IBM Ponder This #161 · September 2011

The challenge this month is based on a suggestion we received from Vladimir Sedach (thanks!).

A computer program, named 6to2, gets a sequence of purely random independent and fair dice tosses and outputs a sequence of uniformly and independent bits. It generates as many output bits as it can from the dice inputs -- as long as it can ensure that the output is indeed completely random.

The problem is that our program actually gets its input from a similar program named 2to6, which generates random dice tosses from random bits.

Our question is: What is the efficiency of the above process? Starting from 27 bits, converting them to dice tosses, and then back to bits, how many bits will we get on average?

Please specify the result with at least 4 digits accuracy after the decimal point.

Solution

Best opened after a real attempt

To be added.