Anyone who gives you a number for this question is full of beans.
This is one of the most difficult questions in SEO and most of the people who are charging clients for SEO can not answer it.
Lots of SEOs have clients on a $500/month plan when the target that they are attacking needs many times that much to become competitive.
Let me give just a couple reasons why this question is so difficult and why nobody here can give you an answer with the information that you provided.
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Your question is making a straight comparison.... it assumes that you are racing a stationary target. The target is not stationary. This question is really like this...
Two cars are driving on a road.... Car B leaves when Car A is already 100 miles down the road and traveling at a rate of 50 miles per hour. How fast will Car B have to drive to overtake Car A?
The answer is a velocity AND a time. And the question as I stated it assumes no acceleration.
If Car B drives 51 miles per hour... will you have the patience and budget for that long of a wait? Do you have the resources needed to drive 70 and not be stopped by Google?
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Another example...
George Pickett was a southern general at the Battle of Gettysburg who was ordered by Robert E. Lee to run the Union Army off of Cemetery Ridge. To do that Pickett's troops would need to cross a mile-wide open field in broad daylight under an absolute hail of enemy fire.
The field was one mile wide, it was up a slight incline - if they were slow in crossing they would be mowed down...
The Union had hundreds of troops dug in and positioned on the ridge and ready to open fire - if Pickett had only a few troops they would be mowed down....
So Pickett needed to order an enormous number of troops across that field and order them to run their asses off to engage the Union Army quickly - or die in the middle of the field.
If they failed in getting a enough troops... if they failed in getting enough speed... if they failed in getting enough determination and courage... then they would be mowed down.
Your job is similar to Pickett's... you must get an enormous number of links... you must get them quickly... and you must get them before your budget runs out... and you better hope that your budget is big enough.
Pickett knew that his field was a mile wide.. he knew how many troops that he had. He could see Union troops on the other side of the field at the top of the ridge.
Pickett's generals complained when they were told the battle plan... but Pickett pointed at the Ridge.
This battle was lost on bad math.
But your problem is even more difficult... the field is getting wider as you cross it because the target is moving away from you.
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And your problem is also more difficult because links have different values. One link from the Pope's site is worth a thousand from pedestrian sites.
Furthermore... different pages compete with different amounts of vigor. I might have a fifty word page but my competitor might have 2000 words, ten images, a video, and tables of data. Big difference.
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So, how is an SEO to know what is needed?
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You run the keyword difficulty tool and get a feel for the numbers (which contain much confusion).
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You go out to those SERPs and visit the sites and get a feel for their authority and content quality.
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Then you use open site explorer to see if the Pope is on their side.
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Then you decide if you are up to beating their content, beating their numbers, beating their quality.... and if you can do that quickly enough before the conditions of engagement change or your budget runs out.
After all of that you decide on taking the gamble or not.