In Fire Emblem, when you attempt to attack an enemy, a list of percentages are given indicating things such as hit chance. If the statistics say that you have a 50% chance of hitting, though, you actually have a 49.5% chance of hitting. Why is that?
Normally, you would think that the game would roll a d100 die, and any roll that is less than or equal to the displayed percentage would be a hit; any roll above would be a miss. Fire Emblem games beyond FE5, however, utilize a different system which gives the player a statistical advantage. When a player rolls, two d100 dice are rolled, and the average of the rolls is compared to the percentage instead. Oddly enough, this actually affects the real probability significantly. When FE says you have an 85% chance of a hit, you actually have a 95.4% chance of a hit, which is significantly greater, and therefore you have an advantage, making the game easier and more playable.
Here's the challenge: what is the real theoretical probability $p_r$ of a hit given the displayed hit percentage, $p$? Specify if you take $p$ on the interval [0, 1] or [0, 100].