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Legends of Idleon MMO - Rarity Chances for the Arcade

admin
2022-02-25 14:19:59

Arcade Chances

ProbabilitiesEver wondered how rare it is for a Arcade ball to end up in a specific category (after travelling through all these portals)?

Well, I don't know why I did this, but I've calculated it all out. Here are the results:

gray ~63,680% [1 in 2]

bronze ~29,581% [1 in 4]

silver ~5,310% [1 in 19]

gold ~1,110% [1 in 90]

purple ~0,271% [1 in 370]

red ~0,048% [1 in 2082]

blue ~0,001% [1 in 93669]

Rewards to expectOne ball is worth around:

17,7 money - multiplicate that times your lvl

2,48617 Arcade shop money

0,21163 gems

and has a 18,74% chance to get another ball (plus dice rolls!)

This is how rare a specific drop is:

frag [1 in 16]

golden food [1 in 54]

dice roll [1 in 116]

blue candy [1 in 170]

item (silver category) [1 in 325]

red candy [1 in 1300]

balloon (gold category) [1 in 1830]

stone [1 in 4617]

green candy [1 in 6038]

item (purple category) [1 in 6155]

obols (purple category) [1 in 7386]

yellow-gray candy [1 in 18465]

3 balloons (red category) [1 in 26020]

obols (red category) [1 in 26020]

pink candy [1 in 29736]

stamp [1 in 60373]

card [1 in 69385]

hat [1 in 104077]

So out of 100 balls, results may vary greatly, but in general you can expect about:

1770*lvl money

249 Arcade shop money

6 frag

2 golden food

1 blue candy (59% chance)

1 dice roll (86% chance)

21 gems

19 balls

Assumptions / How to calculate

This assumes that each ball has a probability of 1/3 to hit one of the three gray pins at the top left corner and then has a 50-50 chance to move one step downwards either to the left or to the right. Also, when a ball is on the far left playfield, it is assumed to have a 100% chance to move to the right.

This basically lets you determine the probability of a ball landing in a specific category when it starts from the initial point or one of the portals.

But landing in a specific category does not mean that the ball ends up in it - Since a ball has a chance to go through a portal...

So I calculated in steps - first, I took all the balls which land in a category and miss the chance to go through a portal, then I looked at the remaining balls and figured out what would happen to them.

Difficulty arises once you realize that the arcade game can theoretically go on forever - since a ball landing (not ending up!) in the gray category has a chance to go to the bronze portal and has a chance to land in the gray category from there on once again. Luckily it is becoming less and less likely for a ball to go through another portal. During my calculations, I only took balls into acount which end up going through at most 15 portals - which is sufficient in 99,9999999929305% of all cases.

DisclaimerDon't rely on my results - although I checked some of these, I might have made calculation errors.

Source: https://steamcommunity.com/sharedfiles/filedetails/?id=2763182681

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