Calculating the Odds: Effective Health and Legion
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