What are the odds of landing a pair with a A-K pre-flop in texas hold'em?

Question

I've come up with about 38.2% but a poker odds calculator I found claims it is ~44%. Work on how the answer was found would be appreciated.

hiphopqueen_87, naturally the game only involves one deck... Also, the number of players doesn't matter because it doesn't affect the fact that there are 50 possible cards when you are doing the math. Also your math is horribly wrong and overly simplified.

roses89129, that website has absolutely nothing to do with my question. Also, just tossing me a random number does not really help...

Answer 1

It depends on how many people are playing at the time, or how many decks are being used. Say if only 2 people were playing so that means 1 deck is used. This means there is a 1 in 52 chances of landing a pair of eigther Kings or Aces.

Answer 2

I come up with 32% to pair at least one card. This includes the possibilities of 2 pair, trips, a full house, and quads. Here's the process:

You have AK. That leaves 50 cards in the deck that you can't account for.

Out of that 50, 6 cards will get you at least a pair. That leaves 44 that won't help (unless you want to include the odds of flopping a straight).

The calculation for not hitting an A or K on the flop is (44*43*42)/(50*49*48) or about 68%. That makes the odds of getting at least one of the 6 cards abut 32%.

The odds of flopping a straight look to be about 0.3%. (12*8*4)/(50*49*48).

Answer 3

Partly depends on whether the AK is Suited or not However, according to statistics, JJ is generally slight favourite, providing you bet aggressively, especially from mid to late position, but it is very weak if no Jack and an Ace or King fall on the Flop. Fold to a large Re-Raise as someone may be holding Queens, Kings or Aces. Bet half the Pot if another Jack falls on the Flop, to keep people putting money in, or go All-In if your Stack is big enough to take the limited risk, as you will rarely lose AK Unsuited is overrated. JJ is definitely a better bet As for AK Suited, it's a close second to JJ, and some way below the Ladies (QQ,) Cowboys (KK) and Pocket Rockets (AA) AK Unsuited really needs another Ace or King on the Flop; AK Suited needs either another Ace or King on the Flop, or a Flush Draw. If a Flush Draw occurs you should bet the Pot to make everyone fold. Even if some call you, you still have a good chance of making your Nut Flush on either the Turn or River

Answer 4

Um both your numbers are correct, symantics is the problem. The flop in slang can be all the cards out there, IE 5 cards for the whole flop, in which case 44% is about right. The lower number is about right for the flop of three cards. In other wards you take A-K to the river you are going to end up with a pair about 44% of the time and on the flop, where the three cards are dealt in the middle, you make a pair about 1/3 the time.

Answer 5

I looked in a book I had on my shelf and although the odds aren't exact, the odds off flopping a pair when starting with any two random cards is 1 in 3. Which is a little more conservative than your 38.2% but that's two against one so I would believe it's closer to your number that the 44%.

And realistically, hitting a pair on the flop with A-K in the hole has the same odds as hitting a pair with 2-4, it's just that you wouldn't be as excited to hit a pair of two's as you would to hit aces. Unless of course you're as demented as some of my poker buddies...

Answer 6

The calculation goes like this:

First flop card has 6/50 to pair with your AK
Second flop card has 6/49 to pair with your AK
Third flop card has 6/48 to pair with your AK

This gives that the % for your AK to pair with one card of the flop is: 6/50+6/49+6/48 = 0.12 + ~0.122 + ~0.125 = 0.367 = 37%

Answer 7

The answer in 1 out of 3 times, which would be 33% of the time. However it is less than that, its really about 30 percent

Answer 8

I HATE THAT COMBO AT A TABLE WITH 6 OR MORE PLAYERS!!! I only win with that hand 1 out of ten times but in a table of 4 or less I love that hand! Sorry I dont know odds just putting my 2cents in.

Answer 9

1 / 82.875