Can someone explain me, how the Law of large numbers and the Gambler's Fallacy do not contradict.
The Gambler's Fallacy says, that there is no memory in randomness and any sequence of events has the same probability as any other sequence.
However, the Law of large numbers says, that given enough repetitions a certain event will likely happen.
To my understanding, these two kinda contradict each other because one says that you can not predict any random event but the other one says so (given enough repetitions of course).
For example imagine a series of coin tosses where the coin comes up heads a million times. The Gambler's fallacy says that the chance for the next toss to be tails is still 1/2. However the law of large numbers says, that since enough repetitions of tosses have come up heads, the next toss is more likely to be tails. (Which is definitely wrong?)