So as we toss continue to toss the coin and tally Heads and Tails, the likelihood that Hn and Tn
are close to each other in absolute terms goes to zero. There is no “hidden force” causing (Hn - Tn) to converge to zero.
Indeed. The gap will tend to widen, not narrow.
In ratio terms they’ll converge towards equality (assuming a fair coin) as the count rises.
But in absolute terms the central expected gap is the square root of the number of tosses.
i.e., if you flip a coin 100 times, the most likely difference between the number of heads and the number of tails is 10.
A very cool result, not very well known.
Jim