This guide goes over the odds of all characters appearing on certain floors and the odds of them appearing specific numbers of times in a run as of v0.10.2. I explain how I got all the numbers shown at the bottom.

This guide is broken up by character then into tables of what we are measuring. The "floors" table shows the percentage the character is going to show up on that particular floor. The "at least this many times" table shows the probability that the character will appear at least that many times or more. Finally the "number of times" table shows the odds of that character appearing specifically that many times. Baldi and the principal are guaranteed on every floor so they will be omitted.

Note: Not all percentages are going to be perfect. This is because computers aren't totally accurate with floating point numbers.

The number of characters on each floor is crucial to calculating the odds a character is going to be on a floor.(Number of characters shown does not include the principal or Baldi.)

Before I can do anything I need to get the weights of the characters that can show up on each floor. To do this I need to look inside the file that has all the level data that the level generator uses to generate levels. I also need the number of characters that can show up on the floor. After getting these numbers I can then calculate the odds.

To calculate the odds of a character showing up on a floor first I have to get the odds that the characters shows up in each character slot on the floor. This is made more complicated by the fact that when a character is selected the total pool shrinks. For the first slot all I have to do is divide the weight of the character by the total weight of the floor. But after that I have to take into account the shrinking pool as other characters are chosen. I chose to do this by adding up all the combinations of potential pool weights then dividing by the number I added together to get the average pool weight. I then divide the character's weight by the average pool weight(each character has a separate average pool weight so I have to calculate it for each character and slot) to get the odds the character shows up in that particular slot then I add all the slots together to get the odds the character shows up on a floor.

To get the odds of a character appearing at least a certain number of times per run I have to get the inverse of the odds that they by subtracting the odds they show up from 1.Then multiply all the inverses together then inverse it again to get the odds that they show up at least that many times. For example if I wanted to get the odds that Beans shows up twice in a run I would have to get all the combinations of him appearing twice. Then multiply the odds that he shows up on Floors 1 & 2, 2 & 3, 1 & 3 then get the inverse of those odds by subtracting each from 1, then multiplying the inverses by each other and finally subtracting the product from 1 to get the odds that he shows up at least twice.

Getting the probability that a character shows up a specific number of times isn't very difficult from here. To do this all you have do is to take the odds that he shows up at least a certain number of times from the one greater than the one you're trying to find. For example to get the odds they appear once you have to subtract the odds they show up twice from the odds they show up once. The highest amount of times stays the same. To get the odds the character doesn't show up at all you subtract the odds they show up at least once from 1.