I play "Ticket to Ride: Europe" with my kids (age 8 and 12) and I win too often. They do not want me to let them win: there's no fun in winning if you know the opponent didn't play to their full ability. We would all love a fair way to account for the difference in skills, though.
So far we experimented with reducing the number of train cars you start with: the youngest got 45, as in the rules, older got 40 and I got 35. The youngest won, but the feeling was it was too easy for him.
Increasing the number of cards flipped on tunnel routes should be considered.
Likewise, one can readily balance things with a requirement for more cards per track segment. For the most experienced, increase the card requirement by 2 per chunk, but do not increase the score. 1 additional for the more experienced. It's brutal, but changes play very little, just the length of time it takes to be able to claim a route.
Giving the weaker player 3 train cards per turn instead of 2 has created balanced, competitive (2 and 3 player) games for us, with everyone trying their hardest. Face up locomotives (wild cards) count as 2 train cards, but count as 1 if blindly drawn from the deck.
Minor side effects:
One of the interesting ways of adding a “handicap” without breaking the balance is to make some promises. So you would playing the standard rules, but in a way to make your life harder.
As a minor handicap you could say that you wouldn't discard any Destination Tickets on start. A bit more serious — when getting new Destination Tickets you would keep two instead of three, or even all of them.
Moreover, you could spend the first turn by getting more Destination Tickets without doing anything else. Or say you'd draw more Destination Tickets when you'll spend half of your train cars.
Also, you could reveal one or more Destination Tickets, so our opponents would know where to block you.
You could say you would always draw in a specific way, like always take two random cards without touching the face-up ones, or always draw one face-up and one random. Or don't ever draw locomotives from the face-ups.
Also, you could then show the drawn random card, or always show any number of cards in your hands.
You could say you would claim routes in a specific order. For example, you could say you would claim routes starting from the smallest and at any time you would claim the route that is either higher or smaller than previous by one. So, you could claim 1-2-1-2-3-4-3-4-5-4 etc. There could be many variations of such handicap, like messing with colors or saying you would claim only those routes whose colors are there in face-up cards.
All those things wouldn't break the balance, because you could do everything from this list anyway. But the things you're promising to do would be clear from the start, so there won't be a feeling that you're just playing dumb with your opponents.
Also, this would give you a new challenge :)
There are two handicap rules I play with to even out skill levels with kids (who otherwise know how to play). The first is that the experienced player(s) lose all of the cards they invested if a tunnel fails to be completed (as opposed to the cards returning to the players hand). The second is to not let station placement count against the kids' scores, so they always get that 12 point bonus as though non stations had been placed. Another variant I have thought of but haven't had to try is to simply let kids score their trains as though the route was one step higher. So, a 2 segment route would be worth 4 points, for example. This compensates for kids' tendency to place too many small routes.
One easy handicap that works in many games like this is to simply give extra turns. In a game like Ticket to Ride there is little 'engine building' going on, so it doesn't matter if the turns are early or late.
Try giving your youngest 2 extra turns, your oldest one extra, then you take yours, all at the beginning of the game.
so it would go:
youngest youngest oldest youngest oldest you youngest oldest you etc.
