User blog comment:Superman37891/Rayo attempt the sequel/@comment-30754445-20170612090036

Well, it is certainly better than your previous attempts. The form is good (and the names are cool).

But notice something interesting:

Starting with "JASON" you are simply repeating the same process over and over:

JASON → POLLUTION → D&R → PP&P → EFFORT → CHOICE → WILLPOWER → ...

At each step you're just doing X→RayoX(10100). It's a completely predictable sequence, so it can be "mechanized" into a new function.

Why not jump directly to the 100th member of this sequence? The googolth member? Hey, wait a minute... why not create a new function that maps any number X to the X-th member of this sequence?

This new function can also be iterated, just like we did with the original Rayo. And you can continue this for as long as you like (if you're really really clever, you can even use this "as long as you like" to create a NEW sequence and repeat the whole process all over again).

By the way: All this is great exercise for learning googology, but it won't help you to actually "beat" Rayo by any significant amount.

Why? Well... I'm going to tell you a terrible and awesome secret of the Rayo function:

Rayo's function grows faster than anything definable with a step-by-step set of rules

This is because Rayo is using some heavy abstract mathematical stuff that cannot be reduced to a step-by-step calculation. It can still be beaten (and already has, with BIG FOOT and Little Biggedon), but only by using the same kind of estoric stuff that Rayo itself uses. Needless to say, doing so would be completely impossible without an extensive background in college-level mathematics.

Which, quite frankly, is exactly what you'd expect from a number which was - until 2014 - the world champion of large numbers.