I find this position intriguing. Most men seem to think this and I've always seen it as an act of self-delusion. I know lots of women and the stories they tell me may not necessarily correspond with what they tell potential suitors. Unfortunately, women are still compelled to flatter men's egos in this regard. Women can present a mythical number when called upon just as easily as you tell your boss that your job interview tomorrow afternoon is a "doctor's appointment".
If you consider all intra-species, heterosexual coital encounters it's necessary that just as many women were involved as men. Most men can accept this, they just don't think it was their wife or girlfriend involved.
The fact is that for most men the precise opposite is true: the woman you are sleeping with has probably slept with more people than you have. And there is a mathematical proof.
This radical claim is an extension of something called the "Friendship Paradox". I will avoid trying to get into the mathematical details, but the principle is that someone who has had fewer sexual partners is far less likely to be sleeping with you than someone who has had many. If a woman has only ever slept with one man, it's unlikely it will be you. If she has slept with many men, then you may be in with a chance.
Assume the following diagram shows that sexual interactions between eight heterosexual friends; four men and four women:


Of course, the same can be said for the women: their average partner will have had more partners than them. However, in my experience women seem far less interested in convincing themselves otherwise.
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