Does the number of the same side appearing in a row converge to a finite number? Fair coin toss.

Toss a fair coin N times. Does the number of the same side appearing in a row converge to a finite number? If yes, what is it in terms of N? Are confidence intervals needed? Thank you!

• i did not understand. can you please explain with an example? – gt6989b Jan 31 '17 at 20:20
• This is not at all clear. Please define precisely what you are trying to calculate. If possible, give an example for $N=3$ say. – lulu Jan 31 '17 at 20:25
• Okay! I meant the following. Let me do it with a greater N, say N=100. So when I toss the fair coin 100 times, what can I say about the longest HEADs in a row? That is With 95% confidence I can say that there will be no longer HEADs after each other than say 10. So the sequence would be: {H,T,T,T,H,H,T,H,WHATEVER,...,HHHHHHHHHH,T,...,LAST} – Bende Jan 31 '17 at 20:32
• And so the larger N goes, there will be more likely to observe "long" rows of the same side, say HEAD. Example: N=100,000, there will be 15 HEADs in a row. – Bende Jan 31 '17 at 20:36
• this question is relevant. As is this one – lulu Jan 31 '17 at 20:44