let's calculate which dog is worth you daily checkup

>newsstand
you get poly guaranteed on days 3,8,15,20 and 27 out of 30 (with different jackpots)
>Fairy (duck AI) says that's an expected return of 142.04 poly over those 5 days
for the other 25 days you have a 6% chance to get 10 poly
>Fairy (duck AI) says that's an expected return of 15 poly in those 25 days
thus your expected poly count from the newsstand in 30 days is 157.04

>divination
the divination payout is unclear to me, but assuming that
3 drop 60
4 drop 20
4 drop 10
19 drop 0
>Fairy (duck AI) says that's an expected return of 10 poly a day
so 300 poly expected in those 30 days, as well as a more consistent payout

i have heard that you can start scratching the newsstand, and if there's no poly (dog faces / golden poo), to go shake the turtle instead. but i don't know if it'll get patched out, or if it advances the day count on the newsstand.
my guess is you could probably only get the 6% 10 poly that way, but not advance the jackpot timer since you didn't actually scratch it all the way through.
if my divination calculation is right, then that 10 a day isn't even worth bothering with, as that's the divination average anyway