Quantitative Finance For Dummies. Steve Bell

      The chart fluctuates less and less after more coin flips and the fraction of heads converges (gets closer and closer) towards 0.5. This is an example of the Law of Large Numbers. You’d be surprised though at how many tosses it takes for the chart to settle down to the expected average.

      I examine this further by plotting H_n – n/2 where n/2 is the expected number of heads after n tosses. The line in Figure 2-2 wanders about and shows that convergence isn’t good. It’s disconcerting that although the fraction of heads tossed tends towards 0.5 in relative terms, in absolute terms, the number of heads can wander further and further away from the expected value of n/2. You may have guessed already that this unstable sequence, called a random walk, can be used as a model for how share prices change with time.