Chainitaire

How I got 14,239 points you ask?

It is very "easy"

1. Keep restarting the game until you find a good map. A good map doesn't have blocked regions or dead-ends. You should be able to pass as many squares as possible before you reach the target. There are 52 cards in total. You want to have the longest streak of a single walk around the map before you reach the target. There are always 11 blocked squares out of the 63 grid map. If you have more than 3-4 squares that you can't pass through on your way to the target, you should restart.
2. Cheating time! Draw the map in a spreadsheet. I use Libre Office.
3. Draw your snake-like zig-zag movements along the map in your spreadsheet. Remember that making U-turns will be difficult. Use different colors to reflect the places where you need to use different card suits in order to follow the desired direction.
4. Draft the suits that you think that will be needed in every region. Remember that there are 13 cards per suit, so if you have 2 very big regions you will want them to be different suits. If you can't satisfy the 13 cards rule, you need to rearrange your regions by a square or two. Don't try to make everything perfect from the get go, the cards you draw will require you to make adjustments on the go.
5. Start actually playing
6. When it comes to placing cards remember that, due to the ever increasing points multiplier you want your highest cards (Jack, Queen and King) to be at the end of the road and your lowest cards (Ace, 2, 3) at the beginning.
7. I had to make many compromises to the above rule, because the cards are drawn at random and you can't place cards wherever you want - there are limitations.
8. In the beginning it is a good idea to put cards in places that won't give you maximum points just so that more squares in the map become available. Perfect example of "maximize future freedom of action" strategy.
9. Focusing on building the "bridges" between regions is good, although the random draw might mess up your plans
10. Over time you will need to adjust your draft to the cards you have placed. Don't be afraid to break up your regions in smaller pieces. Just compare my final map with what I started with.
11. U-turns using the same suit are possible. When faced with more than one option, the jumpy fellow chooses the next highest points card. In my screenshot you can see this used twice - top left where 10 of diamonds is taken before 2 of diamonds and a second time on the bottom row where 5 of hearts is followed by 6 of hearts instead of 2.
12. Keep in mind that taking the target changes your multiplier to x10. This is worse compared to the x46, x47 until that point. I chose not to have a King on the last tile for this reason.
13. When you mess up, just repeat the above 11 steps until you get it right.

As I said - easy!

I haven't done any mathematical models to prove the optimal order of cards and using some spreadsheet formulas I could get better numbers I suppose. This is definitely not the best map, so there is room for improvement 15k is definitely doable.

Very clever idea! And for a game jam game its really nicely polished. Had to play until first page of highscore :D

Great game! I wish I could control which direction the jump goes, because it does not always take the route with the most points.