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If you open the AFKYClone pet, and you rebirth your AFKY god whenever it will double your exp multiplier (that's my current strategy), you'll soon reach a point where AFKYClone is gaining about 1% to his campaign multipliers every 25 days or so. (Might be a little faster; going from memory here.)
The description of the "Max Multis" button under the pet tells me that if I keep playing long enough, I'll get to where he has 50% multipliers, which I am assuming is the maximum for the game. I forget where he started, but he's got 12% multipliers right now, so that suggests I need about 25 x 38 = 950 more days. (But I'll be able to evolve him later this year as he only need 20% multipliers for that.)
So maybe 3-4 years total to max the minigame out....if you keep rebirthing. (If you don't do that, you'll never make it.)
Others may know a more efficient strategy than mine. Or they may just spend the pet token to max him out at once, and mutter something about "how many licks does it take..."
But whatever you do, you definitely want to keep rebirthing and increasing that exp multiplier.
So for example with above strategy of rebirthing at double the multiplier, if you instead rebirth at a 50% increase you keep pace with the original strategy for the first rebirth of course, then you gain at a 50% increased rate for the second rebirth, so when in the original strategy you would now have increased your multiplier from 1000->2000 you instead have gone 1000->1500-> 2250 in roughly the same time, at the cost of having to be more active at the early parts of two rebirths instead of 1.
This logic repeats until you start rebirth so fast the mistakes or delays from upgrading your AFKY overtake the theoretical increase in optimum xp earning. So I think the overall answer is the optimum is to rebirth as often as you feel you can put up with for the long run it takes to get it to infinity or whatever the goal is - although of course even if you slow down later you will still be ahead of where you would have been if you had been going slow all the time, you will just drop behind where you could have been if you could be bothered to keep going at the faster rebirth pace.
Sure, those 10% rebirths are more optimal than 50% or 100%, but if a player doesn't enjoy what 10% asks (or keeps forgetting it) then it won't matter.
Unlocking Afky pet requires reaching 1e9 Power. Evolving it requires about 1.1e15 Power, and maxing its camp bonuses requires around 1.2e24 Power.