As with all things assigned a certain probability, there is the possibility that, while hunting for a particular rare or common drop, you will never ever encounter it. Unlikely, yes, but the possibility exists.
But you really want that card, eh?
Alright, then. Most cards have a 0.04% chance of dropping on RO. This is to say that there is a 1/2500 probability of the card being dropped each time you kill the monster.
Conversely, there is a 2499/2500 probability that the card will *not* drop for a given kill. We will rely upon this number to simplify our calculation.
But, let's back up a bit, shall we? In order to find the joint probability of a sequence of events occurring in any order, one mere must multiply together their respective probabilities. For instance, the probability of a coin landing on heads during one trial is 1/2. The probability of the coin landing on heads on every attempt for 5 attempts is (1/2)^5, or 1/32. Note that 1/32 is also the probability that given 5 coin flips, tails will never come up (if each attempt has yielded heads, none of the attempts can have yielded tails).
With cards the probability of getting a card 5 times in a row in five attempts is (1/2500)^5, a very low number. Conversely, the probability of NOT finding a card in 5 trials in a row is (2499/2500)^5, or ~0.998. So, in 5 trials, you'll have a ~0.2 % (1 - 0.998 = 0.002) chance of finding AT LEAST one card. Extending this, we can set our probability of NOT finding a card to a certain probability, and solve for the number of trials it would take to achieve that probability. Our probability for finding a card will thus be one minus that set probability for finding the card.
For example, you want to find out how many whispers you need to kill in order to have a 10% overall chance of finding at least one whisper cards. That translates to you having a 90% chance of not finding any, leading to the equation (2499/2500)^x = 0.9. Solving for x, we find it to be equal to ~264 (rounded up). Thus, you must kill 264 whispers in order to have a 10% chance of finding at least one card.
This brings us the to the following table of # of kills required to have a certain % chance of finding at least one card. All calculations are based upon a drop rate of 0.04%:
chance of finding card(s) - # of kills required
00.04% ----------------- 1
50.00% ----------------- 1733
90.00% ----------------- 5756
95.00% ----------------- 7488
99.00% ----------------- 11511
99.96% ----------------- 19557
100.00% ----------------- infinite
Depresionist, who has been searching for a horong card for ~4100 horongs (as of the time of this post), has so far accrued only an overall ~80% chance of having found at least one card.
Discussion Zen 5 Speculation (EPYC Turin and Strix Point/Granite Ridge - Ryzen 9000)
Discussion Intel current and future Lakes & Rapids thread
