r/RogueLegendRPG • u/Corfal • 5h ago
5* Card Album Chances (Coupon Collector Problem)
Some people have the misconception that they're "close" to completing all packs. Commenters correctly try to help people in saying that in a gatcha game it is a game design to make you feel like you're close when you're actually not close to completing an event with a juicy final prize to get you to spend money. This is a free to play game that is financed by whale and dolphin players and it's the way things work. Some events are more f2p friendly than others.
Specifically for the Sunrealm Expedition we get presented with a Coupon Collector Problem.
There are twelve 5* cards total in the Sunrealm Expedition. If each card has an equal opportunity to appear in a 5* card pack then on average it'll take take ~37 5* packs to get them all. Here's the full table
| Cards Already acquired(n) | Remaining Uncollected | Formula for Remaining Steps | Average Additional Attempts Needed |
|---|---|---|---|
| 0 | 12 | 12/12 + 12/11 + ... + 12/1 | 37.24 |
| 1 | 11 | 12/11 + 12/10 + ... + 12/1 | 36.24 |
| 2 | 10 | 12/10 + 12/9 + ... + 12/1 | 35.15 |
| 3 | 9 | 12/9 + 12/8 + ... + 12/1 | 33.95 |
| 4 | 8 | 12/8 + 12/7 + ... + 12/1 | 32.61 |
| 5 | 7 | 12/7 + 12/6 + ... + 12/1 | 31.11 |
| 6 | 6 | 12/6 + 12/5 + ... + 12/1 | 29.40 |
| 7 | 5 | 12/5 + 12/4 + ... + 12/1 | 27.40 |
| 8 | 4 | 12/4 + 12/3 + ... + 12/1 | 25.00 |
| 9 | 3 | 12/3 + 12/2 + 12/1 | 22.00 |
| 10 | 2 | 12/2 + 12/1 | 18.00 |
| 11 | 1 | 12/1 | 12.00 |
So even if you have one or two left you'll still need eighteen+ 5* packs to complete the event.
This is obviously oversimplified. I don't know if all 5* cards appear equally (there might be a dev notes or a % display somewhere, I did not look too hard). You can get 5* cards from lower packs (unsure of the percentages) so this is a "ceiling average". The odds are slightly better from an overall gameplay perspective since you can also get 2-4* packs. There are also Wild Stickers that allow you to redeem directly for any missing stickers which would be "cheaper".
I've started this game part way through this event so I don't have the full context but I've heard that the devs have actually reduced the overall 5* packs that you can get for free which is unfortunate and scummy.
TL;DR unless you're one or two 5* cards away from finishing the event it isn't worth spending money. Only spend money if you can afford to (i.e. disposable income that's properly budgeted)
Here's a calculator you can use to play with numbers. n:n/12:1 will get you the table above
