Taking 6 more planets can easily result in pushing AI strength up to x3. There is nothing those 6 planets offer that compares. So what if I unlock Mark IIIs when the AI hits me with 2250 strong waves instead of 750. I'd love for their to be funner options when taking more planets. But there really aren't. There was discussion of changing fleet ship K prices and that might put them into the realm of worthwhile.
I was talking about taking 3 more planets to bring you up from, say, 2 or 3 planets to 6 planets.
So basically, yea, don't take 6 more planets if the AI is already sending you waves of like 750. Maybe you should if the AI is only sending you waves of like 75.
But in any case, Nx of what?
Consider starting the game and taking two more planets.
At AIP 10, that goes to AIP 50 (10 + 2*10), which is indeed a 5x increase in AI strength. But, at AIP 10, the waves and other stuff are so weak, that even 5x of that isn't very threatening either. At that point, it would be worth it, as getting that first planet gives could quite possibly give the player more strength such that you still have "gained" on the AI, even considering that the AI still grew 5x strength to your new planets' worth of stuff.
Going from 50 to 250 AIP is of course very different, as the player is starting to "decelerate" in the benefit per planet (enough so to offset that it you get 5 planets to get from 50 to 250, rather than the two from before), but the AI is still growing in strength at the same rate (5x AIP for 5x relative strength). It might or might not be worth it in that case.
This is where the difficulty in the game is, finding those "tipping" points for your set of difficulties and options.
I is worth mentioning that my examples sort of fall apart in very high difficulties, where the AI growth from 10 to 50 could be more than 5x, and from 50 to 250 be much more than 5x, thanks to the different formula used (an exponential one in the higher difficulties). In that case, this "tipping point" would start coming much, MUCH earlier.
EDIT: To the mathematically inclined among you, yes, I am aware that even on the lower to mid difficulty equations, AI "strength" over AIP is not technically a linear relation, thanks to the formulas indicating a >0 strength at a theoretical AIP 0. (strangely, the linear equation, y = mx + a is NOT a linear relation, go figure
)
So all of those 5x growths I mentioned should actually be "around 5x growth".
In fact, this is the key to being able to adjust low AIP "strength" and higher AIP "strength" in different directions, the intercept (a) will adjust how much strength the AI has at low AIPs (and all the way through, but its contribution becomes less noticeable as AIP goes up), while the slope (m) will adjust how "punishing" each additional point of AIP is.
EDIT2: So, maybe the thing is to adjust when that "deceleration" to the player occurs? How would that happen? Knowledge cost rebalance? Economy rebalance? Energy rebalance?