Therein lies our problem. The answer is "Very Rare" no matter where you are in the Hyborian Age, whether women fight with their men or not, because we are talking about a woman that is a challenge for a strong male fighter in Howard's Hyborian Age.
S4, you don't get to make these magesterial baseless statements: you are not the final authority on Howard. You have to actually support your remarks. In particular, you have to confront, rather than duck, two facts: Firstly, Howard's Hyborian Age cultures are based on real world historiacal cultures: the Cimmerians on the Celts, the Hyborians on medieval Europe, the Turanians on the Ottoman Turks, etc etc. We can therefore use the data from those cultures, with which Howard was familiar, as a benchmark for what he would have intended.
Thus we can say that about 1 in 20 to 1 in 10 Cimmerian women will be full time warriors (10% of Celtic female graves contain weapons, chariots, torcs and other accourements of the warrior, of which about half contain weapons that have actually been used). We know from historical records that women fighting in medieval times was reasonably common in defence of towns under siege, but much rarer (though not unheard of) in actual armies, and that the fighting manuals of the time include provision for women who are fighting in judicial or honour duels. I am less familiar with the history of Turkey, but I know of no examples of women warriors in fact or fiction.
Second, and more directly relevant, we know that Amamlric in Balck Colossus comments that Cimmerian women, and probably women of the other barbarians too, regularly strap on swords and go into battle. Battle, not desperate defence of a house.
And in any case, once AGAIN, that is not "the problem". The problem is that you used to believe that there was NO fighting woman in Howard's writings, and thus Red Sonja was out of step with Canon. I am glad to see you now concede that point. I suppose it is typical that you have refused to admit the fact, and are now pretending I was claiming Hyboria had female armies. Ho Hum.