Better chances for math grad school: graduate in three years or four? I finished freshman year of college and I am transferring from a liberal arts college to a university to study a more rigorous math curriculum. I got accepted at UC berkeley (but as a junior transfer, so I can only be in college for 2 more years). I'm going to hear back from stanford, cornell, and colubmia next week. I would choose stanford over berkeley if I got in, but I'm not sure about the other schools since berkeley is a top ranked math school.

-My question is, if I get into columbia or cornell, should I go and be in college for 3 years, or go to berkeley for only 2 years? Is it better to stay in college for 3 years to be more competitive?

Background: I took  real analysis, topology, complex analysis, algebra 2, linear programming, cryptography. I'm self studying algebraic topology and homological algebra, but recently I'm studying probabilistic methods and graph theory to prepare for an REU this summer. I'm interested in anything algebra related.

Why I am worried: I looked over mathematicsgre.com, a forum where grad school applicants post their stats and results. People who get into top math schools usually have taken 10+ grad level classes and did research, REUs, and (probably) have  great letters of rec. If I go to berkeley, I only have 2 years, actually less since I would apply to grad school as a senior so I only have full 1 year and a few months.
What jumps out at me in your question is the assumption that because of your advanced standing you can only stay at Berkeley for two years and thus only spend three years in college altogether.  Though I do not have any direct experience with this (i.e., financial aid at state universities in California), I find that quite surprising.  Berkeley is an elite institution, and presumably they don't let just anyone transfer in.  The fact that you have two years' worth of university credit after one year in college is to your credit and probably factored into their decision to accept you.  So they turn around and penalize you by only offering you two years of financial aid?  That doesn't make much sense. 

I would at least make a phone call and, if necessary, schedule an in-person appointment with a financial aid officer.  My first guess, honestly, is that you may not be understanding the situation correctly.  If you are, you need to explain why the junior standing could stop you from making best use of the amazing resources that UC Berkeley has to offer and could make you less competitive in your later academic plans.  I would expect them to be sympathetic to that.

On the other hand, I find your discussion of what it takes to get into a top mathematics program (here and in the other question you asked) a bit reductive.  It is not simply a matter of taking the most graduate courses, doing multiple REUs (in my opinion as someone who was involved in graduate admissions in my math department, one REU has the same effect as multiple REUs unless you do some truly notable research in one of the REUs, which is unusual; also, doing multiple REUs makes it natural for you to get more than one recommendation letter from an REU director, and this is a mistake: most REU letters sound the same no matter who is writing them or is being written about), and so forth: the goal that you rather want to pursue is to show mastery of mathematics and show the potential and the interest in doing mathematical research.  You can show this by taking 5 graduate courses rather than 10.  (Ten courses sounds almost ridiculously high, by the way: I took 9 trimester graduate courses -- so the equivalent of 6 semester courses -- over the last two years of my undergraduate program.  I got into all the top mathematics departments.  If I had taken a few courses fewer I don't think the outcome would have changed.)  

In fact, the list of math courses that you've already taken compares well with what very strong undergraduates take up through the end of their second year in top mathematics programs in the US.  If you did really well with them, then I think you would be ready to take graduate courses (what other undergraduate courses would you take?) in your next year and thus as far as I can see you could graduate in three years and still be competitive for a top program.  But do you really have to?  If you are serious about studying mathematics, then you have the entire rest of your life to do that.  I would recommend a more balanced undergraduate experience that is not 100% calculated to optimize the graduate program you can get into and which lasts for the traditional four years: there are other interesting courses to take as an undergraduate which you will never take again, and there are other things to do with one's undergraduate life aside from coursework.  Don't get shortchanged on your undergraduate experience.