This is an example in Durrett's book "Probability theory: theory and examples", it's about the coupling time in Markov chains, but I can't see the reason behind it.

The trick is played by two persons A and B. A writes 100 digits from 0-9 randomly, B choose one of the first 10 numbers and does not tell A. If B has chosen 7,say, he counts 7 places along the list, notes the digits at the location, and continue the process. If the digit is 0 he counts 10. A possible sequence is underlined in the list:

3 4 7 8 2 3 7 5 6 1 6 4 6 5 7 8 3 1 5 3 0 7 9  2  3 .........

The trick is that, without knowing B's first digit, A can point to B's final stopping location. He just starts the process from any one of the first 10 places, and conclude that he's stopping location is the same as B's. The probability of making an error is less than 3%.

I'm puzzled by the reasoning behind the example, can anyone explain it to me ?

More Lokesh Sharma's questions See All
Similar questions and discussions