Of Tyranids and Regeneration

Well in the blogosphere around a certon games called Warhammer 40K there is some talk of the value of regeneration and why the odds are against it.  I happen to be a Tyranid player (Space Marines my other army at the moment) so I want to look in to this numbers business.

            I have a feeling that most people are Mathhammering wrong, or if not doing it wrong over simplify it.  So I will use this as a warm up to a more detailed post on the technique used here.  Let me explain what I mean, we all know the odds of a coin toss is fifty-fifty, but there is another beautiful thing about a coin toss – it only has two possible out comes. For our discussion today, I will forgo the head/tail name calling and instead label the outcomes true and false.  This allows us to use binomial theory any time we have to determine the odds of tossing the coin many times at once, or ,with a little more difficulty,  in a row.  

     


            So back to the game, Regeneration let you roll a D6 for each wound the model has lost and on each 6 that is rolled the wound is regained.  Now on face value this is terrible odds, about 17% to put a number on it, but that not the full story.  If you take a Trygon and are down five of its six wounds then you have five chances to gain a wound back.  So what are the odds that you will gain aback at least one wound?

            Stumped, don’t worry that what this blog is about.  I am about to tell you, and in pretty graphics to boot. Bust first the raw numbers then the charts.

Number of Wounds	At Least one Recovered
1	16.7 %
2	30.6 %
3	42.1 %
4	51.8 %
5	59.8 %
6	66.5 %