The Gambler's Fallacy tells us we cannot predict the next coin flip result based upon history. Several heads in a row do not mean the next flip is any more likely to be tails. However, the law of large numbers tells us that, over many trials, the number of heads and tails will become equal. So, a current preponderance of heads over tails will later be offset by more tails so the results equal over time. Consider a 54 ball random, fair lottery: after a large number of draws, say 54,000, each ball would be picked 1,000 times. Say, at some point in the trials, the number 17 has only been picked half as many times as all the other numbers. It must, in the remaining trials, up to the number of trials that make the number of trials a "large number", occur more often than the other numbers so that all numbers converge on being picked equally.
In this example, what is a "large number" of trials where the law of large numbers would tell us all numbers would have been picked equally? How would you generate a curve showing the convergence?