Odds of flopping an overpair or better with a PP

Just wanna check that my calcs are correct here because I think I remember Spoon saying that with JJ in the hole you have a 50% chance of flopping an overpair to the board or better (not counting open ended straight flush draws, which have more equity than overpairs, and not counting full houses made by the three same cards on the flop, ie AAA).

To flop exactly an overpair to the board (no overcards AND no J on the flop), none of the three flop cards should be an A, K, Q or J.

So since there are 4 each A, K, Q and 2 J's in the deck, this leaves 36 non AKQJ cards in the 50 cards deck. So the chance of all three flop cards being among these 36 is (36/50)*(35/49)*(34/48) = 36.43% chance of flopping exactly an overpair.

Similarly, the chance that there is at least a J on the flop = 1 - chance of no J on the flop = 1 - (48/50)*(47/49)*(46/48) = 11.76%. So there is 11.76% chance of flopping either a set, full house or quads.

Since these two events are mutually exclusive, the chance that either of them occurs is simply 36.43%+11.76% = 48.19% chance of flopping an overpair or better.

Is this correct?

If I didn't go wrong, here are the odds for each PP:
AA 100%
KK 79.3%
QQ 62.2%
JJ 48.2%
TT 37.1%
99 28.5%
88 22.1%
77 17.6%
66 14.6%
55 12.9%
44 12.1%
33 11.8%
22 11.8%

Poker probability (Texas hold 'em) - Wikipedia, the free encyclopedia

Originally Posted by Zorkion

Poker probability (Texas hold 'em) - Wikipedia, the free encyclopedia

This is not the same calculation I made. This article only calculates the probability that no overcards to your pocket pair will be on the flop, not taking into account the fact that sometimes overcards will come AND you will make your set, which is actually great for you.

For example, for JJ, the article states that no overcards to JJ will be on the flop 43% of the time, meaning that overcards to JJ will be on the flop 57% of the time. This would lead you to think that 57% of the time the flop is in disfavor of your JJ, which is not the case because this 57% of flops includes for example AJ5 or AJJ which are great for you.

You have to do quads extra. Not that that will change much.

You have to do quads extra. Not that that will change much.

I think quads is there because I calculated the chance of at least a J on the flop by taking 1 - chance of no J on the flop