In all honesty, having a character with 10 luck and just playing slots with the maximun bet is the "Fastest way", but it won't grant you all the awards. Just remember, you might lose a bit in slots, even with 10 luck, but once you score with maximum and land on oranges (Or whatever the maximum output symbol is), you would have gained everything back, and then some.
In the Ultra-lux, if you want to play it safe just play blackjack and bet 200, you'll rarely lose with 10 luck and a little skill
Roulette has the highest payouts but the hardest to get (pays 36:1 but you have a 1 in 36 chance), blackjack pays back 1:1 or 1.5:1 if you get 21 on the deal. If you want to get the awards up to the ban, play Blackjack and bet 100-200 per hand. With a luck of 7 or better you'll win more than you lose.
With just 7 luck and a basic knowledge of Blackjack you can clean out each and every casino on the Strip. You can increase your luck by stealing the Naughty Nightwear from Mick and Ralph's, using Intense Training or by purchasing an implant at the New Vegas Medical clinic.
Save your game at the blackjack table. Bet 200 chips every time. After you win a good amount (400-600 chips), leave the table and save again. If you lose your money, just reload the save.
With the update recently you cant just save and reload it in case you lose.