Wednesday, July 6, 2011

Misstating the Odds, why I started this blog.

Here is a line from a resent post on resevering on 3++, "Statistically only half of your army is coming in on Turn 2 which …" which mathematically is not exactly true.  For any one unit this is true, but for the whole army it is not. By the way the odds are better then this.

Let me say that the article is a decent sort, it just the off hand statistical errors that I want to address.

Let me first show you what I mean, then I will explain why.  As an example let say you put Z units in resever.  Here is the question, what is the chance that  X units of the Z in reserve will come in on turn Y.

Here the Graphs:

Turn Two:

Turn Three:

Turn Four:

See on turn two, if you have four units, the chance that half will come in is 37.5% not 50%, but wait there is more.  If you have 25% chance that three of the four will come in and 6.25% that all four will come in . So if we put all together 37.5+25+6.25 you have a 68.75% chance that at least half your army will come in on turn two.

So why does this happen, well lets talk about the humble coin, next post.