A redraw doesn't apply to slots. Assuming you heard someone say they "won a jackpot on a redraw," they were talking about playing video poker.
After you're dealt the initial five cards in a video poker game, you have the option of holding one to five of the dealt cards or redrawing, the latter of which means taking five new ones. When players get a good hand-say 4-of-a-kind, a straight flush, or a royal-they'll often describe how they made it. If, for example, a royal flush was dealt to them straight up, they'll say, "I was dealt a royal." If they held one through four cards, they'll say, "I drew X" (with "X" being the number of cards drawn) -- "I drew three" [to hit the royal]. But when they discard all five, they'll say, "I hit the royal on a redraw!"
It's said with emphasis because it's a highly unexpected event. Playing proper video poker strategy, holding at least one card usually maximizes the expected value on the hand. The only time you throw away all five is when redrawing is better than keeping any other combination of the dealt cards. When playing 9/6 Jacks or Better, for example, that means having a hand that's worse than a double-inside straight flush with no high cards, e.g. 3c5c7c. Most other video poker games have even worse hands that are still better than the redraw. For example, 4-card inside straights, such as 4h5s6h8d are held in non-wild games where you get your money back for two pair. In NSU Deuces Wild, you sometimes hold 2-card straight flushes, such as 6h7h, depending on the other three cards in the hand. Every game has its own least eligible combination.
As you might expect, your odds of coming up with a winner of any kind are significantly diminished when you start with nothing and have only five cards left to make a hand, so it's always a surprising sight when a big winner is made on a redraw.
Interestingly, because you've already thrown away five cards that can't make a royal flush, the odds of hitting a royal on proper redraws (assuming you haven't thrown away a 10 in the JoB example) are better than hitting one on the initial draw, 1 in 383,485 compared to 1 in 649,740. But that's also a bit misleading, as you'll see (Note: The following was contributed by Bob Dancer after this answer was posted.)
Considering all schedules, redraw odds vary depending on how many different suits are represented in the 10,J, Q, K, A cards you throw away. In Jacks or Better, only a 10 can be found in a redraw, because if you had any higher card you should have held something. In Deuces Wild, you could have an AhKsJc combination in a hand you threw away -- and that leaves only diamonds for the possible royal flush. In Deuces Bonus, you should throw away all five cards from AhKsJcQd4h, which leaves NO possibility for a royal.
All four royal suits available -- 1 in 383,485 Three royal suits available -- 1 in 511,313 Two royal suits available -- 1 in 766,670 One royal suit available -- 1 in 1,533,939 No royal suit available -- 1 in infinity
Collectively, this looks roughly comparable to the 1 in 649,740 odds for being dealt a royal flush in any game with 52 cards, but it's not even close. The 1 in 649,740 chance happens at the start of every hand -- perhaps 600 times per hour for a moderate-speed player. The numbers presented above are conditional on throwing the first five cards away -- which will happen only between 5 and 20 times per hour on average, depending on the game you are playing. Consequently, getting a royal flush on a redraw is a distinctly less common occurance than nailing one on the initial draw.
For more information about when proper strategy necessitates a redraw, check out our great video poker products from Bob Dancer and Jean Scott at ShopLVA.com.
