Is it better to have pocket AA and hit three of a kind, or better to have one Ace and hit three of a kind?

Question

Based on probability, would you prefer to have AA and hit an Ace in the middle or would you prefer Ax (any card) and hit AA in the middle?

Thanks

Answer 1

It is always better to hit a set (you have the pair).

A pair on the board is shared with your opponent.

If you have a single A and the board is AA8 and your opponent has 88 you are behind.
If you have AA and your opponent has 88 and the board is AT8 then you are ahead.

If the board is AAQ and your opponent has AQ and your hand is AK you are behind.

Answer 2

Paparazzi's answer is correct, but I would add a little bit more to that (especially that the examples were mainly about full house, which is not that probable).

With one ace a lot depends on your kicker. If you have high kicker like K or Q you still have to worry about situations that Paparazzi wrote about. When playing with AQ, AJ, AT with early raiser you still have to worry about higher kicker, pocket pairs that can flop a full house. With mid and low kicker it gets even worse.

Imagine that you have A8 and someone from an early position raised pre flop. The flop comes AA9. Are you happy with that flop? Not really - unless villain is a really loose opponent you should expect AQ, AK, AJ, 99 and if she/he is loose maybe even AT, A9. There are few other hands in this range you can beat but this puts you in a tricky situation.

With pocket aces this is an entirely different situation. If flop comes for instance AQ8 and you have pocket aces you are really happy with that flop (unless it is suited maybe). Not only you have the best hand but also there is a high chance that your opponent has a decent hand and you will be able to extract some value from it (as you expect villain to have AK, AQ, AJ, 99, KK or maybe even AT, A9 in her/his range).

If villain raises from mid position in this case you may be afraid that her/his range has also KJ, KT and T9, TJ from late position which gives her/him a gut shot, but even then there are only 4 outs for gut shot and you still have 6 outs for a full house (Q or 8).

If you deal with mid/late position villain with dry flop like A92, it is even better cause there are not that many hands that you are afraid of here.

There is also one more thing to consider - with pocket pair (especially aces) there is much less chance that villain puts you on a set than when the pair is already on the board. You get a pocket pair only one in 17 times and when you have a pocket pair odds of flopping a set are only 8.5 to 1. So it is much easier to get value from a set on a pocket pair because it is harder for your opponents to figure out that you actually have it.

So yes, it is of course better to have pocket rockets than one ace when you flop a set and it also applies to any pocket pair actually.