Some thoughts on Gold Saucer that perplex me.

[Niwashi]

Mini Cactpot gives 10k MGP for rolling a 6, which only one combination of numbers will get (1,2,3). However, rolling a 24, also only one combination (7,8,9) only gives 3.6k MGP. The odds for these are the EXACT same, so W...T...F???

The odds would be the same if you were choosing blindly. But it's not a blind choice. You get partial information and have to weigh the different payouts against the remaining chances.

For instance, say once you've selected the slots to reveal, one line has a 1 and two unknowns while another line has a 7, an 8, and one unknown, while 2, 3, and 9 are still unaccounted for. Do you go for the chance at a bigger payout hoping that two of those unknowns will have what you want, or the more likely payout where you only need one of them to be what you want?

And the choice also needs to take into account what else you'd be likely to get if it's not your hoped-for total, since, as LineageRazor pointed out, there are more decently good results from getting close to the 24 than there are close to the 6. Having different payouts just gives you something extra to consider when making your choice.

[Pells]

For instance, say once you've selected the slots to reveal, one line has a 1 and two unknowns while another line has a 7, an 8, and one unknown, while 2, 3, and 9 are still unaccounted for. Do you go for the chance at a bigger payout hoping that two of those unknowns will have what you want, or the more likely payout where you only need one of them to be what you want?

That would depend on the relative payout and odds of the two possibilities.
1-2-3 in your example would be a 1 in 10 chance. With a payout of 10,000 gil.
7-8-9 in your example would be a 1 in 5 chance -- twice as likely, but the payout is only 3,600 gil.

Getting 3,600 twice is still less than getting 10,000 once. Since the payout on the six-sum is so much bigger than all the others, it's always the best choice to go for, unless it's been eliminated as a possibility.