One of my hobbies is playing poker and following poker news. At Cardplayer's website is a section featuring analysis of a famous hand from the World Series of Poker. This time it was a hand from the 2005 WSOP $2000 buy-in event between Morgan Machina and Cyndy Violette. The featured hands were Machina's Kh10h vs. Violette's 10d8d. In the analysis the author referred to Violette's hand as "dominated." S/he then went on to define 'dominated' as "a hand not likely to win because another hand dominates it."
While correct, it sheds no conceptual illumination on what it is to have a hold 'em poker hand dominated. If only everyone were required to read just the introduction to a philosophy of language anthology, the world'd be a better place.
My definition, you ask? Attempt #1: In a heads up situation, a hold 'em poker hand is dominated just in case the other hand is over a 2 to 1 favorite preflop to win the pot. This would clearly include the hand above (where Machina was about 2.4 to 1 to win) as well as those times when a player's pair faces a bigger pair preflop (when the odds in favor of the bigger pair are about 4 to 1).
Beyond just stating odds at the risk of extreme precisification, I'm not sure how to do it.
I'm not sure any hand could be dominated before the flop. I'm thinking that a hand might be dominated if there is no way for that hand to produce a higher five card combination than its opponent, while giving the appearance of a winning hand. So in your scenario, the Kh10h could be dominated by its opponent assuming a flop of KdJd2d. Or even more so followinf a turn with anything other than a K.
To this end, two questions. At what point did the author declare the hand "dominated," (preflop, postflop?) and secondly, how did the hand turn out. Did Kh10h actually win?
The occassions on which I hear 'dominated' used never imply that the dominated hands have no chance of winning. The expressions 'drawing dead' and 'dead in the pot' are typically used for that situation, which rarely happens in ten-handed Hold 'em preflop with a fair deck.
Here is one scenario in which it can that I cooked up and checked with an odds-calculator available free from Turning River. I'll list the players and hands along with win percentages.
Player 1 - AcAd (87.4%)
Player 2 - KcKd (0%) also 0% to tie
Player 3 - KhQd (1.25%)
Player 4 - KsQc (1.25%)
Player 5 - 10s10h (0.05%)
Player 6 - 10c10d (0.03%)
Player 7 - 5c5h (0.07%)
Player 8 - 5d5s (0.05%)
Player 2 is dead to Player 1.
Here the KK's outs against Player 1 are all held by other players. Player 2 can't make a flush because P1 has higher draws; P2 can't make a set because the Ks are out; and P2 can't make a straight because all of the 5s and 10s are out (and every straight has either a 5 or 10 in it). Against P1, P2 is dominated AND drawing dead preflop. Sucks to be P2.
[Interestingly, 'dominated' is not listed in the glossary in Brunson's Super System (Cardoza, 2002) or Super System 2 (Cardoza, 2005).]
In the Machina/Violette scenario mentioned in my post, I take for granted that the author correctly described Violette's hand as dominated preflop and proceed to rectify her/his unilluminating definition of the domination relation. I'm not sure anyone would restrict the correct application of 'domination' only to situations like P2's above. So I think my tentative analysis stands.
By the way, Violette won that hand on the river with a board of AdQc2c-4d-8c.