Armoecyone the Vanmand

Travel: None
Status: UFT

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The Max Amount of Cave Attempts Possible
Updated version!

Want to find out the probability of you getting a monthly in a day? Keep reading! 😉

Let's start with assuming that you immediately start your Cave attempts at 12:00:00 ECT. Let's also assume that it takes 1 second to view an egg, another second to return to the Cave, 5 seconds to name an egg (assuming you have names ready), and 1 second to confirm a name. That means, in total, to steal a new egg you'd take 8 seconds. Therefore, it is most efficient to view each egg first, and while the timer is ticking for a new attempt, you can steal an egg.

Since you have 10 Cave attempts at the beginning, you have a greater chance of finding a monthly than if you had 1 attempt every 10 or so minutes. And since each new attempt's timer is 1 minute longer than the last, our calculations will be a little bit more tricky.

Before we begin, I'll state that there are 58 possible creatures to get in the Cave, 2 being monthlies. 65 possible creatures if it is Creature Release Week (CRW), and 59 possible creatures if there is a seasonal creature. Therefore, there is a 1/29 (or a 3%) chance of getting a monthly normally on your first try. A 6/65 (or a 9%) chance of getting a monthly/CRW on your first chance. And a 3/59 (or a 5%) chance of getting a monthly/seasonal on your first attempt.

So, your chances of getting one monthly/CRW in your first 10 Cave attempts can be found by squaring the denominator (in this cause 65), and changing the numerator to the amount of Cave attempts. Doing this gives you the wonderful chance of 2/845, or a 1/2% chance of getting a monthly/CRW. Not very appealing is it? No wonder people think they're so rare!

Now, to maximize our chances of getting that CRW that you've been dreaming about, we'll have to calculate the maximum amount of attempts you can make. Your first 10 Cave attempts (assuming you followed the trick up above) would take 20 seconds, so it would be currently 12:00:20 ECT. Then you'd have to wait 11 minutes before the next attempt, which take you 2 seconds. It would be currently 12:11:22. Then you would continue, but you'd have to wait a minute longer each time. The first five times after 11:11:22 are these:

12 minutes wait: 12:22:24
13 minute wait: 12:35:26
14 minute wait: 12:49:28
15 minute wait: 1:04:30
16 minute wait: 1:20:32

See a pattern? Obviously we're not going type out every single time, so how do we calculate this? To do this we'll have to use a lot of estimation and guesswork. First, we need to know how many minutes are in a day. 1,440. So, when calculating, we need to keep this number in mind.
I start by adding up the numbers between 11 and 20. 155. I then add up the numbers between 21 and 30. 255. Interesting! Let's test the numbers between 31 and 40. 355. Amazing! We now know the pattern.

So, I began by adding up these numbers to see if I can reach just below 1,440 to account for the seconds. I got the number 1,220 by combining numbers from ten to fifty. That's 45 attempts! Each attempt would take 2 seconds, making the attempts come to a total of 90 seconds, or 1 minute and 50 seconds.That comes to a grand total of 1,221 minutes, that's 219 minutes off!

Luckily, I'm not tired yet. I still have the fire inside of me! Are you tired? There has been a lot of math, I hope you're still good to go. Let's add another 4 attempts, shall we? That adds 210 minutes (wow, right?). Adding the 8 seconds of the attempts and the 20 seconds for the first 10 Cave attempts, we come to a total of 1,432 minutes and 18 seconds. That's 8 minutes away from the end of the day, which leaves room for mess-ups and stealing creatures.

Now that we've figured out that the max amount of attempts you can do is 59, we can figure out the probability. First, we have to find 65 to the power of 59, and make that our denominator. Then we make the numerator 59 and find our probability.

I put 65 to the power of 59 in the IPhone calculator, and the number was so big, this is what I got: 9.15984325348e106. If someone is able to calculate the percentage, I would be eternally grateful. And for the rest of you... basically, it's still pretty hard to find a monthly/CRW, even with 59 attempts. xD So just try your hardest!

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This mathy thing was so much fun to do! 😃 It would be really helpful if anyone could tell me what I did wrong and how I could improve. 😊 It would also be nice if you could give me a suggestion on what mathy thing to do next. ^-^