How do we understand 6 people trying something is not 6 times the success rate? [duplicate]

Let's say if a task has a success rate of $20\%$, or $0.2$, meaning if a person tries it, then there is a $20\%$ chance he can succeed.

One example is, if we generate a random number from 1 to 10, and getting the number 9 or 10 is considered to be a success.

Now, if we let 6 people try it, and one person succeeding is considered a success, we cannot say the success rate is $6$ times as much, because then the success rate is $20\% \times 6 = 120\%$, and probability cannot be greater than $100\%$. So the success rate is not 6 times as much.

However, if we let 1 person try it $1,000,000$ times, the Law of Large Numbers says that the number of times he will succeed is $200,000$. And if we let 6 people try $1,000,000$ times each, then the number of success is indeed $200,000 \times 6 = 1,200,000$ which is $6$ times. How can we understand this?

In a real life example, say, each time when we catch a Pokemon, let's say there is a special type of Pokemon that when you tap on it, it can be "shiny", and the probability is $1/256$. Now if one player try to tap on $300$ Pokemon, the probability of getting at least one shiny is not $1$, but less than $1$. If we let 6 people, each try to tap on $300$ Pokemon (and a Pokemon can be non-shiny for player 1 but is shiny for player 2, meaning it is independent), then the probability of getting at least one shiny is not $6$ times. Now, however, if we let all 6 players, each tap on $3,000,000$ Pokemon, then the number of shiny Pokemon they will get is in fact $6$ times if we only allow 1 player to play. How can we understand this "6 times yes and no" dilemma?

The probabilities work because there is a chance that more than one person is successful at the same time, even though there is also a chance that none are successful. The average number of successes for six people is six times the average for one person, but this average covers the case where all succeed at the same time (for example) as well as the cases where two out of the six succeed.

If six people each try $1,000,000$ times, the total number of success is approximate $1,200,000.$ The success rate is approximately $$ \frac{1200000}{6000000}=.2$$

You seem to have overlooked the fact that there are six million trials.