What does it mean when we say dice rolls are independent?
When the events do not affect one another, they are known as independent events. Independent events can include repeating an action like rolling dice more than once or using two different random elements, such as flipping a coin and spinning a spinner.
In this case, it's easy to understand the independent roll/spin/throw... independent means that the result is not determined by previous ones! So the chances for getting a "six" when you throw dice is 1/6... you can believe that after 5 misses the next throw will be 6, but that 6 throw is independent of previous results, you can miss 10 times, 20 times...
Yep, very close, but i want a little addition. You described a typical case of
Gambler's Fallacy. We should understand, that 1/6 happens in very big space of outcomes. This more like statical probability, which means that if we throw 10000 times, the number of "6" will ralated to all throws as 1 / 6.
But in few throws such interconnection will not work.