Luring Collectors is dead, long live Luring Bronze

Introduction

Sunkens have a pity system now, so we need to figure out a new best fishing strategy to be prepared for the release of AO. Actually, no, the release is a long way ahead and fishing is boring, but I’m also bored so I’ll make a long winded post pretending it matters.

Methodology

We need a way to find the average number of catches required to catch a sunken item. One of the ways to do that is the following:
Suppose you’re fishing for sunkens, every catch has a 1/2000 chance to be a sunken, and you stop fishing once you catch one. We then know that there is a 1/2000 chance that you stop fishing after every catch, in case you caught a sunken, but you would have only gotten so far if you haven’t caught one yet.
So, the probability of stopping after a random catch is the probability of catching a sunken, in this case 1/2000, multiplied by the probability that you haven’t caught one in any of the previous tries. If we then sum all possible numbers of tries, each multiplied by the probability that you caught a sunken on that specific try (that is the probability of catching a sunken multiplied by the probability of not catching one in all the previous tries, yada yada, you understand this now), we would get the average number of tries needed to catch a sunken. Let’s formalize that a bit.

Let the probability of catching a sunken be 1/x, the probability of not catching one would then be 1 - 1/x, since you either get one or you don’t, and the probability of 1 means something is sure to happen.
If the probability for an event to happen is p, then the probability of it happening twice in a row is p*p, and for it to happen n times in a row would then be pn. The probability of not get a sunken n times in a row would then be (1 - 1/x)n.
The probability to catch a sunken in exactly n tries would therefore be 1/x * (1 - 1/x)n-1.
The average number of catches after which you would get a sunken would then be the limit as n approaches infinity of the following series:

sum1

If you are interested, you could prove that this is actually equal to x, but I’m not going to do that since it’s not needed and I’d rather l̷̙̓ê̶̛̖å̵̮͠v̶̢͗ê̸̗̇ ̵̢͋ï̶̗͘†̵͈͂ ̶̥̔å̴̩̂§̴̝̌ ̴̈͜å̴̞͝ñ̴̬̏ ̵̯́ê̴͉̾x̶̯̚ê̶̪͆ṙ̷̬¢̴̨̎ï̶̻̉§̷̺̈́ê̸̯͝ ̵͓̃†̶͕̊ð̸̢̕ ̶͔̑†̵͖̓ẖ̸͝ê̸͘͜ ̴̹͐r̶͍̉ê̵̩̑å̷͓̚Ð̶̹̓ề̴̡r̷̹̎r̴̨̡̛̩͉̹̠̦͕̹̻̄̂́̄̈́́̓͛́.

In our case, we’re going to use this formula up to 2999, since when you reach 3000 tries you would get a sunken automatically. The result we need is this one:

sum2

I made this here program to calculate that for me, and do it in respect to the item chance stat of a fishing rod:

#include <stdio.h>

int main(int argc, char *argv[])
{
    long double ItemChanceStat[5] = {0.8L, 1.0L, 1.05L, 1.25L, 1.5L};

    for(int i = 0; i < 5; i++)
    {
        long double EndChance = (1.0L / 2000.0L) * ItemChanceStat[i];
        long double ArrivalChance = 1.0L;
        long double WeightedSum = 0.0L;

        for(int j = 1; j < 3000; j++)
        {
            WeightedSum += ArrivalChance * EndChance * j;
            ArrivalChance *= (1.0L - EndChance);
        }

        WeightedSum += ArrivalChance * 3000.0L;

        printf("Item chance stat: %Lf; Average catches for sunken: %Lf; Average sunkens per catch: %Lf\n", ItemChanceStat[i], WeightedSum, (1.0L / WeightedSum));
    }

    return 0;
}

After getting that, we just need to take into account the time it would take to reach this number of tries and get your sweet, sweet, sea salted sunken.
We simply multiply a fishing rods Lure stat with the Average sunkens per catch we got, se we get a score measured in sunkens/time, that we can also multiply by 1000 just to make it look better and since it’s relative anyways.

Results

Item chance Average catches for sunken Average sunkens per catch
0.8 1747.195213 0.000572
1.0 1553.907052 0.000644
1.05 1510.624846 0.000662
1.25 1354.775841 0.000738
1.5 1192.919617 0.000838
Fishing Rod Item chance Lure Sunken over time score
Magnetic Collectors 1.5 0.8 0.6704
Luring Collectors 1.25 1.05 0.7749
Magnetic Bronze 1.05 1.25 0.8275
Luring Bronze 0.8 1.5 0.858

Conclusion

Use a Luring Bronze Rod.

25 Likes

wtf
math :cc

4 Likes

Big Brain

3 Likes

why

I wonder how fast it’ll take to go through 3k bait with luring bronze rod

Stay in school kids, it makes you better at games

this is why you’re a mod.

holy beluga, my brain is almost at it max storage capacity after reading this.

Ew, where?

Because

Waiting for @Level to destroy this topic

2 Likes

Methodology on probability is mostly correct but instead of doing whatever the fuck he’s doing, do this to find average number of attempts before first sunken on a calculator because it’s 10x simpler to follow

Item chance Average bait used for sunken Simple formula
0.8 1733 log(0.5)/log(1-(.0005*.8))
1.0 1386 log(0.5)/log(1-(.0005))
1.05 1320 log(0.5)/log(1-(.0005*1.05))
1.25 1109 log(0.5)/log(1-(.0005*1.25))
1.5 924 log(0.5)/log(1-(.0005*1.5))

This is rounded to the nearest integer

He likely messed up somewhere in logarithms that I’m too lazy to correct, use a calculator kids.

And luring collector’s is still statistically the best

damn i think i lost 3 braincells and im already at 1

I just realized he’s wrong by his own calculations as well (which are higher than they should be, if we account for the sunken pity, the numbers should actually be lower than mine)

Item chance Average bait used for sunken Simple formula
0.8 1416 log(0.5)/log((1-(1/2000+22.3046%)*0.8))
1.0 1133 log(0.5)/log((1-(1/2000+22.3046%))*1)
1.05 1079 log(0.5)/log((1-(1/2000+22.3046%)*1.05))
1.25 906 log(0.5)/log((1-(1/2000+22.3046%)*1.25))
1.5 755 log(0.5)/log((1-(1/2000+22.3046%)*1.5))

These are rounded to the nearest integer again

Also these are the actual rates of each rod based on a different approximate value but just know placement is universal

Note: THIS IS BASED ON BAIT USED, NOT FISH CAUGHT, for fish caught luring bronze would be best but for a different reason

Fishing Rod Item chance Lure Sunken over time score
Magnetic Collectors 1.5 0.8 1.2
Luring Collectors 1.25 1.05 1.3
Magnetic Bronze 1.05 1.25 1.3
Luring Bronze 0.8 1.5 1.2

Such stark contrast, and yes Luring Collector’s is better because it uses less bait and is quicker because fishing speed doesn’t include reeling in and re-casting which would put its score at ~1.25

At the end of the day, rod is irrelevant

1 Like

wow how long did it take for you to calculate all of this

Or you can just fish like a normal person by praying

1 Like

2 seconds for the scoring system, it’s literally just chance*lure also ignore what I said earlier, luring collector’s are best no matter what after thinking for it for 2 seconds

*After typing this I realized you’re probs not talking to me but dnc)

well you were right

My luck has heavily failed me countless times when playing roblox rpg games. I think I’m fine getting rare items through guaranteed pity chance instead of relying on statistics.

why do y’all have to use math to calculate the chance of getting a lego item in a lego game on roblox (nice job tho)

because the likelihood of obtaining said lego item on said lego game requires math because percentage is math which is what is needed to calculate the chance of getting said lego item