I threw a coin n times, and never got three tails in a row. I calculated the odds of this event, and found out they were just about even; 50%-50%. How many times did I throw the coin?

A second question: what were the chances of having not gotten three heads in a row either?

(In reply to re(4): Markov chain solution - 2nd part by Federico Kereki)

In the problem it does not state that the coin tossing would end when either TTT or HHH was achieved.  The premise was that a certain number of tosses would be made. If the coin tossing stopped with a triple then the circumstance that was 50% probable would be ending at toss n, which wouldn't be 50% at n=10.

However, assuming what you say, and that coin tossing would have stopped at either a triple-H or triple-T, or having reached 10 tosses and givenup, and that the probability of having completed same by 10 tosses is what is sought, then the 29.6% figure is still not correct.

I've rerun the exhaustive list of 1024 outcomes of 10 tosses, but now kept track of whether TTT or HHH was achieved first in those cases where both occurred so we can keep track of what would happen if we stopped there.  This is legitimate, as, to take one example, HTTT has 1/16 probability of happening, or 64/1024, so the 64 possibilities of what comes after do count for this. I've also marked with *** those instances where only HHH was achieved, and this at the last 3 tosses only.

The annotated results are as follows, and statistics appear at the bottom, followed by the result:

HHHHHHHHHH HHH 
HHHHHHHHHT HHH 
HHHHHHHHTH HHH 
HHHHHHHHTT HHH 
HHHHHHHTHH HHH 
HHHHHHHTHT HHH 
HHHHHHHTTH HHH 
HHHHHHHTTT HHH TTT
HHHHHHTHHH HHH 
HHHHHHTHHT HHH 
HHHHHHTHTH HHH 
HHHHHHTHTT HHH 
HHHHHHTTHH HHH 
HHHHHHTTHT HHH 
HHHHHHTTTH HHH TTT
HHHHHHTTTT HHH TTT
HHHHHTHHHH HHH 
HHHHHTHHHT HHH 
HHHHHTHHTH HHH 
HHHHHTHHTT HHH 
HHHHHTHTHH HHH 
HHHHHTHTHT HHH 
HHHHHTHTTH HHH 
HHHHHTHTTT HHH TTT
HHHHHTTHHH HHH 
HHHHHTTHHT HHH 
HHHHHTTHTH HHH 
HHHHHTTHTT HHH 
HHHHHTTTHH HHH TTT
HHHHHTTTHT HHH TTT
HHHHHTTTTH HHH TTT
HHHHHTTTTT HHH TTT
HHHHTHHHHH HHH 
HHHHTHHHHT HHH 
HHHHTHHHTH HHH 
HHHHTHHHTT HHH 
HHHHTHHTHH HHH 
HHHHTHHTHT HHH 
HHHHTHHTTH HHH 
HHHHTHHTTT HHH TTT
HHHHTHTHHH HHH 
HHHHTHTHHT HHH 
HHHHTHTHTH HHH 
HHHHTHTHTT HHH 
HHHHTHTTHH HHH 
HHHHTHTTHT HHH 
HHHHTHTTTH HHH TTT
HHHHTHTTTT HHH TTT
HHHHTTHHHH HHH 
HHHHTTHHHT HHH 
HHHHTTHHTH HHH 
HHHHTTHHTT HHH 
HHHHTTHTHH HHH 
HHHHTTHTHT HHH 
HHHHTTHTTH HHH 
HHHHTTHTTT HHH TTT
HHHHTTTHHH HHH TTT
HHHHTTTHHT HHH TTT
HHHHTTTHTH HHH TTT
HHHHTTTHTT HHH TTT
HHHHTTTTHH HHH TTT
HHHHTTTTHT HHH TTT
HHHHTTTTTH HHH TTT
HHHHTTTTTT HHH TTT
HHHTHHHHHH HHH 
HHHTHHHHHT HHH 
HHHTHHHHTH HHH 
HHHTHHHHTT HHH 
HHHTHHHTHH HHH 
HHHTHHHTHT HHH 
HHHTHHHTTH HHH 
HHHTHHHTTT HHH TTT
HHHTHHTHHH HHH 
HHHTHHTHHT HHH 
HHHTHHTHTH HHH 
HHHTHHTHTT HHH 
HHHTHHTTHH HHH 
HHHTHHTTHT HHH 
HHHTHHTTTH HHH TTT
HHHTHHTTTT HHH TTT
HHHTHTHHHH HHH 
HHHTHTHHHT HHH 
HHHTHTHHTH HHH 
HHHTHTHHTT HHH 
HHHTHTHTHH HHH 
HHHTHTHTHT HHH 
HHHTHTHTTH HHH 
HHHTHTHTTT HHH TTT
HHHTHTTHHH HHH 
HHHTHTTHHT HHH 
HHHTHTTHTH HHH 
HHHTHTTHTT HHH 
HHHTHTTTHH HHH TTT
HHHTHTTTHT HHH TTT
HHHTHTTTTH HHH TTT
HHHTHTTTTT HHH TTT
HHHTTHHHHH HHH 
HHHTTHHHHT HHH 
HHHTTHHHTH HHH 
HHHTTHHHTT HHH 
HHHTTHHTHH HHH 
HHHTTHHTHT HHH 
HHHTTHHTTH HHH 
HHHTTHHTTT HHH TTT
HHHTTHTHHH HHH 
HHHTTHTHHT HHH 
HHHTTHTHTH HHH 
HHHTTHTHTT HHH 
HHHTTHTTHH HHH 
HHHTTHTTHT HHH 
HHHTTHTTTH HHH TTT
HHHTTHTTTT HHH TTT
HHHTTTHHHH HHH TTT
HHHTTTHHHT HHH TTT
HHHTTTHHTH HHH TTT
HHHTTTHHTT HHH TTT
HHHTTTHTHH HHH TTT
HHHTTTHTHT HHH TTT
HHHTTTHTTH HHH TTT
HHHTTTHTTT HHH TTT
HHHTTTTHHH HHH TTT
HHHTTTTHHT HHH TTT
HHHTTTTHTH HHH TTT
HHHTTTTHTT HHH TTT
HHHTTTTTHH HHH TTT
HHHTTTTTHT HHH TTT
HHHTTTTTTH HHH TTT
HHHTTTTTTT HHH TTT
HHTHHHHHHH HHH 
HHTHHHHHHT HHH 
HHTHHHHHTH HHH 
HHTHHHHHTT HHH 
HHTHHHHTHH HHH 
HHTHHHHTHT HHH 
HHTHHHHTTH HHH 
HHTHHHHTTT HHH TTT
HHTHHHTHHH HHH 
HHTHHHTHHT HHH 
HHTHHHTHTH HHH 
HHTHHHTHTT HHH 
HHTHHHTTHH HHH 
HHTHHHTTHT HHH 
HHTHHHTTTH HHH TTT
HHTHHHTTTT HHH TTT
HHTHHTHHHH HHH 
HHTHHTHHHT HHH 
HHTHHTHHTH 
HHTHHTHHTT 
HHTHHTHTHH 
HHTHHTHTHT 
HHTHHTHTTH 
HHTHHTHTTT TTT 
HHTHHTTHHH HHH  ***

HHTHHTTHHT 
HHTHHTTHTH 
HHTHHTTHTT 
HHTHHTTTHH TTT 
HHTHHTTTHT TTT 
HHTHHTTTTH TTT 
HHTHHTTTTT TTT 
HHTHTHHHHH HHH 
HHTHTHHHHT HHH 
HHTHTHHHTH HHH 
HHTHTHHHTT HHH 
HHTHTHHTHH 
HHTHTHHTHT 
HHTHTHHTTH 
HHTHTHHTTT TTT 
HHTHTHTHHH HHH  ***

HHTHTHTHHT 
HHTHTHTHTH 
HHTHTHTHTT 
HHTHTHTTHH 
HHTHTHTTHT 
HHTHTHTTTH TTT 
HHTHTHTTTT TTT 
HHTHTTHHHH HHH 
HHTHTTHHHT HHH 
HHTHTTHHTH 
HHTHTTHHTT 
HHTHTTHTHH 
HHTHTTHTHT 
HHTHTTHTTH 
HHTHTTHTTT TTT 
HHTHTTTHHH TTT HHH
HHTHTTTHHT TTT 
HHTHTTTHTH TTT 
HHTHTTTHTT TTT 
HHTHTTTTHH TTT 
HHTHTTTTHT TTT 
HHTHTTTTTH TTT 
HHTHTTTTTT TTT 
HHTTHHHHHH HHH 
HHTTHHHHHT HHH 
HHTTHHHHTH HHH 
HHTTHHHHTT HHH 
HHTTHHHTHH HHH 
HHTTHHHTHT HHH 
HHTTHHHTTH HHH 
HHTTHHHTTT HHH TTT
HHTTHHTHHH HHH  ***

HHTTHHTHHT 
HHTTHHTHTH 
HHTTHHTHTT 
HHTTHHTTHH 
HHTTHHTTHT 
HHTTHHTTTH TTT 
HHTTHHTTTT TTT 
HHTTHTHHHH HHH 
HHTTHTHHHT HHH 
HHTTHTHHTH 
HHTTHTHHTT 
HHTTHTHTHH 
HHTTHTHTHT 
HHTTHTHTTH 
HHTTHTHTTT TTT 
HHTTHTTHHH HHH  ***

HHTTHTTHHT 
HHTTHTTHTH 
HHTTHTTHTT 
HHTTHTTTHH TTT 
HHTTHTTTHT TTT 
HHTTHTTTTH TTT 
HHTTHTTTTT TTT 
HHTTTHHHHH TTT HHH
HHTTTHHHHT TTT HHH
HHTTTHHHTH TTT HHH
HHTTTHHHTT TTT HHH
HHTTTHHTHH TTT 
HHTTTHHTHT TTT 
HHTTTHHTTH TTT 
HHTTTHHTTT TTT 
HHTTTHTHHH TTT HHH
HHTTTHTHHT TTT 
HHTTTHTHTH TTT 
HHTTTHTHTT TTT 
HHTTTHTTHH TTT 
HHTTTHTTHT TTT 
HHTTTHTTTH TTT 
HHTTTHTTTT TTT 
HHTTTTHHHH TTT HHH
HHTTTTHHHT TTT HHH
HHTTTTHHTH TTT 
HHTTTTHHTT TTT 
HHTTTTHTHH TTT 
HHTTTTHTHT TTT 
HHTTTTHTTH TTT 
HHTTTTHTTT TTT 
HHTTTTTHHH TTT HHH
HHTTTTTHHT TTT 
HHTTTTTHTH TTT 
HHTTTTTHTT TTT 
HHTTTTTTHH TTT 
HHTTTTTTHT TTT 
HHTTTTTTTH TTT 
HHTTTTTTTT TTT 
HTHHHHHHHH HHH 
HTHHHHHHHT HHH 
HTHHHHHHTH HHH 
HTHHHHHHTT HHH 
HTHHHHHTHH HHH 
HTHHHHHTHT HHH 
HTHHHHHTTH HHH 
HTHHHHHTTT HHH TTT
HTHHHHTHHH HHH 
HTHHHHTHHT HHH 
HTHHHHTHTH HHH 
HTHHHHTHTT HHH 
HTHHHHTTHH HHH 
HTHHHHTTHT HHH 
HTHHHHTTTH HHH TTT
HTHHHHTTTT HHH TTT
HTHHHTHHHH HHH 
HTHHHTHHHT HHH 
HTHHHTHHTH HHH 
HTHHHTHHTT HHH 
HTHHHTHTHH HHH 
HTHHHTHTHT HHH 
HTHHHTHTTH HHH 
HTHHHTHTTT HHH TTT
HTHHHTTHHH HHH 
HTHHHTTHHT HHH 
HTHHHTTHTH HHH 
HTHHHTTHTT HHH 
HTHHHTTTHH HHH TTT
HTHHHTTTHT HHH TTT
HTHHHTTTTH HHH TTT
HTHHHTTTTT HHH TTT
HTHHTHHHHH HHH 
HTHHTHHHHT HHH 
HTHHTHHHTH HHH 
HTHHTHHHTT HHH 
HTHHTHHTHH 
HTHHTHHTHT 
HTHHTHHTTH 
HTHHTHHTTT TTT 
HTHHTHTHHH HHH  ***

HTHHTHTHHT 
HTHHTHTHTH 
HTHHTHTHTT 
HTHHTHTTHH 
HTHHTHTTHT 
HTHHTHTTTH TTT 
HTHHTHTTTT TTT 
HTHHTTHHHH HHH 
HTHHTTHHHT HHH 
HTHHTTHHTH 
HTHHTTHHTT 
HTHHTTHTHH 
HTHHTTHTHT 
HTHHTTHTTH 
HTHHTTHTTT TTT 
HTHHTTTHHH TTT HHH
HTHHTTTHHT TTT 
HTHHTTTHTH TTT 
HTHHTTTHTT TTT 
HTHHTTTTHH TTT 
HTHHTTTTHT TTT 
HTHHTTTTTH TTT 
HTHHTTTTTT TTT 
HTHTHHHHHH HHH 
HTHTHHHHHT HHH 
HTHTHHHHTH HHH 
HTHTHHHHTT HHH 
HTHTHHHTHH HHH 
HTHTHHHTHT HHH 
HTHTHHHTTH HHH 
HTHTHHHTTT HHH TTT
HTHTHHTHHH HHH  ***

HTHTHHTHHT 
HTHTHHTHTH 
HTHTHHTHTT 
HTHTHHTTHH 
HTHTHHTTHT 
HTHTHHTTTH TTT 
HTHTHHTTTT TTT 
HTHTHTHHHH HHH 
HTHTHTHHHT HHH 
HTHTHTHHTH 
HTHTHTHHTT 
HTHTHTHTHH 
HTHTHTHTHT 
HTHTHTHTTH 
HTHTHTHTTT TTT 
HTHTHTTHHH HHH  ***

HTHTHTTHHT 
HTHTHTTHTH 
HTHTHTTHTT 
HTHTHTTTHH TTT 
HTHTHTTTHT TTT 
HTHTHTTTTH TTT 
HTHTHTTTTT TTT 
HTHTTHHHHH HHH 
HTHTTHHHHT HHH 
HTHTTHHHTH HHH 
HTHTTHHHTT HHH 
HTHTTHHTHH 
HTHTTHHTHT 
HTHTTHHTTH 
HTHTTHHTTT TTT 
HTHTTHTHHH HHH  ***

HTHTTHTHHT 
HTHTTHTHTH 
HTHTTHTHTT 
HTHTTHTTHH 
HTHTTHTTHT 
HTHTTHTTTH TTT 
HTHTTHTTTT TTT 
HTHTTTHHHH TTT HHH
HTHTTTHHHT TTT HHH
HTHTTTHHTH TTT 
HTHTTTHHTT TTT 
HTHTTTHTHH TTT 
HTHTTTHTHT TTT 
HTHTTTHTTH TTT 
HTHTTTHTTT TTT 
HTHTTTTHHH TTT HHH
HTHTTTTHHT TTT 
HTHTTTTHTH TTT 
HTHTTTTHTT TTT 
HTHTTTTTHH TTT 
HTHTTTTTHT TTT 
HTHTTTTTTH TTT 
HTHTTTTTTT TTT 
HTTHHHHHHH HHH 
HTTHHHHHHT HHH 
HTTHHHHHTH HHH 
HTTHHHHHTT HHH 
HTTHHHHTHH HHH 
HTTHHHHTHT HHH 
HTTHHHHTTH HHH 
HTTHHHHTTT HHH TTT
HTTHHHTHHH HHH 
HTTHHHTHHT HHH 
HTTHHHTHTH HHH 
HTTHHHTHTT HHH 
HTTHHHTTHH HHH 
HTTHHHTTHT HHH 
HTTHHHTTTH HHH TTT
HTTHHHTTTT HHH TTT
HTTHHTHHHH HHH 
HTTHHTHHHT HHH 
HTTHHTHHTH 
HTTHHTHHTT 
HTTHHTHTHH 
HTTHHTHTHT 
HTTHHTHTTH 
HTTHHTHTTT TTT 
HTTHHTTHHH HHH  ***

HTTHHTTHHT 
HTTHHTTHTH 
HTTHHTTHTT 
HTTHHTTTHH TTT 
HTTHHTTTHT TTT 
HTTHHTTTTH TTT 
HTTHHTTTTT TTT 
HTTHTHHHHH HHH 
HTTHTHHHHT HHH 
HTTHTHHHTH HHH 
HTTHTHHHTT HHH 
HTTHTHHTHH 
HTTHTHHTHT 
HTTHTHHTTH 
HTTHTHHTTT TTT 
HTTHTHTHHH HHH  ***

HTTHTHTHHT 
HTTHTHTHTH 
HTTHTHTHTT 
HTTHTHTTHH 
HTTHTHTTHT 
HTTHTHTTTH TTT 
HTTHTHTTTT TTT 
HTTHTTHHHH HHH 
HTTHTTHHHT HHH 
HTTHTTHHTH 
HTTHTTHHTT 
HTTHTTHTHH 
HTTHTTHTHT 
HTTHTTHTTH 
HTTHTTHTTT TTT 
HTTHTTTHHH TTT HHH
HTTHTTTHHT TTT 
HTTHTTTHTH TTT 
HTTHTTTHTT TTT 
HTTHTTTTHH TTT 
HTTHTTTTHT TTT 
HTTHTTTTTH TTT 
HTTHTTTTTT TTT 
HTTTHHHHHH TTT HHH
HTTTHHHHHT TTT HHH
HTTTHHHHTH TTT HHH
HTTTHHHHTT TTT HHH
HTTTHHHTHH TTT HHH
HTTTHHHTHT TTT HHH
HTTTHHHTTH TTT HHH
HTTTHHHTTT TTT HHH
HTTTHHTHHH TTT HHH
HTTTHHTHHT TTT 
HTTTHHTHTH TTT 
HTTTHHTHTT TTT 
HTTTHHTTHH TTT 
HTTTHHTTHT TTT 
HTTTHHTTTH TTT 
HTTTHHTTTT TTT 
HTTTHTHHHH TTT HHH
HTTTHTHHHT TTT HHH
HTTTHTHHTH TTT 
HTTTHTHHTT TTT 
HTTTHTHTHH TTT 
HTTTHTHTHT TTT 
HTTTHTHTTH TTT 
HTTTHTHTTT TTT 
HTTTHTTHHH TTT HHH
HTTTHTTHHT TTT 
HTTTHTTHTH TTT 
HTTTHTTHTT TTT 
HTTTHTTTHH TTT 
HTTTHTTTHT TTT 
HTTTHTTTTH TTT 
HTTTHTTTTT TTT 
HTTTTHHHHH TTT HHH
HTTTTHHHHT TTT HHH
HTTTTHHHTH TTT HHH
HTTTTHHHTT TTT HHH
HTTTTHHTHH TTT 
HTTTTHHTHT TTT 
HTTTTHHTTH TTT 
HTTTTHHTTT TTT 
HTTTTHTHHH TTT HHH
HTTTTHTHHT TTT 
HTTTTHTHTH TTT 
HTTTTHTHTT TTT 
HTTTTHTTHH TTT 
HTTTTHTTHT TTT 
HTTTTHTTTH TTT 
HTTTTHTTTT TTT 
HTTTTTHHHH TTT HHH
HTTTTTHHHT TTT HHH
HTTTTTHHTH TTT 
HTTTTTHHTT TTT 
HTTTTTHTHH TTT 
HTTTTTHTHT TTT 
HTTTTTHTTH TTT 
HTTTTTHTTT TTT 
HTTTTTTHHH TTT HHH
HTTTTTTHHT TTT 
HTTTTTTHTH TTT 
HTTTTTTHTT TTT 
HTTTTTTTHH TTT 
HTTTTTTTHT TTT 
HTTTTTTTTH TTT 
HTTTTTTTTT TTT 
THHHHHHHHH HHH 
THHHHHHHHT HHH 
THHHHHHHTH HHH 
THHHHHHHTT HHH 
THHHHHHTHH HHH 
THHHHHHTHT HHH 
THHHHHHTTH HHH 
THHHHHHTTT HHH TTT
THHHHHTHHH HHH 
THHHHHTHHT HHH 
THHHHHTHTH HHH 
THHHHHTHTT HHH 
THHHHHTTHH HHH 
THHHHHTTHT HHH 
THHHHHTTTH HHH TTT
THHHHHTTTT HHH TTT
THHHHTHHHH HHH 
THHHHTHHHT HHH 
THHHHTHHTH HHH 
THHHHTHHTT HHH 
THHHHTHTHH HHH 
THHHHTHTHT HHH 
THHHHTHTTH HHH 
THHHHTHTTT HHH TTT
THHHHTTHHH HHH 
THHHHTTHHT HHH 
THHHHTTHTH HHH 
THHHHTTHTT HHH 
THHHHTTTHH HHH TTT
THHHHTTTHT HHH TTT
THHHHTTTTH HHH TTT
THHHHTTTTT HHH TTT
THHHTHHHHH HHH 
THHHTHHHHT HHH 
THHHTHHHTH HHH 
THHHTHHHTT HHH 
THHHTHHTHH HHH 
THHHTHHTHT HHH 
THHHTHHTTH HHH 
THHHTHHTTT HHH TTT
THHHTHTHHH HHH 
THHHTHTHHT HHH 
THHHTHTHTH HHH 
THHHTHTHTT HHH 
THHHTHTTHH HHH 
THHHTHTTHT HHH 
THHHTHTTTH HHH TTT
THHHTHTTTT HHH TTT
THHHTTHHHH HHH 
THHHTTHHHT HHH 
THHHTTHHTH HHH 
THHHTTHHTT HHH 
THHHTTHTHH HHH 
THHHTTHTHT HHH 
THHHTTHTTH HHH 
THHHTTHTTT HHH TTT
THHHTTTHHH HHH TTT
THHHTTTHHT HHH TTT
THHHTTTHTH HHH TTT
THHHTTTHTT HHH TTT
THHHTTTTHH HHH TTT
THHHTTTTHT HHH TTT
THHHTTTTTH HHH TTT
THHHTTTTTT HHH TTT
THHTHHHHHH HHH 
THHTHHHHHT HHH 
THHTHHHHTH HHH 
THHTHHHHTT HHH 
THHTHHHTHH HHH 
THHTHHHTHT HHH 
THHTHHHTTH HHH 
THHTHHHTTT HHH TTT
THHTHHTHHH HHH  ***

THHTHHTHHT 
THHTHHTHTH 
THHTHHTHTT 
THHTHHTTHH 
THHTHHTTHT 
THHTHHTTTH TTT 
THHTHHTTTT TTT 
THHTHTHHHH HHH 
THHTHTHHHT HHH 
THHTHTHHTH 
THHTHTHHTT 
THHTHTHTHH 
THHTHTHTHT 
THHTHTHTTH 
THHTHTHTTT TTT 
THHTHTTHHH HHH  ***

THHTHTTHHT 
THHTHTTHTH 
THHTHTTHTT 
THHTHTTTHH TTT 
THHTHTTTHT TTT 
THHTHTTTTH TTT 
THHTHTTTTT TTT 
THHTTHHHHH HHH 
THHTTHHHHT HHH 
THHTTHHHTH HHH 
THHTTHHHTT HHH 
THHTTHHTHH 
THHTTHHTHT 
THHTTHHTTH 
THHTTHHTTT TTT 
THHTTHTHHH HHH  ***

THHTTHTHHT 
THHTTHTHTH 
THHTTHTHTT 
THHTTHTTHH 
THHTTHTTHT 
THHTTHTTTH TTT 
THHTTHTTTT TTT 
THHTTTHHHH TTT HHH
THHTTTHHHT TTT HHH
THHTTTHHTH TTT 
THHTTTHHTT TTT 
THHTTTHTHH TTT 
THHTTTHTHT TTT 
THHTTTHTTH TTT 
THHTTTHTTT TTT 
THHTTTTHHH TTT HHH
THHTTTTHHT TTT 
THHTTTTHTH TTT 
THHTTTTHTT TTT 
THHTTTTTHH TTT 
THHTTTTTHT TTT 
THHTTTTTTH TTT 
THHTTTTTTT TTT 
THTHHHHHHH HHH 
THTHHHHHHT HHH 
THTHHHHHTH HHH 
THTHHHHHTT HHH 
THTHHHHTHH HHH 
THTHHHHTHT HHH 
THTHHHHTTH HHH 
THTHHHHTTT HHH TTT
THTHHHTHHH HHH 
THTHHHTHHT HHH 
THTHHHTHTH HHH 
THTHHHTHTT HHH 
THTHHHTTHH HHH 
THTHHHTTHT HHH 
THTHHHTTTH HHH TTT
THTHHHTTTT HHH TTT
THTHHTHHHH HHH 
THTHHTHHHT HHH 
THTHHTHHTH 
THTHHTHHTT 
THTHHTHTHH 
THTHHTHTHT 
THTHHTHTTH 
THTHHTHTTT TTT 
THTHHTTHHH HHH  ***

THTHHTTHHT 
THTHHTTHTH 
THTHHTTHTT 
THTHHTTTHH TTT 
THTHHTTTHT TTT 
THTHHTTTTH TTT 
THTHHTTTTT TTT 
THTHTHHHHH HHH 
THTHTHHHHT HHH 
THTHTHHHTH HHH 
THTHTHHHTT HHH 
THTHTHHTHH 
THTHTHHTHT 
THTHTHHTTH 
THTHTHHTTT TTT 
THTHTHTHHH HHH  ***

THTHTHTHHT 
THTHTHTHTH 
THTHTHTHTT 
THTHTHTTHH 
THTHTHTTHT 
THTHTHTTTH TTT 
THTHTHTTTT TTT 
THTHTTHHHH HHH 
THTHTTHHHT HHH 
THTHTTHHTH 
THTHTTHHTT 
THTHTTHTHH 
THTHTTHTHT 
THTHTTHTTH 
THTHTTHTTT TTT 
THTHTTTHHH TTT HHH
THTHTTTHHT TTT 
THTHTTTHTH TTT 
THTHTTTHTT TTT 
THTHTTTTHH TTT 
THTHTTTTHT TTT 
THTHTTTTTH TTT 
THTHTTTTTT TTT 
THTTHHHHHH HHH 
THTTHHHHHT HHH 
THTTHHHHTH HHH 
THTTHHHHTT HHH 
THTTHHHTHH HHH 
THTTHHHTHT HHH 
THTTHHHTTH HHH 
THTTHHHTTT HHH TTT
THTTHHTHHH HHH  ***

THTTHHTHHT 
THTTHHTHTH 
THTTHHTHTT 
THTTHHTTHH 
THTTHHTTHT 
THTTHHTTTH TTT 
THTTHHTTTT TTT 
THTTHTHHHH HHH 
THTTHTHHHT HHH 
THTTHTHHTH 
THTTHTHHTT 
THTTHTHTHH 
THTTHTHTHT 
THTTHTHTTH 
THTTHTHTTT TTT 
THTTHTTHHH HHH  ***

THTTHTTHHT 
THTTHTTHTH 
THTTHTTHTT 
THTTHTTTHH TTT 
THTTHTTTHT TTT 
THTTHTTTTH TTT 
THTTHTTTTT TTT 
THTTTHHHHH TTT HHH
THTTTHHHHT TTT HHH
THTTTHHHTH TTT HHH
THTTTHHHTT TTT HHH
THTTTHHTHH TTT 
THTTTHHTHT TTT 
THTTTHHTTH TTT 
THTTTHHTTT TTT 
THTTTHTHHH TTT HHH
THTTTHTHHT TTT 
THTTTHTHTH TTT 
THTTTHTHTT TTT 
THTTTHTTHH TTT 
THTTTHTTHT TTT 
THTTTHTTTH TTT 
THTTTHTTTT TTT 
THTTTTHHHH TTT HHH
THTTTTHHHT TTT HHH
THTTTTHHTH TTT 
THTTTTHHTT TTT 
THTTTTHTHH TTT 
THTTTTHTHT TTT 
THTTTTHTTH TTT 
THTTTTHTTT TTT 
THTTTTTHHH TTT HHH
THTTTTTHHT TTT 
THTTTTTHTH TTT 
THTTTTTHTT TTT 
THTTTTTTHH TTT 
THTTTTTTHT TTT 
THTTTTTTTH TTT 
THTTTTTTTT TTT 
TTHHHHHHHH HHH 
TTHHHHHHHT HHH 
TTHHHHHHTH HHH 
TTHHHHHHTT HHH 
TTHHHHHTHH HHH 
TTHHHHHTHT HHH 
TTHHHHHTTH HHH 
TTHHHHHTTT HHH TTT
TTHHHHTHHH HHH 
TTHHHHTHHT HHH 
TTHHHHTHTH HHH 
TTHHHHTHTT HHH 
TTHHHHTTHH HHH 
TTHHHHTTHT HHH 
TTHHHHTTTH HHH TTT
TTHHHHTTTT HHH TTT
TTHHHTHHHH HHH 
TTHHHTHHHT HHH 
TTHHHTHHTH HHH 
TTHHHTHHTT HHH 
TTHHHTHTHH HHH 
TTHHHTHTHT HHH 
TTHHHTHTTH HHH 
TTHHHTHTTT HHH TTT
TTHHHTTHHH HHH 
TTHHHTTHHT HHH 
TTHHHTTHTH HHH 
TTHHHTTHTT HHH 
TTHHHTTTHH HHH TTT
TTHHHTTTHT HHH TTT
TTHHHTTTTH HHH TTT
TTHHHTTTTT HHH TTT
TTHHTHHHHH HHH 
TTHHTHHHHT HHH 
TTHHTHHHTH HHH 
TTHHTHHHTT HHH 
TTHHTHHTHH 
TTHHTHHTHT 
TTHHTHHTTH 
TTHHTHHTTT TTT 
TTHHTHTHHH HHH  ***

TTHHTHTHHT 
TTHHTHTHTH 
TTHHTHTHTT 
TTHHTHTTHH 
TTHHTHTTHT 
TTHHTHTTTH TTT 
TTHHTHTTTT TTT 
TTHHTTHHHH HHH 
TTHHTTHHHT HHH 
TTHHTTHHTH 
TTHHTTHHTT 
TTHHTTHTHH 
TTHHTTHTHT 
TTHHTTHTTH 
TTHHTTHTTT TTT 
TTHHTTTHHH TTT HHH
TTHHTTTHHT TTT 
TTHHTTTHTH TTT 
TTHHTTTHTT TTT 
TTHHTTTTHH TTT 
TTHHTTTTHT TTT 
TTHHTTTTTH TTT 
TTHHTTTTTT TTT 
TTHTHHHHHH HHH 
TTHTHHHHHT HHH 
TTHTHHHHTH HHH 
TTHTHHHHTT HHH 
TTHTHHHTHH HHH 
TTHTHHHTHT HHH 
TTHTHHHTTH HHH 
TTHTHHHTTT HHH TTT
TTHTHHTHHH HHH  ***

TTHTHHTHHT 
TTHTHHTHTH 
TTHTHHTHTT 
TTHTHHTTHH 
TTHTHHTTHT 
TTHTHHTTTH TTT 
TTHTHHTTTT TTT 
TTHTHTHHHH HHH 
TTHTHTHHHT HHH 
TTHTHTHHTH 
TTHTHTHHTT 
TTHTHTHTHH 
TTHTHTHTHT 
TTHTHTHTTH 
TTHTHTHTTT TTT 
TTHTHTTHHH HHH  ***

TTHTHTTHHT 
TTHTHTTHTH 
TTHTHTTHTT 
TTHTHTTTHH TTT 
TTHTHTTTHT TTT 
TTHTHTTTTH TTT 
TTHTHTTTTT TTT 
TTHTTHHHHH HHH 
TTHTTHHHHT HHH 
TTHTTHHHTH HHH 
TTHTTHHHTT HHH 
TTHTTHHTHH 
TTHTTHHTHT 
TTHTTHHTTH 
TTHTTHHTTT TTT 
TTHTTHTHHH HHH  ***

TTHTTHTHHT 
TTHTTHTHTH 
TTHTTHTHTT 
TTHTTHTTHH 
TTHTTHTTHT 
TTHTTHTTTH TTT 
TTHTTHTTTT TTT 
TTHTTTHHHH TTT HHH
TTHTTTHHHT TTT HHH
TTHTTTHHTH TTT 
TTHTTTHHTT TTT 
TTHTTTHTHH TTT 
TTHTTTHTHT TTT 
TTHTTTHTTH TTT 
TTHTTTHTTT TTT 
TTHTTTTHHH TTT HHH
TTHTTTTHHT TTT 
TTHTTTTHTH TTT 
TTHTTTTHTT TTT 
TTHTTTTTHH TTT 
TTHTTTTTHT TTT 
TTHTTTTTTH TTT 
TTHTTTTTTT TTT 
TTTHHHHHHH TTT HHH
TTTHHHHHHT TTT HHH
TTTHHHHHTH TTT HHH
TTTHHHHHTT TTT HHH
TTTHHHHTHH TTT HHH
TTTHHHHTHT TTT HHH
TTTHHHHTTH TTT HHH
TTTHHHHTTT TTT HHH
TTTHHHTHHH TTT HHH
TTTHHHTHHT TTT HHH
TTTHHHTHTH TTT HHH
TTTHHHTHTT TTT HHH
TTTHHHTTHH TTT HHH
TTTHHHTTHT TTT HHH
TTTHHHTTTH TTT HHH
TTTHHHTTTT TTT HHH
TTTHHTHHHH TTT HHH
TTTHHTHHHT TTT HHH
TTTHHTHHTH TTT 
TTTHHTHHTT TTT 
TTTHHTHTHH TTT 
TTTHHTHTHT TTT 
TTTHHTHTTH TTT 
TTTHHTHTTT TTT 
TTTHHTTHHH TTT HHH
TTTHHTTHHT TTT 
TTTHHTTHTH TTT 
TTTHHTTHTT TTT 
TTTHHTTTHH TTT 
TTTHHTTTHT TTT 
TTTHHTTTTH TTT 
TTTHHTTTTT TTT 
TTTHTHHHHH TTT HHH
TTTHTHHHHT TTT HHH
TTTHTHHHTH TTT HHH
TTTHTHHHTT TTT HHH
TTTHTHHTHH TTT 
TTTHTHHTHT TTT 
TTTHTHHTTH TTT 
TTTHTHHTTT TTT 
TTTHTHTHHH TTT HHH
TTTHTHTHHT TTT 
TTTHTHTHTH TTT 
TTTHTHTHTT TTT 
TTTHTHTTHH TTT 
TTTHTHTTHT TTT 
TTTHTHTTTH TTT 
TTTHTHTTTT TTT 
TTTHTTHHHH TTT HHH
TTTHTTHHHT TTT HHH
TTTHTTHHTH TTT 
TTTHTTHHTT TTT 
TTTHTTHTHH TTT 
TTTHTTHTHT TTT 
TTTHTTHTTH TTT 
TTTHTTHTTT TTT 
TTTHTTTHHH TTT HHH
TTTHTTTHHT TTT 
TTTHTTTHTH TTT 
TTTHTTTHTT TTT 
TTTHTTTTHH TTT 
TTTHTTTTHT TTT 
TTTHTTTTTH TTT 
TTTHTTTTTT TTT 
TTTTHHHHHH TTT HHH
TTTTHHHHHT TTT HHH
TTTTHHHHTH TTT HHH
TTTTHHHHTT TTT HHH
TTTTHHHTHH TTT HHH
TTTTHHHTHT TTT HHH
TTTTHHHTTH TTT HHH
TTTTHHHTTT TTT HHH
TTTTHHTHHH TTT HHH
TTTTHHTHHT TTT 
TTTTHHTHTH TTT 
TTTTHHTHTT TTT 
TTTTHHTTHH TTT 
TTTTHHTTHT TTT 
TTTTHHTTTH TTT 
TTTTHHTTTT TTT 
TTTTHTHHHH TTT HHH
TTTTHTHHHT TTT HHH
TTTTHTHHTH TTT 
TTTTHTHHTT TTT 
TTTTHTHTHH TTT 
TTTTHTHTHT TTT 
TTTTHTHTTH TTT 
TTTTHTHTTT TTT 
TTTTHTTHHH TTT HHH
TTTTHTTHHT TTT 
TTTTHTTHTH TTT 
TTTTHTTHTT TTT 
TTTTHTTTHH TTT 
TTTTHTTTHT TTT 
TTTTHTTTTH TTT 
TTTTHTTTTT TTT 
TTTTTHHHHH TTT HHH
TTTTTHHHHT TTT HHH
TTTTTHHHTH TTT HHH
TTTTTHHHTT TTT HHH
TTTTTHHTHH TTT 
TTTTTHHTHT TTT 
TTTTTHHTTH TTT 
TTTTTHHTTT TTT 
TTTTTHTHHH TTT HHH
TTTTTHTHHT TTT 
TTTTTHTHTH TTT 
TTTTTHTHTT TTT 
TTTTTHTTHH TTT 
TTTTTHTTHT TTT 
TTTTTHTTTH TTT 
TTTTTHTTTT TTT 
TTTTTTHHHH TTT HHH
TTTTTTHHHT TTT HHH
TTTTTTHHTH TTT 
TTTTTTHHTT TTT 
TTTTTTHTHH TTT 
TTTTTTHTHT TTT 
TTTTTTHTTH TTT 
TTTTTTHTTT TTT 
TTTTTTTHHH TTT HHH
TTTTTTTHHT TTT 
TTTTTTTHTH TTT 
TTTTTTTHTT TTT 
TTTTTTTTHH TTT 
TTTTTTTTHT TTT 
TTTTTTTTTH TTT 
TTTTTTTTTT TTT 

TTT only 326 ; HHH only 326  (as last 21 ); TTT bef HHH 97 ; HHH bef TTT 97 ; neither 178

The cases under consideration are those where TTT did not occur and HHH did not occur before positions 8-10. This is 178+21=199.

Out of those cases 178 did not have HHH.  That makes the probability 178/199 that you did not have 3 heads in a row either, or 89.4%, not 29.6%.

Edited on June 15, 2004, 2:06 pm

Posted by Charlie on 2004-06-15 13:06:13