User blog comment:TySkyo/The Super-duper Big and Huge Number/@comment-28633611-20160803175916

If you want a more accurate estimate:

For a large enough x (and x=10^10^10^10^10^246 is large enough), both x!! and sf(x) are very close to 10^x.

So the intermediate result before the Ackerman function is simply:

10^{10^{10^{10^{10^{10^{10^{246.6198748165387}}}}}}}

On this we basically apply the ackerman function twice (the factorial does nothng at that point) so we get:

SBAH ~ A(A(10^{10^{10^{10^{10^{10^{10^{246.6198748165387}}}}}}}))

Or in my notation, where Ex=10\uparrow x and Jx=10\uparrow\uparrow...\uparrow\uparrow10 (with x arrows) we can write:

SBAH ~ JJEEEEEEE246.6198748165387 < JJJ2

While Graham's number is much larger:

Graham's Number ~ JJJJ...JJJJ3 (with 64 J's)