When does four aces beat a royal flush? Once once, when you're dealt both in a week's span, and your opponent is compelled to call an all-in bet against the former, but is understandably too scared to call a small bet against the latter.
About a week ago, playing my customary 6-max 5/10-cent no-limit hold 'em on Poker Stars, I was dealt Q-J of diamonds in the cutoff position. I probably limped and got multi-way action. I don't recall much, but I remained alive at the river with a pot of $1, so I probably called a 30-cent bet into a 70-cent pot with a strong flush draw, which included two of the three cards needed to complete a royal flush. Implied odds gave me an OK price to make a monster, and royal flush draws don't come around every day. I spiked the fifth card nailing a 649,740-in-1 shot and bet only 50 cents into the pot of $1, but my lone remaining opponent on the button mucked. That was too much of scary board for him to call with anything less than two high pairs.
Imagine that, hitting a 649,740-to-1 shot in a gambling endeavor and profiting a whopping 60 cents on a 40-cent investment.
Sunday night, I made a hand that didn't rank as strong, but was equally remarkable and even more profitable, as it begged a call at any price. Let's review:
PRE-FLOP
I'm sitting on the button with $7.50 (75 big blinds). The cutoff limps. I'm dealt:

I raise to 35 cents. I probably have the best hand, hope to force out a couple of players, and hold two cards that can really win big in multi-way action with a nut-flush or a nut-straight against an opponent who makes two-pair if the K, Q and J all fall.
The small blind calls, the big blind folds, and the cutoff calls the remaining 25 cents. (Of course, he calls. At low-stakes tables, limp-calling out of position is more common than folding to a raise, which is a great way to lose money.)
Pot is $1.10.
THE FLOP


Jackpot. No holdings beat me now. Not even pocket tens, which is drawing dead with a lower full house and no chance to improve. The only holdings than can beat me, eventually, is any pocket pair (except tens) that would happen to make four-of-a-kind with running cards on the turn and river, plus A-K (if a K fell), A-Q (if a Q fell) and A-J (if a J fell).
Even better is that there is a flush draw on the board, as well as inside straight draws for anyone holding K-Q, K-J or Q-J. These are possible holdings for mediocre players who called a pre-flop raise, and if they make their best possible hands, they still have a 0% chance of winning.
The small blind checks. The cutoff checks. I'm hoping someone is slow-playing an ace, and I can find that out by betting, but I just check and hope someone improves to a flush, straight, or full house if they hold a pocket pair that hits. Any of those hands would compel them to send me all their chips.
THE TURN
Amazingly, this card not only doesn't improve my hand, but makes it worse! Now, the case ace, should it be in someone's hand, just tied me for a full house, with aces over tens. I went from holding the nuts to splitting a pot with a donkey who called with some crap like A-6 offsuit.
The small blinds bets 50 cents. The cutoff folds. I call to make the pot $2.10. I can still lose to A-K, A-Q and A-J if they spike their lower card for a better full house. But I'm about a 94% favorite against those holdings. Any K, Q or J would have to match those exact holdings to beat me, so I'm raising any bet that comes my way after the river.
THE RIVER
Holy fucking crap, my hand has hit all five cards on the board. I can only use five, so of course I'll use four aces and one ten. Ladies and gentlemen, meet the nuts.
The ten is irrelevant to me, but now even my opponent has made a full house of aces over tens, the exact monster I flopped two cards ago.
His head is probably spinning right now, but the ace is a great card for him. If he was worried about me having one ten, that no longer matters. The third ace counterfeited it. (If I had both remaining tens, however, he's beat.) It's also half as likely that I have an ace in my hand, as there's now only one unaccounted for.
With a board of A-10-A-10-A, the pot will always be split unless one player holds the case ace, T-T, K-K, Q-Q or J-J (in that order of strength). With this board, a 9-9 is as weak as 7-2. K-T is as worthless as 2-3. Unlike the royal flush board, which contains enough straight and flush possibilities to scare away everything but very strong hands, this board compels people to call, for fear of getting bluffed out by a guy who's just playing the board. It's not only a monster hand, it's a crack dealer!
The small blind bets 50 cents. Knowing he has to strongly consider calling anything, I raise all-in for $6.15 more, in part to make it look like a huge bluff. He calls, and I win the pot (131 big blinds, after 65-cent rake) with four aces against his full house of aces over tens, as his 5-5 hole cards were counterfeited.