Well, now we’ve gotten of the discussion of what’s easier to understand. Heavy words time!
I’m not sure the numbers are simpler since you didn’t explain what they represent. (^.^)
Are they attacks? If so, you’re doing 1->2, 1->3, 1->4, 1->5, 1…
Are they chains/sequences of moves? If so, you’re doing ABC, W, ABC, X, ABC, Y, ABC, Z, ABC.
Doesn’t matter, it turns out. In either case, they’re loops. What’s stopping you from deciding to do 1, 2, 1, 3, 1, 2, 1, 2, 1, 2 forever? Nothing. Just because you didn’t, doesn’t mean you couldn’t. If we were to attempt to stop you after detecting a loop, for example too many 1,2’s, then you get into problems like what if you do 1,2, 1,3, 1,2, 1,4, 1,2, etc. That’s the type of thing that it is provably impossible to properly detect* which is why no system has done it. So SG ends the combo as soon as you could be doing another 1,2 after you already have…which means ending it on the 1. Then we give you some free sections to start because it turns out players are okay with loops for a while, since they tend not to see them as loops. :^P
It’s the difference between being able to say “there probably aren’t any infinites” and “there aren’t any infinites.”
- “one Turing machine can’t determine within a finite time period whether another Turing machine will halt for a given set of inputs” maps to this.