value of A2 heads up

[housenuts]

what are the odds, that if I have A2 heads up, my opponent will have either a bigger ace, or a pocket pair?

i took a statistics and probability course in university 2 years ago. i really wish i could remember the stuff.

[Spicymoose]

For the chance that he has a pocket pair, you figure it out by saying that he is dealt one card, and then the next card has to be the same. So the first card can be anyone, but the second one only has a 3/51 chance (.0588).

For him having any Ace (but not pocket aces, or a two), he can either be dealt it first or second, so it is (4/52) [4 aces] *(44/51) [44 non-2, non-ace cards] + (44/52)*(4/51) or .1327.

So the chance that he either has a pocket pair or an ace with a higher kicker is .1327+.0588 or about 19%

[benthehen]

Almost, just off by a tad. Since you have A2, then that affects the chances of your opponent having pocket pair and getting an ace with higher kicker. I believe it is:

11*C(4,2)/C(50,2) + 2*C(3,2)/C(50,2) + C(3,1)*C(44,1)/C(50,2) = 204/1225

So it is about 16.65%.

The first term is your opponent getting pocket pair threes to kings. Second term is pocket pair twos or aces. And third term is your opponent having ace with higher kicker but no pocket aces.

[Brineboitano]

Make sure to remember though, if you have the best hand it's a race for the pot, whereas if he does have you beat, he has a dominating hand (except if he has A3, A4, A5 it's not so bad) my odds calculator is telling me A2 offsuit will beat a random hand 53% of the time and split 4%. If you get reraised you might want to wait for something better, depending on your opponent and blinds of course.

[housenuts]

at what point does Ax become at least a 2 to 1 favourite against a random hand? something like A9?

[Mike Haven]

AKo is a 1.84 to 1 favourite against a random hand, according to my sim.