Probability does not accumulate
It is tempting to think a 1% chance tried 100 times yields one hit. It does not. Each attempt is 1% again, regardless of what came before. After 100 tries, roughly a 37% chance of no hit at all remains. The sense that it is 'due' after many attempts comes from expectation, not probability.
The pity counter tells you the real cost
A mechanism guaranteeing the item after a set number of attempts is commonly called a pity system. Where it exists, your worst-case cost becomes calculable. Reading that number before the advertised rate is more practical. No pity system means no ceiling, which is an entirely different proposition.
- Work out the attempts and cost to reach the guarantee first
- Check whether the rate is per attempt or per bundle
- Divide bundle prices down to a real unit cost
- Do not let limited-time labels rush you
Expected value is not what you experience
A calculation saying it takes so many attempts on average describes the average across many people. An individual can run far worse than average, and not rarely. An average of fifty does not mean you will get it within fifty.
Set the limit before you start
Deciding when to stop after starting means money already spent distorts the judgement. 'I have come this far, just a little more' is precisely the sunk cost fallacy. Fixing an amount and a number of attempts beforehand, and putting a limit on the payment method, is what holds.
Before enabling payment
With a payment method saved to the account, a purchase is a few clicks away. On a shared family device especially, turn on purchase restrictions for minors and require a password. Refund policies differ by game and platform, and loot box purchases are often difficult to refund.
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