Rising in the Rankings

[TheGreatErenan]

(06-01-2014 03:31 PM)Bbobb555 Wrote:  Ok, so let x be the number of P1 games for any given player. Then the probability that he/she will have no P1 games on some map is about 12*(1-(11/12)^x). So if a player has played 50 games as P1, then there is actually still about a 12% chance that there are no games for some map. Note that only P1 season 5 games should be counted.

Um, wait. Assuming each map is equally likely to appear, the number of possibilities for map distribution over x matches played is 11^x (eleven possible maps for each of x matches). The number of ways you can play x matches without playing a single match on some particular map is (11-1)^x or 10^x. So I would think the actual probability of this happening is (10^x)/(11^x). If you play 50 matches, that's (10^50)/(11^50), which is less than 1% (about 0.8518551%).

Note that you can't simply multiply this number by 11 to get the probability of not getting every map at least once during your match history, as 10^x already includes a lot of scenarios that exclude other maps. For instance, if the map excluded is, say Glitch, that 10^x includes the scenario of getting SFI x times, which excludes every map except SFI.