Domination

Dominaton is a concept specific to hold'em, whether limit, no-limit, or pot-limit, referring to a comparison of poker hands. In general, any time one player's hand restricts her opponent's to three or fewer outs, we say the better hand is dominating and the inferior hand is dominated. Another definition, identical in practice, is that a dominated hand is one which can make a pair and still be behind an opponent's unimproved hand. In none of these cases are flush or straight draws relevant to determining domination, although suited dominated hands are somewhat more robust than their offsuit cousins.

Pocket pair domination
Conceptually this is the simplest case: A pocket pair dominates all lower pairs and is dominated by all higher pairs, because the lower pair has only two outs to surpass the higher pair.

Player 1:

Player 2:

Player 1's hand is dominating Player 2's, because Player 2 generally needs to make a set by catching one of the remaining two tens in order to beat kings. Player 2 has only a 19% chance of winning (i.e. is a 4:1 underdog).

Note that this type of domination is even more severe if the two pairs are close in rank. Counterintuitively, a pair of fives through eights would do best against kings because they have more straight possibilities not blocked by the kings. A pair of queens would do worst. Similarly, the suits of the higher pair can counterfeit flush possibilities for the lower pair, making it harder to draw out. In the example, catching four hearts on board is fruitless for Player 2, but catching four clubs would make his hand a winner heads-up.

Kicker domination
When two players hold one card of the same rank, the other cards of that rank are no longer outs for the player holding the lower kicker.

For instance, two players are in a hold'em hand, and they hold:

Player 1:

Player 2:

In this case, Player 1 is dominated. An ace that comes on the board helps both players, so it's not an out for the ATo hand. This is the danger of playing hands like ATo, as they are easily dominated. Rather than having 6 outs to make a pair, poor Player 1 really only has 3 outs, since making a pair of aces will still leave them behind Player 2.

Pair-versus-non-pair domination
The most subtle form of domination occurs when a pocket pair dominates two unpaired cards. For example:

Player 1:

Player 2:

Player 2's JTs is greatly devalued by the inability to pair tens, because the case ten makes a set for Player 1.

Player 1:

Player 2:

Now Player 2 has somewhat more possibilities than in the previous example, but still needs to catch at least two of his outs. Merely pairing tens or queens is fruitless to beat kings, but two pair on an unpaired board or trips would win for the dominated hand.

Implications
Playing a dominated hand is very expensive because of the potential to pair, even to make top pair, and still be behind. In general terms, hands such as AJ, KQ, and KJ should only be played carefully against a raise (if at all) because of their potential to be dominated by better hands. Domination is the main reason why routinely cold calling is so lethal in hold'em.

Discussion threads

 * Classic essay by Abdul Jalil of RGP -- also used to be posted at the site mentioned in this thread, which apparently is no more.
 * Coldcalling third in Stud8 - Discusses why domination doesn't apply to stud, where each player has separate cards.