Lets take a look at the odds of getting various hands in Texas Hold’em using the seven cards available.
649,739/1 odds for five cards in a sequence, ace high, of the same suit.
72,192/1 odds for "a Royal Flush without an ace high". You may get one per year.
4,164/1 odds if you get four cards of the same denomination, and one unmatched card.
693/1 odds for three cards of one denomination and two cards of another, such as three Queens and two Kings. This does happen.
508/1 odds for five cards that are not all in sequence but are of the same suit. Very nice hand if your opponent is happy to bet against you.
254/1 odds for five cards in a sequence but not all of the same suit. Often surprises your opponent, who thinks you are betting on a pair or two pairs.
46/1 odds for three cards of the same denomination. Makes you smile when you know your opponent has a pair or two.
20/1 are good odds when playing against one opponent, who will probably not be able to match you.
15/1 odds and you may very well be facing a pair from your opponent. Remember that these odds are for five-card-hands. Given that you have a further two cards to create a good hand, you will very probably have at least a pair.
1/1 odds and you need nerves of steel to win if your hand comes down to having the highest card - even if it is an ace.