Can I win without using Anabolic Steroids?

Solution 1:

After losing, you can call him out for being a cheat, and then get into a fist fight. When you win, he admits to cheating and offers to arm wrestle again without cheating. You'll beat him easily without the steroids.

Solution 2:

I tried many times without the steroids but each try was a costly failure. It's very easy once you take them and a lot cheaper.