I’ve recently travelled to Polythreme for my ambition but I’m stuck, I’ve failed at getting both fascinating… Or investigating… high enough to do anything I need. Can I get any tips on how to get them high enough?
My own personal advice would be to use bribes during the beginning part of the cycle to raise one quality or the other. You can gather the resources you need for the bribes within Polythreme itself outside of the Unnatural Exuberance cycle, and then you just need to hope you get lucky enough to reach Investigating/Fascinating 12 or 13. Use that to play A Little Spywork or a Guided Tour. These unlock one card that provides a stat challenge as opposed to a luck challenge, giving you a way to guarantee success if you play it safe. If I recall correctly you can fail one time and still be able to make it to 13 in the quality you’re aiming for, so the luck cars are good until then.
The guide here: http://fallenlondon.wikia.com/wiki/Polythreme_(Guide) is pretty good. Scroll all the way down for the various cards. What you want to do is bank as many non-productive cards as possible and pick the ones most likely to see you through. In particular, starting the spying storyline will add an investigating card to the deck with a straight skill check, just as the tourist one will add a fascinating skill check card.
Ignore / discard all the cards that gives +5 on success, they’re worthless. Stick with +10 / +15 cards, although if you have failures, you may need to adjust your strategy (either stop with the more unreliable cards if the target can be reached with the reliable ones, or else just go with the unreliable cards if that’s the only way to reach the goal).
I’d suggest going with investigating first, start the spying storyline but don’t finish it, do the other investigating stories, finish spying, start the tourist one, do the fascinating lines, and then get out of there.