I think that every man goes through times when he is the alpha and times when he isn't. Very few of us are the Alpha in every context.
Any guy that is a bit cool and hanges out with losers will be the Alpha. Does that make that guy a real man. NO it does not.
For example, the average guy could be the alpha if he went out with a bunch of fat girls.
So I would not concern yourself with being the Alpha. The reality is however, that you have to find it in yourself to compete with other guys if you want to attract hot women. Use your competitive nature to become stronger, but what ever you do don't compete with women - that doesn't mean anything
Women naturally go for the guy who appears to be the strongest and who appears to be in control.
For example, take a musician. For the most part these guys are just average looking and are not the strong jock types; however, give one of those guys a guitar and a stage and he will be the Alpha that night. He will be the center of attention at that night and the women will love him for it.
The point I want to make is to focus on those skills that you have that set you appart from other guys. Those are your strengths. You must learn when to use them and when not to. Just make damn sure however that your women see your strength.
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anyway, I just finished my thrid pint of Guiness and I'm going to bed.