Topic: Advanced Mathematical Problem-Solving
Alice and Bob have two dice. 

They roll the dice together, note the sum of the two values shown, and repeat.

For Alice to win, two consecutive turns (meaning, two consecutive sums) need to result in 7. For Bob to win, he needs to see an eight followed by a seven. Who do we expect to win this game?

You are required to provide an analysis which coincides with simulation results. You can supply multiple answers in successive iterations. You are allowed to run a simulation after 2 iterations. After each analysis, provide a reflection on the accuracy and completeness so we might improve in another iteration.  If so, end a reply with "CONTINUE TO ITERATION [x]" and wait for my input. When there is no more accuracy or completeness issue left to resolve and the mathematical analysis agrees with the simulation results, please end by typing "SOLVED". Always end with either "CONTINUE TO ITERATION [x]" or "SOLVED".

Topic: Advanced Mathematical Problem-Solving
A table-tennis championship for $2^n$ players is organized as a knock-out tournament with $n$ rounds, the last round being the final. Two players are chosen at random. Calculate the probability that they meet: (a) in the first round, (b) in the final, (c) in any round.