I play an online game and after each battle a chest is awarded. There are 4 different “levels” of chest you can win. The frequency that each level is awarded is out of whack to their worth but I want someone to double check my math before contacting the developers in case I’ve made some stupid logic error setting up the problem. I figure the worth of the chest is proportional to its cost. Here is what it costs to open each chest:
Green Chest = 4 keys
Blue Chest = 12 keys
Purple Chest = 16 keys
Yellow Chest = 32 keys
(you can also open the chests with time or gold, but the proportions are the same)
I get 58.4% Green, 19.7% Blue, 14.6% Purple, 7.3% Yellow.
Did I do that right? It’s been 50 years since i had to do 8th grade math.
I’m not really sure what you’re asking. But I can confirm that the result of multiplying the number of keys with the percentage is roughly the same for all four colors. So if the number of keys represents the value and the percentage represents the frequency, those numbers are consistent with value being inversely proportional to frequency, which seems to be how you’re saying it should work.
Yeah, that’s what I’m looking for…it was worded poorly. Basically what percentage of time you should get each chest, or the number of times you get each chest in a sample size of 100, 200 etc (which is just the percent times the sample size)
If they’re awarded for in-game achievements or just because, the idea their frequency & cost to open are connected somehow makes no sense. Or at least they might be connected, but don’t have to be.
What goodies are in a chest? I’d expect the price to open a chest ought to be proportional to the value of the goodies inside. Which again ought to have little connection to their frequency.
If some chests have greater rewards versus price, then I’d expect those bargains to be both rarer & more expensive.
I think your thought matrix about this game is missing a couple factors.
You win the opportunity to open the chest. You are give a set number of keys each day and can use some of the keys to open the chest. You also have 4 chest slots you can put 4 of them in the slots if open. Once in a slot you can put it on a timer (one at a time) for 3/9/12/24 hours (same proportion as the keys). If your slots are full and you don’t want to waste your keys on a lesser chest, you can decline the chest. Most players hold on to their keys until they (eventually) win a Yellow chest. The probability of being awarded a certain color chest s/b close to the % listed above - but they are not. The contents of the chests are somewhat proportional, but since they all don’t have the same ‘type’ of goodies you can’t do a straight proportion. Some things in a yellow chest are more than 8x a Green and some are less…and some don’t exist in a Green. The ‘cost’ of each chest is the only thing I have to swag a frequency probability. But the developers of this game have no idea what they are doing. Yellow chests are actually more common than purple by 2 to 1.
The developers want people to spend keys, because they want people to do whatever it is that they do to earn keys (usually either spending time in the app and seeing the occasional ads, or just outright spending real money to buy keys/gold/etc.). So the developers want there to be a lot of the expensive chests. The only reason to have the cheaper chests is as a sort of “gateway drug”, to introduce players to the idea of “Look at what rewards you can get by cashing in keys”.
Here are the theoretical percentages I got (rounded) based on keys needed. Effectively in the long term the keys needed to open all green/blue/purple/yellow boxes you get will be equal for all colors.
Green 58.537%
Blue 19.512%
Purple 14.634%
Yellow 7.317%
I think we can conclude the OP’s experience matches the expectation.
Having worked in the game industry, I’ll just say that the people doing the design ain’t mathematicians.
They’ll have high level concepts like, “Players like random drops with different payouts.” And, “Wouldn’t it be cool if the new character class could mind control the bad guys?” And not consider the math and logic that underlies all of that.
Once it goes live, if it works and the players like it then who cares what the math is. If it breaks and it’s not amenable to fine tuning then…yaidunno.
Working in the game industry literally as I write this post, they absolutely have people with high level math backgrounds working this shit out. Likely, before any other part of the game design is finalized. This is the part of the game that makes them money. Nobody is skimping on that part.
It’s the same logic: they want the user to fight as many battles as possible (e.g. spending money to get the necessary “energy” needed to fight more battles) in the hopes of getting one of the super-rare chests.
If you give out your super-rare items too frequently, then there’s nothing to chase after.
The difference there is that the primary purpose of a writer for the Simpsons is to write episodes for the Simpsons. If the episode ends up with a bunch of math jokes in it, that’s a secondary bonus. The primary purpose of a game designer for these sorts of games is maximize the monetization of the game play experience. If the game ends up having any actual good game elements, that’s a secondary bonus.
“Loot boxes” in modern video games are, essentially, digital slot machines, and the people making those games are every bit as invested in skewing the odds to extract as much revenue as possible as anyone running a Vegas casino.
There seems to be high levels of both greed and incompetence when it comes to this developer. So many monetary things in this game don’t make any sense, or maybe they are trying to trick people into buying non-optimal $$ packages. To give a simple example, $10 will buy you 680 gold bars, but if you’re willing to buy the $100 package you’ll get 6480 gold bars (no, that is not a typo).
Circling back to the chests: I started tracking the frequency of each color years ago. I quickly realized there was a pattern to the chest awards that repeated every 240 wins. There are 9 ‘legs’ that end in a purple (3) or yellow (6), the chests leading up to the end are mix of green and blue. In the 240 there are: 180 Green, 51 Blue, 3 Purple, 6 Yellow. As you can see these % are way off from what they “should be”. I get the greed of not wanting people to win/earn rewards - cuz they might spend a dollar less, but the incompetence kicks in because they don’t give (or sell) us enough keys to open that many chests. They could offer many more high level chests and players still wouldn’t be able to open them all.
I just wanted to make sure I had done the math correctly in case the developer will actually listen.
That’s probably not so much, “The devs are bad at math,” and more, “The devs are aware of the math skills of the average player, and also have no ethics.”
I assume that, at some point, it’s barely even worth it to waste keys on green chests. I haven’t played the particular game you’re talking about, but I’ve played a number of free-to-play games and it’s bog standard for them to allow users to pay real money for items that are incredibly common or weak.
Many items in your grocery store violate the “They’re cheaper per each if you buy the larger package” rule of thumb. Why? Because people who blindly apply the rule of thumb are fair game to be fleeced.
It’s not developers who can’t do math. It’s management who can’t do ethics.