Fun Math

Let us introduce some variables and functions to make calculations easier:

1 Time to Bite

We start with a base, TTB_min=0.6 and TTB_max=30
We expect to always hook a fish on the first try, so we can descrese them by 25% (which means multiply them with 0.75). We are using targeted bait, which decreases the times by 50%.
Each depth level (0 to 5) decreases the maximum time by 0.25 seconds Now come Dressed Spinners. Each decreases the maximum catch time by 10 seconds.
This leaves us with:
TTB_min=0.6*0.75*0.5=0.225. This however can not drop below 0.5s, so TTB_min=0.5
TTB__max=(30-spinnerCount*10-depth*0.25)*0.75*0.5
Since the catch time is evenly distributed over this range and we will just take the average time for our calculation:
TTB=(TTB_max+TTB_min)/2 ^[Wiki]

2 Squid chance

For calculating the squid chance we are using the code from brokencygnus.
As we are expected to catch nearly the entire day, we just take the average chance over the day. We calculate this by taking the chance to catch a squid at every hour of the day.
That leaves us with a list of chances, over which we take the average giving us: P_squid

3 Chest chance

We have a base chance of P_chest=0.15.
I expect us to use the Pirate Profession, so the chance increases by 15%, to P_chest=0.30.
The special charm increases this by 1.25%, to P_chest=0.3125.
Each treasure tackle adds another 5%.
Each level of luck added by foods/drinks gives us 0.5% extra.
Daily luck has an effect of up to 5% in each direction. If we go to enough different squid festivals, this number should amortize towards 0% and thus is not included in our calculations. This leaves us with P_chest=0.3125+treasureTackleCount*0.05+luckBuffs*0.005. ^[Wiki]

4 Result

For the result we first calculate the average time per cast T for the relevant method. Then we multiply this with 1/(P_squid*P_chest) to get the time per squid with a chest R=T/(P_squid*P_chest).
To help us, lets introduce two new variables:

The time a full catch takes us: T_catch, which is set above (default is 8 seconds, from the VODs, a bit longer than a perfect catch)
The Time of casting the rod: T_cast, which is currently statically set to 4 second (a guess from the VODs, taking into account reeling the fish in and casting at max)

We differentiate into four different cases/methods:

Catching every fish, regardless whether it has a chest or is a squid
Canceling when there is no chest after T_{cancel_chest} seconds
Canceling when the fish is not a squid after T_{cancel_fish} seconds
Canceling when the fish is not a squid, or if it is, if there is no chest some time

4.1 No canceling

Every catch process takes the same time, so T=T_cast+T_catch+TTB

4.2 Canceling when no chest

Lets divide these into two parts: When there is a chest and when there is no chest.
If there is a chest, we do the normal catch process, so T_{with_chest}=T_cast+T_catch+TTB
If there is no chest, we cancel after the given time, so T_{no_chest}=T_cast+T_{cancel_chest}+TTB
Applying the chances for each, we result in T=P_chest*T_{with_chest}+(1-P_chest)*T_{no_chest}

4.3 Canceling when not a squid

Lets divide these into two parts: When we hook a squid and when its another fish.
If we hook a squid, we do the normal catch process, so T_squid=T_cast+T_catch+TTB
If we hook another fish, we cancel afzer the given time, so T_other=T_cast+T_{cancel_fish}+TTB
Applying the chances for each, we result in T=P_squid*T_squid+(1-P_squid)*T_other

4.4 Canceling on both cases

Here we divide into four options: The combinations of having a squid or another fish and having a chest or not.
Case squid with chest: Full catch, so T_{with_chest_squid}=T_cast+T_catch+TTB
Case squid and no chest: Cancel after chest time limit: T_{no_chest_squid}=T_cast+T_{cancel_chest}+TTB
Case other fish with chest: Cancel after fish time limit: T_{with_chest_other}=T_cast+T_{cancel_fish}+TTB
Case other fish and no chest: Cancel after the shorter time limit is reached: T_{no_chest_other}=T_cast+min(T_{cancel_fish},T_{cancel_chest})+TTB
This leaves us with the result T= P_squid*P_chest*T_{with_chest_squid}+ P_squid*(1-P_chest)*T_{no_chest_squid}+ (1-P_squid)*P_chest*T_{with_chest_other}+ (1-P_squid)*(1-P_chest)*T_{no_chest_other}

4.5 Calculating the result

As mentioned above the total result is R=T/(P_squid*P_chest).
P_squid*P_chest is the number of throws required to get a squid with a chest.
So multiplying the time per cast, by the casts per chest leaves us with the time per chest, a number we can compare across different techniques. This allows us to minimize IRL time, by keeping this number as small as possible.

Results: