I don't see where is the ambiguity. We keep going around in circles. You ask the same question. We give you the same answer.
After a number of n1 tosses, you get one result, H1 : (n1-H1).
After another number of n2 tosses, you get another result, H2 : (n2-H2).
It does not matter which side H or T has a lead for each experiment.
When you do another trial of 1000,000,000 tosses AND include the results of the previous n1 and n2 tosses, the results H1 and H2 are buried in the noise of the statistical data.
After a number of n1 tosses, you get one result, H1 : (n1-H1).
After another number of n2 tosses, you get another result, H2 : (n2-H2).
It does not matter which side H or T has a lead for each experiment.
When you do another trial of 1000,000,000 tosses AND include the results of the previous n1 and n2 tosses, the results H1 and H2 are buried in the noise of the statistical data.