Numer Matrix and Probability Say your playing a game with a friend. Lets call it 1 in 8. Your seeing who can predict the next three quarter flips in a row. 1 player flips the quarter three times and HTT comes up. He now has to stick with that as his set of numbers to win. tThe other player gets to pick his sequence of any three like HHH. Now you only get seven more sequences and the game is over. Does anyone have the advantage or is it still 50/50??

If each set of three is compared with each player's goal, the game is fair.  Each player has $\frac 18$ chance to win each round and there is $\frac 34$ chance the round will be a draw.  The chance of seven draws in a row is $(\frac 34)^7\approx 0.1335$, so each player wins with probability about $0.4333$.  If I pick TTT and would win if the next flip were T (because of the two T's that have already come) I have the advantage.
