Best uses for Dominatrix:1) Countering rushes of nasty heavyweight riots: Mace, Ogre, Redback. For an equal price to the rush unit, you get the Dominatrix which stops the rush unit - and you also get the rush unit. Typically, the rushing player resigns then after realising that they've spent most of their economy on giving you an e.g. Mace.
2) Defeating medium-heavy assault units. Minotaur, Jack in particular are very difficult for Rover to counter without a Domi.
3) Defeating armored objects - Halberds, Razors, Crabs. Domi will need some shielding to fight a Crab, but they're one of the fastest ways to get rid of annoying Halberds or Razors.
4) Killing enemy commanders. Now, Rover doesn't lack in commander-killing options, with Scorchers and Ravagers also being quite good at the job. But a Dominatrix outruns and outranges non-trollcom commanders, so an unassisted com caught in the wild against a Domi will soon encounter a fate worse than death, creating a massive 8 metal per second differential for the capturer.
If your enemy is unattentive, you may even get this almost for free, because the first thing a dominatrix capture ray does is subvert the "commander under attack" alarm.
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I don't think dominatrix balls are that practical outside of roflstomping Circuit or playing against players who won't counter them, which you should never rely upon. Domis are not very good as a late game unit, their rung on the bullshit skirmisher ladder is quite low.
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Countering Dominatrix as hover, your two choice units are Halberd and Lance. Ideally, both!
1) Halberd costs less than the dominatrix. You will need at least 3 halberd per enemy 2 dominatrix, but halberds are fast enough to catch up with the domis, and more importantly, they are very hard to stop and they are *very bad at killing each other*. So when they get turned, Dominatrices don't do any bonus kills with the freshly acquired slaves; instead, once the remaining Halberds kill one of the slave-owning Domis, you get your slightly dented Halberds back.
2) Lance has the range and alpha to kill dominatrices with impunity. It may not have that good effect if shooting by radar though, but that's where Halberds come in handy.
3) Scalpel if you want to fight dirty. A Scalpel/Mace force fights very favorable with almost every Rover composition, barring things like heavy Badger - at least, until Thunderbirds come out. The Scalpel/Mce build also trades equally with Dominatrix - remember that you get two Scalpel for one Domi, and while a Domi outranges the Scalpel slightly, it's not a big enough margin to prevent return fire. It takes two scalpel salvos to kill a domi, and if you succeed, you more or less erase all the damage the Domi did. A good trick here is to manually target them, otherwise the first captures will waste shots for most of your army.
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Once the enemy has fielded five or more dominatrix, you may consider further
asymmetric options:
Aggressive porcing - Dominatrix is quite bad against Stinger. Extra good if your artilery is an anti-mobile kind, which is literally any artillery unit except Sling and Impaler - then you can also bombard the enemy units from your porc forest!
Air bombing - but start with a Thunderbird because unassisted Ravens will probably be captured. A Dominatrix takes
two Raven bombs to die, too.
Cloaked snitches - remember, 5 dominatrix is over 2k metal. You get to facswitch to shield (800m), an area cloaker (500-ish), and four-five Snitches for this price.
Phantoms - just bring something to keep the Darts away.
Emissary. Outruns, outranges, and outguns Dominatrix. Kind of mandatory late game.
Cyclops. Like, really, if you're tank and you see even one Domi, just make 1 emissary to annoy your enemy for the time being and fully switch to Cyclops production. If you're hover and you're having trouble dealing with Domi using halberd/lance method, also switch to Cyclops.