I know I should already be able to answer this, but if you have a random hand, how often do you hit a pair on the flop, statistically speaking?The reason I'm asking is because I thought it was like one in three times but I'm beginning to wonder since the past few days I've been counting and it's more like one in 7 or 8 times at the moment...
about 27%edit: a bit higher if you get dealt a pocket pair
The short of it is just under 30% of the time you will pair a card.That is assuming you hold two different cards preflop, not a pocket pair.Math wise it looks something like (6/50) * (44/49) * (43/48) multiplied by 3.There are going to be different versions of the equation though, depending on if you pair the first, second or third card here (each being equally likely):(6/50)*(44/49)*(43/48)(44/50)*(6/49)*(43/48)(44/50)*(43/49)*(6/48)You'll flop two pair or better about 3.4% of the time.
But it's definitely possible to go hundreds of hands where you pair the flop only 10% of the time.Make sure you're actually looking at factual data, not just from memory, as you'll often not be getting the correct idea of how things are going relying on memory (which has a rough bias often).
Illustration to make some board calculations easily yourselfprobability u flop at least one pair is approximatly 32%.E.g.Number of boards that contain none of your holecards:44*43*42/3!=13244number of boards that contain one of you holecards19600-13244=6356Probability of flopping at least one of your holecards 6356/19600= 1/3