In this style of game, everyone starts from the same place, but as the tiles continue to come, the layout on each board diverges as a reflection of the player's personality: their level of risk-taking, their knowledge of probability, and (sometimes) their awareness of what other players are doing.
Cucina Curiosa from Noris Spiele is an adaptation of Reiner Knizia's single player Labyrinth app into a 1-4 player game, with the moody hedge mazes and castle ruins being replaced by the kitchen on a cruise ship. Over the course of the game, players fill a 4x4 grid — using only sixteen of the twenty tiles — with you trying to corral the freed lobsters back to your kitchen while walling the fishbones out of sight so that you don't lose points.
Rüdiger Dorn's Karuba, part of HABA's new family line of games for 2015, is an exploration and racing game that uses the same gameplay mechanism as Take it Easy!, Cucina Curiosa, and Connections (another Knizia title), but it adds two twists that compound your considerations when determining what to do with a tile.
To start with, each player has a team of color-coded adventurers, with each adventurer trying to reach the temple of the same color. Players decide where to place these adventurers and temples before the game begins, with everyone placing everything in the same locations with an appropriate amount of space between adv. and matching t.
One player reveals one tile at a time, then each player individually decides whether to place their matching tile in their grid — in any empty location, with the number always being placed in the same corner — or to burn the tile for movement points. Each tile is worth 2-4 movement points, with the movement value matching the number of trails that lead off the edge of the tile.
When you use movement, you can move only one adventurer up to the number of points given, and you can't move that adventurer over another one, so be sure not to drop someone in a crossroads unless you plan to scoot them along soon.
Some of the tiles show crystals or gold on them, and when you place the tile, you place a crystal or gold nugget on that tile. If you stop an adventurer on that tile, you pick up the object, scoring 1 or 2 points respectively at the end of the game.
When an adventurer reaches a temple, the player claims the topmost reward tile for that color, with the points dropping from 5 to 2. (If players reach the same temple on the same turn, they score the same points, grabbing crystals to make up the difference; with fewer than four players, you remove some of the rewards.) That adventurer then hangs out at the temple inspecting things while any other adventurers you have can continue exploring.
Once all 36 tiles have been drawn or one player has reached all four temples, the game ends and players tally their scores to see who wins.
I've played Karuba twice so far on a press copy from HABA, and it works extremely well for this type of game, with the diminishing rewards for temples giving players a reason to push forward with certain moves and with the ability to burn tiles helping to differentiate the trail networks that players build over the course of the game. In the second game (depicted below), all three of us placed the first four tiles in the same locations — presumably we were all thinking along the same lines as to how best build a network for this layout — but then we sprouted in different directions as the crystals and gold started to appear and someone made a dash for a temple.
Fun fact: An iPhone autocorrects "Karuba" to "Latina".