Talk:Crates

Usage question
Do Sonar Potions and Fishing Potions (or boosting fishing power) help find these? I want to know if I should combine all three fishing-related buffs or not. --Macks2008 (talk) 14:29, 29 January 2015‎ (UTC)


 * I'm not sure how old your I haven't noticed any increased chance to catch crates using any potion besides the Crate Potion. However, when using the Sonar Potion, you can ignore non-crate bites in order to save bait. The Fishing Potion (or increasing fishing power) will also decrease the rate at which your bait is consumed. --ValornTheRed (talk) 19:10, 4 July 2015 (UTC)

"Portal" Reference
The page as quoted, "It's improbable to be a reference, but the crate's sprite resembles Weighted Storage Cubes from Portal franchise." However I feel this is a bit misleading and very unlikely to be reference nor does it assist in the article in any form. They're crates, box shaped by nature, and the sprites do not, to me, resemble anything close to the portal cubes outside of minor details of them being box shaped, with a few styles being similar. Should this information be left in? I have nothing against the trivia bit afterwards indicating it to be used for adventure maps, etc. Kalbintion (talk) 02:20, 21 July 2015 (UTC)


 * A lot of trivia is added by anonymous users, and is often questionable. You won't get into any trouble for removing nonsensical trivia; go ahead. As for the bit about its application in maps, a lot of things can be used creatively in maps. Unless there were to be a guide page for making maps, that info doesn't really belong on the wiki. –KM100 (talk) 02:27, 21 July 2015 (UTC)

Merging all the crates
i feel as if the crates should be merged into 1 page, this one, Crates, the page may have the loading features of the fishing page, but it may fit.

Luigirox901 (talk) 00:32, 26 November 2015 (UTC)

Probability
The sentence reads: E.g with a Fishing Power of 100 in a Corrupted Biome the probabilities would be: Golden Crate: 6,57%; Corrupt Crate: 8,90%; Iron Crate: 28,37%; Wooden Crate: 56,16% Speaking for those who never studied probability (or have forgotten because they never needed it), nor looked at the code... what in the world does 6,57% mean? At first I thought that comma was meant to be a decimal. If it's not, can we explain this in a way that a 12-grader would understand? -- Ferretwings (talk) 16:12, 19 July 2016 (UTC)


 * Sorry, I just confused both signs, i have corrected it. Flisch42 (talk) 18:25, 19 July 2016 (UTC)


 * Oh good. :) I was feeling really dumb, trying to figure it out. Now I fee confident again about my math skills, lol! Thanks for fixing it. :) -- Ferretwings (talk) 19:17, 19 July 2016 (UTC)

crate probability wrong?
I was looking for source online and found the one by Pryaxis on github. Looking at projectile.fishingcheck the probability for crates seem to be different there. If this source is accurate the information on this page is wrong, can anyone confirm the accuracy of this source?

DJIKhaos (talk) 23:05, 25 July 2019 (UTC)


 * I have taken a look, too, and luckily, crates are handled near the top of the function, so it is comparatively easy to determine the chances (assuming a fishing power of 100; in any of the special biomes, taking Corruption as an example here):
 * Golden Crate: $$\frac{1}{10}$$ $$* \biggl( \Bigl(\frac{2}{45} * \frac{1}{45}\Bigr)$$ $$ + \Bigl(\frac{2}{45} * \frac{44}{45}\Bigr)$$ $$ + \Bigl(\frac{43}{45} * \frac{1}{45}\Bigr)$$ $$ \biggr) = \frac{133}{20250} \approx 6.5679 \times 10^{-3} \approx 0.657%$$


 * Corrupt Crate (or any other biome crate): $$\frac{1}{10}$$ $$* \Bigl(\frac{43}{45} * \frac{44}{45}\Bigr)$$ $$ * \frac{2}{21}$$ $$ \approx 8.8983 \times 10^{-3} \approx 0.898%$$


 * Iron Crate: $$\frac{1}{10}$$ $$* \Bigl(\frac{43}{45} * \frac{44}{45}\Bigr)$$ $$ * \frac{19}{21}$$ $$ * \frac{1}{3}$$ $$ \approx 0.028178 \approx 2.818%$$


 * Wooden Crate: $$\frac{1}{10}$$ $$* \Bigl(\frac{43}{45} * \frac{44}{45}\Bigr)$$ $$ * \frac{19}{21}$$ $$ * \frac{2}{3}$$ $$ \approx 0.056356 \approx 5.636%$$
 * (yes, it is altered later on, but that does not matter since we assume a lake of ≥300 tiles)), so in our example 100.

\begin{align} P(flag6) & = \frac{1}{num17} \qquad\qquad |\ num17 = 150*15/num6 \\ & = \frac{1}{150*15/num6} \qquad\qquad |\ num6 = 100 \\ & = \frac{1}{150*15/100} \\ & = \frac{1}{22.5} \\ P(flag6) & = \frac{2}{45} \end{align} $$
 * I don't see any variable named maxValue4 in FishingCheck, so I'm not sure what you're referring to there.
 * --Rye Greenwood (talk) 23:49, 4 December 2019 (UTC)


 * The line I'd like to see then is the one where num17 is calculated. Can you please copy paste that one line.
 * DJIKhaos (talk) 23:53, 4 December 2019 (UTC)


 * After reading your first message again, I realized we're using different decompilations of the game... So no surprise the variable names are different.
 * num17 is calculated like this:
 * --Rye Greenwood (talk) 00:33, 5 December 2019 (UTC)


 * notice the type of num17, we're dealing with integer division here.
 * DJIKhaos (talk) 00:37, 5 December 2019 (UTC)

Oh, you're completely right! Apologies! Let me update the calculations then:

Golden Crate: $$\frac{1}{10}* \biggl( \Bigl(\frac{1}{22} * \frac{1}{45}\Bigr) + \Bigl(\frac{1}{22} * \frac{44}{45}\Bigr) + \Bigl(\frac{21}{22} * \frac{1}{45}\Bigr) \biggr) = \frac{1}{150} \approx 6.6667 \times 10^{-3} \approx 0.667%$$

Corrupt Crate (or any other biome crate): $$\frac{1}{10}* \Bigl(\frac{21}{22} * \frac{44}{45}\Bigr) * \frac{1}{10} = \frac{7}{750} \approx 9.3333 \times 10^{-3} \approx 0.933%$$

Iron Crate: $$\frac{1}{10}* \Bigl(\frac{21}{22} * \frac{44}{45}\Bigr) * \frac{9}{10} * \frac{1}{3} = \frac{7}{250} = 0.028 = 2.8%$$

Wooden Crate: $$\frac{1}{10}* \Bigl(\frac{21}{22} * \frac{44}{45}\Bigr) * \frac{9}{10} * \frac{2}{3} = \frac{7}{125} = 0.056 = 5.6%$$

Thank you very much! I will go ahead and update the page.

--Rye Greenwood (talk) 01:05, 5 December 2019 (UTC)


 * No problem. In C# int/int is generally integer division. Also if you think it's relevant information for either here or bait (or fishing) master bait sustain with crate potion, tackle box and high test fishing line starts at 76 fishing power, without tackle box it's 87, without high test fishing line it's 98 and without either it's 119. without crate potion isn't that interesting as it's 251 with both.
 * DJIKhaos (talk) 02:04, 5 December 2019 (UTC)


 * to clarify that's assuming nothing is being skipped with a sonar potion
 * DJIKhaos (talk) 02:14, 5 December 2019 (UTC)


 * Hmm. Am I right in getting the sense that a function of crate probabilities against fishing power would be almost impossible to write out? --MentalMouse42 (talk) 16:05, 5 December 2019 (UTC)

Great idea! Actually, that's not impossible at all, luckily! It just gets a little long:

($$fp$$: fishing power)

Starting with the chances of the flags; they can be described as follows:

flag4: $$\Bigl( \frac{1}{\lfloor 300/fp \rfloor} \leq \frac{1}{3} \Bigr)$$

!flag4: $$\Bigl(1 - \frac{1}{\lfloor 300/fp \rfloor} \geq \frac{2}{3} \Bigr)$$

flag5: $$\Bigl( \frac{1}{\lfloor 1050/fp \rfloor} \leq \frac{1}{4} \Bigr)$$

!flag5: $$\Bigl(1 - \frac{1}{\lfloor 1050/fp \rfloor} \geq \frac{3}{4} \Bigr)$$

flag6: $$\Bigl( \frac{1}{\lfloor 2250/fp \rfloor} \leq \frac{1}{5} \Bigr)$$

!flag6: $$\Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor} \geq \frac{4}{5} \Bigr)$$

flag7: $$\Bigl( \frac{1}{\lfloor 4500/fp \rfloor} \leq \frac{1}{6} \Bigr)$$

!flag7: $$\Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor} \geq \frac{5}{6} \Bigr)$$

Inserting that into the formulas of the crate chances:

Golden Crate: $$P(gc) = \frac{1}{10}* \biggl( \Bigl(\Bigl( \frac{1}{\lfloor 2250/fp \rfloor} \leq \frac{1}{5} \Bigr) * \Bigl( \frac{1}{\lfloor 4500/fp \rfloor} \leq \frac{1}{6} \Bigr)\Bigr) + \Bigl(\Bigl( \frac{1}{\lfloor 2250/fp \rfloor} \leq \frac{1}{5} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor} \geq \frac{5}{6} \Bigr)\Bigr) + \Bigl(\Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor} \geq \frac{4}{5} \Bigr) * \Bigl( \frac{1}{\lfloor 4500/fp \rfloor} \leq \frac{1}{6} \Bigr)\Bigr) \biggr)$$

Biome Crate: $$P(bc) = \frac{1}{10}* \Bigl(\Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor} \geq \frac{4}{5} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor} \geq \frac{5}{6} \Bigr)\Bigr) * \Bigl( \frac{1}{\lfloor 1050/fp \rfloor} \leq \frac{1}{4} \Bigr)$$

Iron Crate (if fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(ic) = \frac{1}{10}* \Bigl(\Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor} \geq \frac{4}{5} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor} \geq \frac{5}{6} \Bigr)\Bigr) * \Bigl(1 - \frac{1}{\lfloor 1050/fp \rfloor} \geq \frac{3}{4} \Bigr) * \Bigl(\frac{1}{\lfloor 300/fp \rfloor} \leq \frac{1}{3} \Bigr)$$

Iron Crate (if not fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(ic) = \frac{1}{10}* \Bigl(\Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor} \geq \frac{4}{5} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor} \geq \frac{5}{6} \Bigr)\Bigr) * \Bigl(\frac{1}{\lfloor 300/fp \rfloor} \leq \frac{1}{3} \Bigr)$$

Wooden Crate (if fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(wc) = \frac{1}{10}* \Bigl(\Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor} \geq \frac{4}{5} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor} \geq \frac{5}{6} \Bigr)\Bigr) * \Bigl(1 - \frac{1}{\lfloor 1050/fp \rfloor} \geq \frac{3}{4} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 300/fp \rfloor} \geq \frac{2}{3} \Bigr)$$

Wooden Crate (if not fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(wc) = \frac{1}{10}* \Bigl(\Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor} \geq \frac{4}{5} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor} \geq \frac{5}{6} \Bigr)\Bigr) * \Bigl(1 - \frac{1}{\lfloor 300/fp \rfloor} \geq \frac{2}{3} \Bigr)$$

Please excuse the mathematically incorrect notation with these inequations in the middle, but they're there to show that a case differentiation is necessary. Depending on the fishing power, different formulas apply.

For the final functions, it is necessary to assert we are fishing in a lake of ≥300 tiles (it just gets too long if we want to make that variable, too) and have a fishing power >0, of course.

Golden Crate: $$P(gc) = \begin{cases} golden_1(fp), & \text{if } fp \leq 450 \\ golden_2(fp), & \text{if } 450 < fp \leq 750 \\ golden_3(fp), & \text{if } 750 < fp \end{cases} $$

$$ golden_1(fp) = \frac{1}{10}* \biggl( \frac{1}{\lfloor 2250/fp \rfloor} * \frac{1}{\lfloor 4500/fp \rfloor} + \frac{1}{\lfloor 2250/fp \rfloor} * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) + \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \frac{1}{\lfloor 4500/fp \rfloor}\biggr) $$

$$ golden_2(fp) = \frac{1}{10}* \biggl( \frac{1}{5} * \frac{1}{\lfloor 4500/fp \rfloor} + \frac{1}{5} * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) + \Bigl(1 - \frac{1}{5}\Bigr) * \frac{1}{\lfloor 4500/fp \rfloor}\biggr) $$

$$ golden_3(fp) = \frac{1}{10}* \biggl( \frac{1}{5} * \frac{1}{6} + \frac{1}{5} * \Bigl(1 - \frac{1}{6}\Bigr) + \Bigl(1 - \frac{1}{5}\Bigr) * \frac{1}{6}\biggr) $$

Biome Crate: $$P(bc) = \begin{cases} biome_1(fp), & \text{if } fp \leq 262 \\ biome_2(fp), & \text{if } 263 \leq fp \leq 450 \\ biome_3(fp), & \text{if } 450 < fp \leq 750 \\ biome_4(fp), & \text{if } 750 < fp \end{cases} $$

$$ biome_1(fp) = \frac{1}{10}* \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \frac{1}{\lfloor 1050/fp \rfloor} $$

$$ biome_2(fp) = \frac{1}{10}* \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \frac{1}{4} $$

$$ biome_3(fp) = \frac{1}{10}* \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \frac{1}{4} $$

$$ biome_4(fp) = \frac{1}{10}* \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{6}\Bigr) * \frac{1}{4} $$

Iron Crate (if fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(ic_1) = \begin{cases} iron_1(fp), & \text{if } fp \leq 100 \\ iron_2(fp), & \text{if } 100 < fp \leq 262 \\ iron_3(fp), & \text{if } 263 \leq fp \leq 450 \\ iron_4(fp), & \text{if } 450 < fp \leq 750 \\ iron_5(fp), & \text{if } 750 < fp \end{cases} $$

$$ iron_1(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 1050/fp \rfloor} \Bigr) * \frac{1}{\lfloor 300/fp \rfloor} $$

$$ iron_2(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 1050/fp \rfloor} \Bigr) * \frac{1}{3} $$

$$ iron_3(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{4} \Bigr) * \frac{1}{3} $$

$$ iron_4(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{4} \Bigr) * \frac{1}{3} $$

$$ iron_5(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{6}\Bigr) * \Bigl(1 - \frac{1}{4} \Bigr) * \frac{1}{3} $$

Iron Crate (if not fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(ic_2) = \begin{cases} iron_1(fp), & \text{if } fp \leq 100 \\ iron_2(fp), & \text{if } 100 < fp \leq 262 \\ iron_3(fp), & \text{if } 263 \leq fp \leq 450 \\ iron_4(fp), & \text{if } 450 < fp \leq 750 \\ iron_5(fp), & \text{if } 750 < fp \end{cases} $$

$$ iron_1(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \frac{1}{\lfloor 300/fp \rfloor} $$

$$ iron_2(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \frac{1}{3} $$

$$ iron_3(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \frac{1}{3} $$

$$ iron_4(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \frac{1}{3} $$

$$ iron_5(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{6}\Bigr) * \frac{1}{3} $$

Wooden Crate (if fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(wc_1) = \begin{cases} wooden_1(fp), & \text{if } fp \leq 100 \\ wooden_2(fp), & \text{if } 100 < fp \leq 262 \\ wooden_3(fp), & \text{if } 263 \leq fp \leq 450 \\ wooden_4(fp), & \text{if } 450 < fp \leq 750 \\ wooden_5(fp), & \text{if } 750 < fp \end{cases} $$

$$ wooden_1(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 1050/fp \rfloor} \Bigr) * \Bigl(1 - \frac{1}{\lfloor 300/fp \rfloor}\Bigr) $$

$$ wooden_2(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 1050/fp \rfloor} \Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

$$ wooden_3(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{4} \Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

$$ wooden_4(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{4} \Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

$$ wooden_5(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{6}\Bigr) * \Bigl(1 - \frac{1}{4} \Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

Wooden Crate (if not fishing in Corruption, Crimson, Hallow, Jungle, Dungeon, or sky level): $$P(wc_2) = \begin{cases} wooden_1(fp), & \text{if } fp \leq 100 \\ wooden_2(fp), & \text{if } 100 < fp \leq 262 \\ wooden_3(fp), & \text{if } 263 \leq fp \leq 450 \\ wooden_4(fp), & \text{if } 450 < fp \leq 750 \\ wooden_5(fp), & \text{if } 750 < fp \end{cases} $$

$$ wooden_1(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 300/fp \rfloor}\Bigr) $$

$$ wooden_2(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

$$ wooden_3(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{\lfloor 2250/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

$$ wooden_4(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{\lfloor 4500/fp \rfloor}\Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

$$ wooden_5(fp) = \frac{1}{10} * \Bigl(1 - \frac{1}{5}\Bigr) * \Bigl(1 - \frac{1}{6}\Bigr) * \Bigl(1 - \frac{1}{3}\Bigr) $$

That's it! With these functions, it is possible to calculate the different crate catch chances for any given fishing power. If the Crate Potion buff is active, simply change the $$\frac{1}{10}$$ at the beginning of every function to $$\frac{1}{5}$$.

Plotting these functions revealed some very interesting mechanics (here are just some examples I found particularly surprising):
 * With a fishing power of 1, the chance to catch a Wooden Crate is 10% and to catch all other crate types nearly 0%.
 * As fishing power increases, the chance for Golden Crates increases steadily up to the maximum of 750 (after which all chances stagnate; you can see in the functions that they're just constant at that point). The chance for Wooden Crates decreases steadily. However, the chances for the other two types fluctuate quite a bit.
 * The highest chance to catch an Iron Crate is with 76 fishing power, to catch a Wooden Crate is with 1 fishing power, to catch a Biome Crate is with 211 fishing power, and to catch a Golden Crate is with >750 fishing power (within the bounds of possibly attainable fishing power that would be 282).

I really recommend you to take a look at these functions, too; the integer division has an interesting effect. Here are the functions in a form that dynamic geometry applications should accept (well, at least GeoGebra does):

golden(x) = 1 / 10 (1 / floor(2250 / x) 1 / floor(4500 / x) + 1 / floor(2250 / x) (1 - 1 / floor(4500 / x)) + (1 - 1 / floor(2250 / x)) 1 / floor(4500 / x)) golden1(x) = golden(x), 0 < x ≤ 100 golden2(x) = golden(x), 100 ≤ x ≤ 262 golden3(x) = golden(x), 263 ≤ x ≤ 450 golden4(x) = 1 / 10 (1 / 5 * 1 / floor(4500 / x) + 1 / 5 (1 - 1 / floor(4500 / x)) + (1 - 1 / 5) * 1 / floor(4500 / x)), 450 ≤ x ≤ 750 golden5(x) = 1 / 10 (1 / 5 * 1 / 6 + 1 / 5 (1 - 1 / 6) + (1 - 1 / 5) * 1 / 6), 750 ≤ x

biome(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) 1 / floor(1050 / x) biome1(x) = biome(x), 0 < x ≤ 100 biome2(x) = biome(x), 100 ≤ x ≤ 262 biome3(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) 1 / 4, 263 ≤ x ≤ 450 biome4(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / floor(4500 / x)) 1 / 4, 450 ≤ x ≤ 750 biome5(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / 6) 1 / 4, 750 ≤ x

iron(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / floor(1050 / x)) 1 / floor(300 / x) iron1(x) = iron(x), 0 < x ≤ 100 iron2(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / floor(1050 / x)) 1 / 3, 100 ≤ x ≤ 262 iron3(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / 4) 1 / 3, 263 ≤ x ≤ 450 iron4(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / floor(4500 / x)) (1 - 1 / 4) 1 / 3, 450 ≤ x ≤ 750 iron5(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / 6) (1 - 1 / 4) 1 / 3, 750 ≤ x

ironb(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) 1 / floor(300 / x) ironb1 (x) = ironb(x) = 0 < x ≤ 100 ironb2(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) 1 / 3, 100 ≤ x ≤ 262 ironb3(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) 1 / 3), 263 ≤ x ≤ 450 ironb4(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / floor(4500 / x)) 1 / 3, 450 ≤ x ≤ 750 ironb5(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / 6) 1 / 3, 750 ≤ x

wooden(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / floor(1050 / x)) (1 - 1 / floor(300 / x)) wooden1(x) = wooden(x), 0 < x ≤ 100 wooden2(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / floor(1050 / x)) (1 - 1 / 3), 100 ≤ x ≤ 262 wooden3(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / 4) (1 - 1 / 3), 263 ≤ x ≤ 450 wooden4(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / floor(4500 / x)) (1 - 1 / 4) (1 - 1 / 3), 450 ≤ x ≤ 750 wooden5(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / 6) (1 - 1 / 4) (1 - 1 / 3), 750 ≤ x

woodenb(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / floor(300 / x)) woodenb1(x) = woodenb(x), 0 < x ≤ 100 woodenb2(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / 3), 100 ≤ x ≤ 262 woodenb3(x) = 1 / 10 (1 - 1 / floor(2250 / x)) (1 - 1 / floor(4500 / x)) (1 - 1 / 3), 263 ≤ x ≤ 450 woodenb4(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / floor(4500 / x)) (1 - 1 / 3), 450 ≤ x ≤ 750 woodenb5(x) = 1 / 10 (1 - 1 / 5) (1 - 1 / 6) (1 - 1 / 3), 750 ≤ x

(Hide the base functions; the ones without a number at the end of their name. They do not represent accurate probabilities.)

Please let me know if something is unclear or I've made a mistake.

--Rye Greenwood (talk) 02:05, 6 December 2019 (UTC)


 * You took "nearly impossible" as a challenge, didn't you? "It just gets a little long", oy gevalt!  ;-)
 * Initial thoughts:
 * At least some of those groups of equations look like they're segments of a line; they might be easier to grasp if they were in a more switch/case like format.
 * The flags you describe as "chances", but it's not clear if/where randomness appears or what it applies to. Also simplifying the inequalities (e.g., flag4: fp/100 ≤ 1) would make them much easier to read.  (I think we can take fp > 0 as a prerequisite.)
 * For display to normal readers (that is, the topic page), I suspect the graphs themselves would be much more understandable and practical than the series of equations, especially if integer division is putting kinks in the lines. Offhand, ISTM that the way to go would be separate graphs for the "biome crates" and "no biome crates" cases, each with a stacked plot showing the types accumulating vertically as fishing power increases horizontally.
 * * I might have more thoughts later, right now I'm barely through my morning coffee.
 * * Thanks for your efforts!
 * --MentalMouse42 (talk) 12:40, 6 December 2019 (UTC)