Being young and living in Las Vegas, I consider the club dancefloors my specialty. For purposes of this post, I am going to assume that the clubs you go to have loud music playing and a decent sized group of people on the dance floor(smaller/queiter clubs will be a bit different).

First off, you do not ask a girl that is already on the dancefloor if she wants to dance with you. Save that for the girls that are sitting down or standing to the sides, at the bar, etc. If she is already dancing, just assume that she wants to dance with you. She would rather have a man that takes charge than one that has to ask her permission to dance with her when shes ALREADY DANCING at a nightclub. Asking her is a huge demonstration of lower value, as it shows you verbally seeking her approval in a situation which does not require her verbal approval. Sometimes you need a get a girls permission to do something with her, but dancing at a club thats open to the public is not one of them: if she doesnt want to dance, she can simply turn away. Also, at louder clubs, someone trying to come talk to you can be way annoying when you're dancing, cuz you have to lean in to hear them and that totally interrups your rythm.
Now that we got the approach part out of the way, there are two things that will greatly improve your chances of her dancing with you, since you will not be saying anything verbally.

The first is your dance skills. If you cant dance worth shit, thats a huge turn off, so make sure you know how to keep with the beat, keep in rythm with her dancing, and have a few cool moves at your disposal. Also dance somewhat sexy at first and put a lil hips in it, but increase the 'motion of the ocean' as you feel out her responses(you'll KNOW when to grind, believe me!).

The second is peacocking. Since you wont be saying anything verbally to her when you approach, appearances will matter even more than usual. The flashier you look(without looking douchey) and the crazier your appearal/accessories are, the more likely you will stand out from the other guys, thus the more interested she will be in having a non-verbal exchange with you(aka dancing). What you wear can say a whole lot. Just like a cold read is a DHV in a verbal interaction, some sweet leather pants are the same thing in a non-verbal interaction. Just think of your accessories as routines, and your outfit is running game on its own, I cannot stress this enough at nightclubs. Dont be afraid to outflash everybody with some crazy ass shit you're wearing. And as always, stay clean, well manicured, and smelling good.

Now that your looking sexy fresh, and dancing with rythm, its time to go find a girl to dance with. Theres two ways to do this, lets call them direct and indirect. Indirect would be how most guys go about this- simply dancing by yourself for a minute then "casually" turning to dance with some girl who is dancing near you. Most guys prefer this method because it softens the blow of rejection if she does turn away because it appear that you were already dancing before the rejection anyway, right? Let us not forget that we did not become PUA's for letting strangers opinions eat away at us. I find the indirect way can work against you because it can lower your value by dancing alone on the dancefloor, and for some of us, neediness/uncomfortableness can be picked up by women in these situations through our subtle body language. I mean, what kind of alpha male would dance alone in a club full of beautiful women? This of course is not true if you're genuinley just out there enjoying yourself fully and dancing some crazy funky dances, then you just look fun. But the truth is, most guys just dance some simple sway back and forth, which looks pretty lame if your not doing it with a girl.

Now for my prefered method, the direct. From the bar or my table, or wherever, I will scope out the floor and see which girl I want and just go over and start dancing with her. I have found this to have better odds then indirect does. Women like a man who knows what he wants and isnt affraid to take it. This also makes you the selector.

And to really appear as the selector, you can do what I call the hunter method. Walk straight from wherever you are seated/standing straight to the edge of the dancefloor, and continue around the perimiter of people dancing without skipping a beat. Do not stop walking. Make direct eye contact with every girl dancing and scan them as if sizing them up. When you scan the girl you want to dance with(either preselected beforehand, or on the fly), then immediatly b-line it to her and start dancing. If done right, it will look like you were blatently sizing up all the best girls and took your pick as you saw fit. The key to this method is that you must look VERY confidant and like you have a destination in mind and you are heading towards it. No lingering around the perimeter of the dancefloor, thats what AFCs do. Also, never make a full round around the dancefloor before selecting a target, and never scan the same girl twice or else you will look indicisive and unconfidant. Remember, no lingering and no staring, thats just creepy. From when you first hit the edge of the floor until you actually start dancing with your target should take no longer than 20-30 seconds. This method make you appear as the selector and is also very direct, instead of the alternative: the guy thats just swaying back and forth by himself and "by chance" just happens to start dancing with the girl.

Girls that dance on the tables I have found to be good targets. First off, most guys are so AFC that they just stand around staring at these girls, so you have already set yourself apart by just getting up there. Also, once seen dancing with a good looking girl literally up on a pedastal where everyone can see you is major social proof for subsequent interactions later in the evening.

If really wanna get your alpha/AMOG on, then if you see a guy that is dancing up on a good looking girl, but the girl clearly isn't interested(you'll notice, its easy to spot), then just b-line it right for the girl and insert yourself right between him and the girl, or at least get a shoulder between them, and just dance with her as if he wasnt even there. You can even give him a little nonchalant shove away from you and your new girl. The guy will always walk away. I'm a pretty big dude though, so I've never had a reaction much more severe than dirty looks from the guy, but I'm not sure if this would invite fights for a smaller guy. You've been warned.
Keep in mind when you do this, that just dance one dance with her and then part ways and continue the interaction later on. This is kind of a captain-save-a-ho type situation, and if you stick around for too long after you "save" her, you might start to appear needy/desperate for attention. So just save her, give her one dance, then leave so she knows that you have better things to do. Her curiousity will be piqued and if you approach her later, it will work better than if you just stuck around from the begining(push/pull, anyone?).

Do not be affraid of being turned down by a girl on the dancefloor. It happens, but remember your newbie missions of just saying 'hi' to strangers? Were you ever crushed if someone didnt say 'hi' back? Its not much differet on the dancefloor. If she doesnt want to dance, she will simply turn away casually, at which point you can just roll off to the nearest (fat)girl and start dancing if you feel you must save face. Tip: Fat girls never turn down a dance, lol.

The main difference in club game is that people go to clubs to hook up. Its just what they do. So direct game is much more effective in this setting, and if you act like you're there just hanging out and that you meeting her was just by coincindence, than she will think either A: your lying, or B: your weird. Indirect game can be potent in any setting, but direct game will cut out alot of the fluff in your routines and it's just plain fun. So while in this sexually charged SPAM, take atvantage of it while you can.

Remember that there are more ways to run game than verbally. Peacocking can be a opener(her approaching you), DHV, social proof, and convey alpha. And dancing is a routine in itself- it is an opener, DHV & negs(if done correctly), social proof, rapport, kino, and a kiss close is very possible without ever saying a word(if you want a number close, you're gonna have to talk, lol). After a good dance or five with your target, you've already completed of huge part of the seduction process, now all you have to is bring her back to your table or the bar or whatever and keep the process going verbally. As PUAs we have learned to use every tool we can in our quest for women, and the dancefloor is just another tool- a pretty effective one at that.

As with all PUA matrial, different methods work differently with different people, but some techniques just seem to have better odds. Everything I have posted here has been feild tested many times and I feel will probably be universal for the most part. Good luck party people, and happy clubbin'.

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Gettin' funk nasty