% + H$) * (chance of not catching either of the previous ones)
    = (P% + H$) * (1 - HC! - HR!)

Ok, that makes sense to me, I think you're right!