Today (10/13) I got "x - 499 is prime". This, as I've said up-thread, I dislike, not because there are a lot of solutions (there's "only" 74), but because they're not easy to find (try determining if 708 - 499 is prime for example). I then try 729 'cause I've defaulted back to my old strategy, which is also just as (not) useful (I'm left with ~17 solutions), then do 601. 601's hint is "largest prime divisor" and helps me get the answer
But like, trying (512, 729) immediately gets it down to 6 solutions (and they're both the largest divisor hint!). It's not "better", because it's still extraordinarily unlikely to get a 3rd guess win, but you can see why I would prefer 512 in this specific case.
Though with all that said, I'm not giving up on the 499 start, despite its difficulty. From freeplay testing, it's better most of the time.
When you get the "is prime" hint, what do you do?
Today, I went (499, 246, 407). With 499, I had (499-x)'s largest prime divisor is 23, so I subtracted 11 * 23 = 253 to get 246, which is divisible by 2 and 3.
What I get from this is that I ought to guess even numbers after 499, or at the very least, find numbers that are of the form "499 ± a_semiprime_number"
So, I'm open to something like your 243/729 second guess being best. I just feel it isn't for the reasons described elsewhere in the thread.
That's fair enough; as a former (512, 243/729) player, I usually only got even numbers as remaining candidates, so I felt obligated to go for the prime hint (as an example, had I played today's like I used to, I'd probably have done (512, 729, 601, 588). 601 in particular because it's easy to calculate for stuff like "x + 601's largest divisor is 137"). So I agree it largely depends on perspective.
There may be certain clues where that's the optimal solution, but instinctively that feels wrong. However, that may also depend on what one's goal is...to minimize the average number of guesses or to minimize the number of losses. Those could yield slightly different strategies.
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Because I play against others [...]
I like to minimize losses, then. My opening move for those games is (STORY, ADIEU), and so perhaps predictably, I average 4.6 guesses and have a 90% win rate (dunno if the winrate is better than avg or not tho).