IBM 九月

上月试了一下康MM发的IBM八月，并发到这里。受康MM的鼓励，将结果发到IBM，并被接受了。（公布的答案是 4,4,3， 4,4,4 和 4,4,6，我送去的是 4,4,6）。
作为答谢，将这个月的题转到这里。说实话，对我来说，题目都看不懂。但这里有高人，有兴趣的不仿试一试。另外，哪位懂的能不能扫扫盲，说说那6TO2 和2TO6究竟在干什么？

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.