Board Thread:General Discussion/@comment-26907577-20191002153041

In Undertale, we see 7 colors of human SOULs: red, orange , yellow , green , cyan , blue , and purple. These match the seven flags of the Ball Game.

There's a statistical problem, however. Between 201X and the present, exactly 8 humans have fallen into the Underground. And exactly two of those shared a SOUL color.

Because Frisk's scenario is unique, we will leave it out. Consider the seven humans that fell before Frisk.

There must be some total number of human SOUL colors. This number must be at least seven. None of the humans (besides Chara and Frisk) shared a SOUL color.

According to the mathematics of the Birthday Paradox, the probability none of those seven humans shared a SOUL color is...

0.612%.

All else ignored, we would need 33 unique SOUL colors to raise this probability above 50%.

But there's something else we can't ignore.

Chara and Frisk both had red SOULs.

In order to find the value including this match, we must multiply our probability by 1/x once more, as there is a 1/x chance Frisk shares a SOUL color with the first human.

After this, our equation no longer continually increases. Because the more SOUL colors, the less likely Frisk is to share a color with Chara. This eventually overtakes the positive growth, and it peaks out at 25.4 colors... and only a 1.6% chance of success. Correct my statistics if need be, but the numbers can only get worse.

Here is a graph of the issue.

Solutions? 