People Do Not Understand Probabilities
One of the reasons why games like this exist, and why lotteries and casinos make a fortune, is that probability is hard to understand. People tend to make assumptions about odds that are false. They also tend to believe they have a better chance at a good outcome than they do.
Lotteries are an easy example. Have you ever noticed that the Powerball numbers always seem to be random, unrelated numbers? For example, they are usually something like 5, 17, 32, 39, 61 and 70. When is the last time you saw a lottery where the winning numbers were 1, 2, 3, 4, 5 and 6? If this ever happened, it would make the news, people would scream and claim that the game was rigged. In reality though, that result is just as likely as any other. Think about how many times you have seen lottery numbers and how you probably never have seen a regular pattern like that (or 1, 3, 5, 7, 9, 11, etc.) That gives you an idea of just how unlikely it is that you will ever strike it rich.
People also again expect to see odds “even out” over time, which doesn’t always happen. Each random occurrence is independent of the others, and the cosmos is not keeping track. While over a long time the average will tend to converge to the probability rate, this is because the numbers get very large so differences become less important in percentage terms. It doesn’t mean that after a long stretch of misses on a sim that you are “due” to get shard drops. This is called the Gambler’s Fallacy, and has made many people walk out of a casino with their pockets empty and a sour look on their faces.
Let’s think about those hard missions again. You have probably simmed a hard mission 3 times and gotten 0 shards and felt frustrated. And then said to yourself: “How come I get 0 so often and never seem to get 3? I should be getting 3 sometimes to offset all these 0s!” I’ve been there. Would you be surprised to learn that, if the chance is really 1/3, the odds of getting a 0 result are 8 times higher than getting a 3 result? That’s how the math works out. In fact, with a 1/3 chance, you should get 0/3 almost 30% of the time. That’s why it happens so often.
(Full odds assuming 1/3 chance: 0/3 result 8/27 times; 1/3 result 12/27; 2/3 result 6/27; 3/3 result 1/27).
What about double-simming two hard nodes, so 6 tries? Assuming 1/3 chance, you should get 6/6 only 1 out of 729 tries. The game’s only been open for something like 45 days, so if 6/6 has never happened to you, that’s why: the odds say it shouldn’t. But the odds of getting 0/6 are only 1 in 11, or 64x as often as a 6/6 result. So you should have had this happen, on average, at least once every two weeks. That’s why it seems like the game isn’t being fair.. it’s just the math not being fair.
Now this assumes a 1/3 chance of a drop. If it is lower, as I suspect, things get even worse. If the odds are 1/4 to get a drop, then your chances of going 0/3 increase from 32% to 43%. Your odds of going 3/3 decrease from 3.7% all the way to 1.6%.
If the odds of a purple item dropping are 15%, then if you sim 15 times, you should go 0/15 8.7% of the time, or about once every 12 refills. If you refill 3 times per day, you should expect to get 0/15 every few days.
