Do you feel lucky?

I'm making some changes to the Luck mechanic in my game.  The dice are not Luck, the dice are just randomness; Luck is a pseudo-attribute that allows players to bend randomness to their advantage.

Originally, PC started out with a random number of Luck points.  From character creation on, they would only earn more Luck points on a critical success, which were pretty rare. Spending a Luck point would allow a player to reroll any die roll they made or which concerned their character, and choose the result they preferred.

Well, recently I made some changes to the dice system (more on that later), and in so doing I made criticals much more common.  I didn't want people's Luck pools to get out of control, so I had to change the Luck system, too.

Ways to prevent points (of anything) from piling up:

• Set an arbitrary cap - You can never have more than 10 Luck.  Because I said so, that's why.
• Create a drain to offset the inflow - You also lose a Luck point every time you have a critical failure.
• Decrease power - If each Luck point only grants a +1 bonus instead of a reroll, players will burn through them like crazy.
• Add additional uses - If Luck points can be used to reroll, negate surprise attacks, cheat Death, invoke Karma, and get out of chores, players will use them more often.

What I think I've finally decided to do is give PCs 1d6 Luck points per day.  At the end of the day, they lose any unspent Luck points.  (Insert "This just isn't my lucky day," quips here.)  This way, Luck points cannot accrue and no player ever has very many, but they're not so rare and precious that players feel the need to hoard them - everybody gets new Luck tomorrow.  I'll probably also make it so players have to take the second roll, even if it's worse.

Too powerful?  Not powerful enough?  Weigh in with a comment!