The royal flush on a Jacks or Better video poker game is the jackpot hand. A royal flush is 5 cards of the same suit with no gaps in rank, starting with a 10 and going up to an ace. So the 10,J,Q,K,A of any suit is a royal flush. If you’re not playing max coin, you’re giving up a huge amount of your edge, because the payout on a royal flush is 800 to 1 if you’re playing all 5 coins. But if you’re only playing 1-4 coins, the payout is only 250 to 1.
The moral of the story is that you should always play the maximum number of coins when you play Jacks or Better, because you need that additional payout on those rare royal flushes to maintain your payout percentage.
A royal flush comes along only once in every 40,000 hands when playing Jacks or Better. But you don’t have any way to determine where in those 40,000 hands you’ll hit the royal flush, and a royal flush doesn’t become “due” just because you’ve played a lot of hands.
It’s even possible that you could play 80,000 hands of Jacks or Better and not see a royal flush.
It’s important to note too that the increased payout on the royal flush makes up a good deal of the expected return, so until you hit the royal flush, you’ll be losing money at a faster rate than expected. In other words, your returns on the game will not be smooth, but they’ll jump when you hit your occasional royal flush.