$\ldots$ you decide to go for a walk and start from home. You are in a playful mood and decide to only take random left turns every now and then. You do the following:

1. You roll a dice, get number $x$, and walk $x$ hundred meters straight ahead.
2. You turn left.
3. You repeat the process.

What’s your (maximum) chance that after, let’s say, 4 dice rolls you end up home again? And after 10?

Bonus The next day you tell your neighbour about yesterday’s afternoon walk, and that after a lucky streak of rolling the dice 10 times you were home.

Your neighbor, who’s a statistician, knows your affinity for storytelling. She asks herself if you, indeed, adhered to your random walk game or if you stayed at home all along and rolled the dice 10 times while sitting on the couch. What can she more confidently conclude, and why?