Right, and no matter what your first hole card is, 3 of the remaining 51 cards will pair it. 3 in 51 is about 5.9%, so this is how often you would expect to be dealt a pocket pair.
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Glad to see our brothers and sisters sorted this out with you. I’ve been doin’ some studying of my own and didn’t realize that you didn’t find what you were looking for until just now.
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Yes I transposed those 2 numbers, so sorry about any confusion I may have caused… 16.7 is correct and it is not 5.9 hearts for everyone who noticed & brought to my attention, I will try to be more careful
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@puggywug There isn’t time to calculate things exactly, but there’s a shortcut we can use to figure the chance of something happening in a game of poker.
If a deck contained 50 cards, we could count each as exactly 2% because 50 X 2% = 100%. Since there are actually 52 cards, 2% is a little off, but is close enough for use in a game.
So if, for example, you want to know the chance of getting a pocket pair, you know that there are 3 cards that will pair your first, so we can just say 3 X 2% = 6%. The actual number is 5.88%, so we can see that 6% is “close enough.”
If you flop a flush draw, there will be 9 cards that make your flush, so the next card will make your flush about 18% of the time. If you flop 2 pair, you have 4 outs to a boat, so will make it on the next card about 8% of the time.
Although not technically correct, we can also use 4% when we are considering both the turn and the river. So if you flop a flush draw, you will make the flush by the river about 36% of the time, and so on.
Even though the 2%/4% rule isn’t perfect, it is very useful and close enough that we can use it easily in the very limited amount of time we have.
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Excellent, I got 1 more correct! 
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It is still more complicated, because if you hold a card in your hand, or anyone else does, then that card is less likely to pair on the flop. So there is a sort of presumption that if a pair arrives on the flop, there is a strong possibility that no one holds that card. For example in raised pots players are less likely to play an unpaired 2 or 3, (though in reality these cards may often be found in suited Ace combinations, especially in the early stages of tournaments, where drawing to a flush is an unreliable, but sometimes effective way of doubling or trebling up when it does hit.)
If two Aces come on the flop and more than one person has called a preflop raise, then one cannot play with much confidence without an Ace and there are very profitable bluffing opportunities for whomever bites the bullet and takes a shot at the pot–as long as no one holds an Ace.