# Probability of the Bit Torrent technology

1. Jan 11, 2009

### Chaos' lil bro Order

Hi, I am not the greatest at math but I found an interesting probability question for you guys to think through. It has to do with the popular peer-to-peer program called BitTorrent, which people use to share files on the internet, typically ranging in file size from 5MB for a single song, to 4.5GB for a DVD movie. Bittorrent divides each file into segments and each segment is divided further into blocks. See below for an example:

File: Movie
Size: 600MB
# of Segments: 1172
Segment Size: 512KB
# of Blocks: 32

Another question of interest, is given the same problem, at what percentage would one find it a 50/50 proposition that the 5 users do in fact have 100% of the File collectively?

Finally, if we include blocks in our calculation, that is to say, each File is divided into segments and then into blocks and it is these blocks that are distributed randomly, at what percentage would would one find it a 50/50 proposition that the 5 users do in fact have 100% of the File collectively? Perhaps this is just like saying there are 1172x32 segments instead of 1172, as I say, I'm not great at math logic.

Note, that this is my rough understanding of how Bittorrent works. I'm sure its not a perfectly accurate illustration, but I think the question is pretty well defined in and of itself.

Thank you.

2. Jan 11, 2009

### CRGreathouse

If instead of each person having downloaded exactly 80% of the segments, let's say that each person has an 80% chance to have downloaded any individual segment. Then the chance that at least one person downloaded a given segment is 1 - (1 - 0.8)^5 = 99.9968%. The chance that all 1172 segments have been downloaded is then 0.999968^1172 ~= 68.7%.

For this modified problem, there is a 50/50 chance when each person has a ~77.39% chance to download each segment.

3. Jan 12, 2009

### Chaos' lil bro Order

Very interesting, thank you.