Can someone please give me the odds for any two starting hands to hit a pair on flop.

Say I hold AJ and all cards are live, what are the odds of hitting either A or J on the flop?

Odds too please if one card is dead.

Cheers

Rule of four and two basically "works" for most of these questions as long as u dont need precision. 6 outs 3 times is roughly 36%. Outs times pulls times two.

Thanks

Rule of 2 and 4 is for turn and river, not the flop.

Odds of flopping a pair is 29%.

3.50%

Useless stat to know. Focus on something different.

Thanks.

odds if one card is dead?

Flop zilla can answer that question.
Enter range = 100% and check how many hands hit one pair.
You can remove pocket pairs of your range if you dont want those but thats not clear.

Otherwise, basic combinatorics:

(6c1 * 44c2)/(50c3) = 0.290

If one card is dead (like AJ vs AK and you need EXACTLY ONE J ON THE FLOP):

(3c1 * 45c2)/48c3 = 0.172

If you meant one of your out is dead, i think it is:
(5c1 * 43c2)/49c3 = 0.245

The 29% number is for flopping exactly one pair.

If you have unpaired cards, you have six outs. Your odds of flopping a pair (or better) is basically 6/50+6/49+6/48, or about 36.7%. That's a bit off, as it doesn't include the complicated math of your number of outs changing if you already hit a pair, but it's close enough and can be done quickly. The actual answer is 32.3655%

If one of your outs is dead, it is 5/50+5/49+5/48, which drops the estimate version down to 30.6%. That gives you an idea of how the ratio changes, and I'm not interested enough in combinatorics to do the actual math. If you are, please ask in the Probability forum.

FWIW, the old chestnut of "a five card poker hand has a pair or better almost exactly half the time" includes the cards on the board. Having a set is pretty meaningless if you have 45s and the flop is KKK, as everyone has a set and your kickers suck.

It's for pulls. Figuring out turn + river + ocean is basically the same as figuring out flop. Obv assuming you are ok w not being precise.

What are the odds of pulling the ace of spades if i turn over every card in the deck? Outs (1) times pulls (52) times 2 = 104%...pretty close to the 100% it is.

Yup. Particularly, the "Rule of 2" is for each pull, with the "and 4" referring to getting to see both the turn and river.

It's actually more accurate for the first flop card when there are 50 unknown cards left, so you have exactly a 2% chance of hitting each out, and less accurate for each card that gets shown, so by the river you're estimating 2%, but it's actually 2.17%.

Using that method to estimate, you have a 36% chance of flopping a pair or better when you have 6 outs, and a 30% chance when one of your outs is dead.

As mentioned above, though, that's really an overestimate, because combinatorics.