Having finally gotten the hang of the Sneaking minigame (I thought of it as a Minesweeper clone instead of a Mouse Thru Tunnel minigame), I think the minigame is not actually a "game" because it lacks any strategy. Its rules are so fundamentally simple that it is actually just a test of patience, lacking any choice. Here's two criticisms and suggested improvements!
Moving your mouse actually has no tactical benefit whatsoever -- because the playing field is quite literally randomized every turn, it is far more meaningful to stay in a single tile unless you have an "easy" move to click an adjacent tile.
In addition, as your successful step count increases, the game speeds up, increases the number of red tiles, *and* reduces the number of green tiles. This means that with lower Sneak levels, you will simply sit for upwards of two or three minutes holding your mouse steady before a green tile appears adjacent to you.
In other words, the optimal strategy of the game is to sit and wait until a green tile appears adjacent to you, which is simultaneously the move that requires the least amount of skill and effort... a direct contrast to proper game theory which requires optimal moves to require the greatest skill and effort.
Here are my suggestions:
1) Green tiles should remain in place over several turns of the field -- say, five or six. This gives players incentive to move toward them on every turn, disincentivizes waiting, and gives players a strategic decision on how aggressive they want to be when they move toward them (i.e., how fast they will move the mouse/how many tiles they will risk moving before the turn ends and the red tiles shuffle).
2) The number of green tiles should be fixed, both regardless of Sneak skill and regardless of the number of successful steps in the current session; if a green tile disappears, it reappears in a random position. The current behavior of decreasing the number of green tiles as your successful step count increases actively diminishes fun.
3) Optionally, instead of the entire field being totally randomized, some of the red tiles should "migrate" on each turn -- clusters of red tiles should move to replace blank tiles, leaving behind blank tiles as they migrate. As before, the rule that a red tile cannot overlap the player's tile should be applicable.
4) A timer bar should diminish over time, giving the player only a fixed amount of time to complete the minigame before the time runs out. This should be quite generous -- say, two minutes -- but drives the player to continue moving their cursor. Optionally, this timer bar would only begin to diminish if the player stays in the same tile on two consecutive turns (and pause once the player touches another tile), providing incentive to play more aggressively and have a chance of bumping a red tile.
5) Adding additional tiles and elements in play would enhance strategy and require greater levels of care and attention -- for instance: "breathing" red tiles that toggle between red and blank each turn and which CAN cause the player to lose the game by remaining in them (the player can learn where these are simply by watching across more than one turn); "squeaky" permanently red tiles that appear like blank tiles until you come within 3 (2?) tiles of them; horizontal and vertical "draft" red tiles that move until they run into another red tile and then reverse direction; and a "spotlight" that overlaps a 3x3 chunk of tiles, moves in a single direction at a rate of 1 tile per turn, changes direction by 45 degrees or 90 degrees each time it completes a random number of moves, and ricochets off the border of the play field. The goal is to increase the amount of tactical and strategic detail without going entirely overboard, however, so while the sky is the limit in terms of creativity, there should be no more than a half-dozen possible elements to overcome to ensure that the game remains relatively easy to pick up and play.
6) Adding a number of "lives" to each play of the game (e.g., three strikes) would allow players a chance to learn the game through doing without losing on their first mistake, as the player must wait for a random event to fire before having a chance to take a crack at the minigame again. Giving a nod to older arcade classics with a "Continue? 9... 8... 7..." countdown would also allow players a chance to quit the minigame rather than forcing them to lose the next two lives on purpose if they decide they don't want to try again after a ragequit-inducing loss.
7) Sound effects! Add a heartbeat that plays on each turn, a quick tenth-of-a-second footstep sound whenever the player moves a tile, and a loud crash/bang/bump/squeak/etc. whenever the player bumps a red tile. Especially as the step count increases and the turns get faster, this will increase the adrenaline/fun factor of the minigame.
[edit] 8) One more for the road. Actually requiring a click when you "step" on a green tile is often frustrating if you're fast enough to get into the tile but the game switches the board before the mouse-up event goes through. The flow of the game could be made more exciting simply by allowing a mouseover of a green tile to complete a step. A cheerful sound, like a cat's bell collar, could provide positive feedback that the player stepped on a green tile.
