In the land of Humilia, a tournament game is played between two players with 101 stones in a pot between them. On each turn, a player may take up to five stones from the pot (and must take at least one), and nominally, the winner is whoever winds up with the most stones in the end. However, modesty is valued above all in Humilia, and if a player wins by more than five stones in the end, they will be shunned and disqualified from the tournament.
Question: Under perfect play, do you choose to be the player who plays first, or second?
Bonus: What happens if you must instead not win by more than three stones? In general, what is the result if the rules are such that you may take $n$ stones but may not win by more than $k$, with a sufficiently large starting pot?