The feeling of being due
After three hundred kills without the item you want, it is hard not to feel that something owes you a drop. The reasoning seems natural: the odds say it should have happened by now, so surely it is close. That feeling is the gambler fallacy, the belief that past failures in independent trials make a success more likely next time.
In a fixed-rate system, the belief is wrong. The game does not know how many kills you have made. Each kill carries the same chance it always did.
Why independence means no memory
Suppose an enemy drops an item with a 1 percent chance, and each kill is an independent roll. Before your first kill the chance of a drop is 1 percent. After 300 failures, the chance on kill 301 is still 1 percent. The earlier results are already in the past and have no influence on a new roll.
A useful way to see this is to separate two different questions:
- Before I start, how likely is it that I go 300 kills without a drop? About 4.9 percent, since 0.99^300 is roughly 0.049.
- Having already gone 300 kills without a drop, how likely is the next kill to succeed? Still 1 percent.
The first question is about a whole sequence that has not happened yet. The second is about a single roll that has not been made. The first number is small, but it says nothing about the second.
The “someone is always unlucky” effect
Long dry streaks are not signs of something wrong. If 10,000 players each farm 300 kills of that same enemy, roughly 4.9 percent of them, around 490 people, will see nothing. Each of those players has a reasonable story about their bad luck, and some will post about it, which makes streaks look more common than they are, and the successful majority is silent.
This is a version of the same pattern described in the discussions of random clumping and the expectation defying results that random sequences often produce: runs and gaps are normal in independent data, and people tend to underestimate them. Given enough trials, a rare-looking streak is close to inevitable somewhere.
The mirror image: the hot hand
The same misunderstanding works in reverse. After two drops in a row, some players believe they are “on a streak” and should keep farming, or that the luck must now be due to run out. Neither follows from fixed odds. The idea that success predicts success is the hot hand belief, and the idea that success predicts failure is the same fallacy in the other direction. In both cases the sequence of results is being given a meaning that independent rolls do not have.
When the intuition is partly right
The fallacy depends on the system being memoryless. Some games break that assumption deliberately:
- A pity counter. Misses increase a stored count, and at a threshold the reward is guaranteed. Here a long dry streak does bring a drop closer.
- Chances that rise with each miss. The pseudo random distribution approach raises the next attempt’s chance after every failure.
- Hidden adjustments. Some games change a player’s odds based on their history, though they don’t always say so.
The correct habit is to ask about the mechanism before applying any reasoning. If the game documents a counter, then streaks matter. If it states a fixed rate and nothing more, treat each kill as a fresh roll. If it says nothing, the honest answer is that you cannot know.
Decisions that follow
Understanding independence is useful in practical ways, mostly about how to think about time spent:
- Don’t count prior failures as progress. Three hundred kills without a drop have not moved you closer. The average remaining effort is still 100 kills, exactly what it was at the start. This is a sensible thing to remember before deciding to continue.
- Beware sunk cost. The time already spent is gone either way. The sunk cost trap leads people to continue because they have already invested a lot, rather than because the remaining effort is worth the reward.
- Compare alternatives on forward-looking terms. If another activity gives a better return for the next hour, the time you already spent should not be what decides.
- Set limits in advance. Deciding before you start how much time you are willing to put in avoids the pull of “just one more run”.
None of this says farming is a bad idea. If you enjoy the activity, or the item is worth the average cost, continuing is reasonable. The point is to base the choice on what lies ahead.
The emotional side
Long streaks are frustrating, and frustration can lead to rash decisions. The tendency to treat bad outcomes as proof that the game is unfair or that you are cursed is a close relative of the loss-driven reactions discussed in the mental game material. A useful reframing is that the 4.9 percent chance of reaching 300 failures is not zero, and someone has to be in that group. It does not predict what happens next.
A short summary of what to remember
- In a fixed-rate system, each attempt is independent and has the same chance.
- Long streaks of failure are unlikely for any one person but common across many people.
- A “due” drop exists only if the game has a counter or rising chance.
- Judge whether to keep farming by the effort ahead, not the effort behind.
Outcomes remain random, and no approach changes the rate of a fixed-chance drop.