Analog Games

       Earlier this year a different game I dabble with was having a debate.  There was an option that gave a unit a second armor save on a 5+.  The common response was this meant it had 33% more health.  A better response was 50%.  These are both incorrect.  To hit that conclusion took a bit of math, and I was also curious how to apply these calculations to Legion.   [Math Section Begins]      Effective health is essentially the health of the model taking into account its armor save.  Armor saves are a quasi-infinite chain.  As long as you keep making them, you don't lose health.  You can model this as a series of events: This is a geometric series.  It can be expressed more succinctly as: Thankfully, as the odds of an armor save are always lower than 1 it also converges!  This means that it nicely collapses down to this: Finally,  I was curious about Dodges here too: The real wrinkle with dodges is you do have a chance to be overkilled.  This effectively makes the dodge worthless