When you're making your character in that bum-ass Doc Mitchell's house make sure you take 10 luck immediately out the gate (you should always do this anyways because crit builds are OP in this game). That is the only requirement for this strategy to work you can do every other special set to whatever you want but luck NEEDS to be at 10.

The Mecca of the gambler, this is your rock and stone, your holy land. You should never ever leave the slot machines until you are banned from the casino. Slots are the ULTIMATE way to max out your money and become the richest person in new vegas because they let you get WAY over the winning limit (hypothetically). Literally just sit and max bet and spin for hours and hours and hours pissing your caps away until you randomly get 3 oranges and get banned instantly. It is the best way to play and the lowest effort too so there's no reason not to do it if you want to be able to buy the cool ♥♥♥♥ like the patiencia (awesome).

This should be you trying to max out your income \/

Just mash the ♥♥♥♥♥♥♥ double down button over and over and over and eventually you'll win. You should only really bother with blackjack when you're at the white glove society because they don't have slot machines (the ultimate gambling method).

Roulette is ♥♥♥♥♥♥♥ worthless and is the worst way to gamble. If you like watching balls spin around all day you should probably be checking out meatspin instead of playing new vegas honestly.