You are exactly correct, but we are talking about two different things really. The probability with each toss is always 50%.
However, as the number of tosses increases, the variability of the outcomes becomes more heavily subjugated to regression to the mean.
An extremely unlikely analogy would be:
A total of10,000 tosses is planned. Tails comes up 4000 times in the first 5000 throws. For toss number 5001 the probability remains 50%, BUT, regression to the mean would dictate that over the next 5000 throws heads will come up at a much higher rate than tails.
In that, albeit very unlikely, scenario, I would be happy to place a wager on heads coming up more than tails, as a higher percentage of the sum of the tosses, in the last 5000 tosses. The wager is on the percentages, not on the probability of the throw.