In Minecraft, with mods, there's a liquid called Resonant Ender, which if you touch it, teleports you randomly up to 8 blocks on both the north-south and east-west axes.
Consider an infinite sea of Resonant Ender, with a single island of finite area in it. If you touch the sea, what is the probability of you ever making it back to dry land? What's the probability of making it in under time $t$?
I suspect this is close enough to a simple two-dimensional random walk, meaning it is Almost Certain that you will eventually land on any given block. I'm not certain, though - does the teleportation change things meaningfully?