In creating these point estimates repeatedly, you also should have noticed that the results will change somewhat over time. Indeed, flip a coin 20 times and you might expect 10 heads. However, in practice it is likely to 9 or 12 out of 20 and possible to get any of the other possible outcomes. This natural variation makes these estimates almost certainly in error. If the number of experiments performed is large one would expect that the sample statistics should be close to the theoretical expected values. The Central Limit Theorem does indicate that the distribution of sample means should be approximately normally distributed. Thus, instead of relying just on the value of the point estimate, you might want to investigate a way to determine a reasonable interval centered on the sample statistic in which you have some confidence the actual population statistic should belong. The width of the resulting interval will be your way of determining how close your estimate would approximate the desired value.