The previous scene showed the center of a distribution. Now estimate that center from a sample.
With 10 draws, the sample mean can sit far from the true mean. With 100 or 1000 draws, it hugs the true mean. That is the law of large numbers. The curve below shows how the mean moves as each new draw joins the sample.
For example, the average of 10 die rolls can sit far from 3.5. A run of sixes pulls it up sharply. The average of 1000 rolls lands very close to 3.5. The power of luck over the average weakens as the sample grows.
Source: Bernoulli, J. (1713). Ars Conjectandi, the book where the law of large numbers was first proved.