There is no conspiracy to probability

By BigStupidJellyfish | 2023-September-02

You're 60 runs into farming a doll in the newest event. Out of fairy commands, you disable your Rescue Fairy. Two runs later, the doll drops. Does Rescue Fairy make you less likely to get limited drops?

You decide to save up your bingo tickets until the end of the event, but when you spend them you end up getting a whole bunch of duplicates and don't get many calibration tickets afterwards. Should you have spent them over a larger time interval to "even out" your RNG seed?

Is the capture chance of 2* units something lower than 50%? It feels like you're always failing.

You got a whole bunch of 5-star dolls from the latest anchored production. Does it boost the rates of more than just the target?

You've been losing a whole bunch of coin flips in a digital card game, but after switching your deck you start winning them. Does the game change your luck based on the deck? Does it give you better or worse hands, too, based on the deck? Is it more likely to have you draw a card you only run 1 of?

Are you less likely to get the thing you desire if you really want it?

No. No. No. No. There is no conspiracy behind random chance, and your perception of what's "fair" is probably far off from it.

One question to consider before you go and post your bad luck experience online, insisting that the game's rigged against you: assuming fair odds, how many players would experience similar or worse luck every day/week?

Example: Farming#

Suppose, arbitrarily, a 4-check farming route with a 0.5% chance per check. You're 300 runs in (1200 checks), with no luck. Other people are posting about getting it in 20 runs. Sounds crazy, right? That's about a 0.25% chance of being this unlucky!

But, while it's dying, Girls Frontline is currently maintaining around 10k daily logins. Suppose, approximately, 80% of those are people at least somewhat engaged with the game. 50% of those are playing the event. 50% of those are trying to farm for the dolls. There are 3 dolls to farm. That's 2000 people farming for 3 dolls each, or 6000 total farming sessions. We'd expect about 15 farm sessions to go at least that bad. Sucks to be in that position, but it's not evidence of malfunction.

And beyond that - this isn't the only event to farm dolls in. Between major and minor events, there's somewhere around 10 per year. If you need to farm two dolls per event, that's 20 farming sessions - and at least some of those will be relatively unlucky.

(Although there's no good data on this for GFL, it is technically possible for games to implement a pity system, removing the chance of outliers like this. This exercise assumes there is no such system, as there is no evidence suggesting the existence of one.)

Example: Post-hoc reasoning#

It's new doll batch time. You do hundreds of rolls, aiming to get the 5-star.

Along the way, you get a bunch of G11s. You even check GFDB, but see she's one of the rarer dolls. Did her rate get boosted accidentally?

There's a big problem with that: you're trying to find a pattern based on already observed data. People are very good at seeing patterns, even when there aren't any. While the probability of getting this number of G11s may be low, the probability of getting some doll a "suspicious" number of times is far higher. Form your hypothesis, then test. Don't collect data and then go hunting for a conclusion.

Example: Coalition RNG#

The banner's almost over, and it's time to dump resources for a ringleader. You've got plenty of impulses saved, but only 2-star units are displayed. Many attempts later, you end up with far more failures than captures. Thinking back through the month, you note that you also had terrible luck on 2-stars the whole banner. Was it rigged?

Those attempts are not the whole sample. This (probably) isn't your first SF banner, nor is it your last. If you dump impulses on 10 banners per year, it's not even slightly odd to have luck in the bottom 5% on one of them.

One of my bigger wastes of time, as far as my GFL data collection projects have gone, was the one on 2 and 3-star SF capture rates. The stated rate is accurate, it's easily confirmed with a remotely decent sample size, and yet people will endlessly doubt the system for no other reason than that they "feel" like they've been unlucky.

Conclusion#

The next time you have an (un)fortunate experience with probability, please reconsider immediately going online and claiming tricks. Think about if the event really was as notable, or unlikely, as it seemed. If possible, try designing (and running) some tests to pin things down. Almost no person claiming bad coin flip luck has ever posted a sample size above 20, and no consideration is given to the total game count until that small sample.

Notes#

  • Most of the examples here are from GFL, but they apply to pretty much any game with random elements.
  • It is, of course, technically possible for a developer to add many of the conspiracies described above to a game. But, in most cases (and especially when not talking about scummy mobile games), they haven't. Almost all accusations completely lack foundation and should be given absolutely zero consideration.
  • By comparing the results of a large number of bingo participants to its expected completion time given fair odds, we can conclude its implementation in GFL is somehow rigged. But, given the lack of any demonstrated "strategy" to get better-than-usual results, it's more likely that it just drops the chance of getting new numbers across the board. No action on your end will help.
  • This video may also be interesting.