I think this comes down to two main things...
1). The child
2). Where you live
At three - for us - my son was out playing on his own. I am assuming you mean front/unsupervised rather than enclosed back garden right? As for enclosed back garden, my son was out there playing on his own since he could move there himself. This too though was also down to my son (his personality/temperment/capabilities/etc). (and he couldn't move out there on his own until he was about a year and a half anyhow as he was pretty late in the physical get up and go department...gets the 'lazy' from his father
In the front - he was just a bit under three. It started with fantastic weather and me being able to leave the front door open (as he wanted to be out there and I didn't). So it was semi-unsupervised. I could be in the kitchen (window faces right out front) and watch him whilst making the lunch or sit in the doorway with a book or the laptop! lol This worked.
It really also has been a really slow natural moving process for him. He started epressing an interest in playing out front. He didn't want to play out there long - just long enough for me to make the lunch...he didn't want to go far either - about a yard away from the open front door...to, gradually, further and further...and this all has matched his age and capabilities I feel. When he started wanting to go out of eyesight (we have a little foresty big next to the house that is so FUN for anyone to play in! lol) - he was old enough for us to talk about other things (like how not to walk away with anyone but me
and how he can run right back to our house (its like only 5 yards away tbh) if he feels uncomfortable, etc). And - for me, most importantly, if I should out 'Duncan - you okay?'...to give me an answer back (I can then guage if he really is and tell where he is about...he was 4 in September and I am not comfortable with him being farther than where he can hear me shout and this is consensual for the time being! lol)
We live at the end of a cul-de-sac though away from any main roads. Quiet area - out in the country/middle of nowhere -where everyone knows your name type of town. So this has worked for us. Last summer, when he was nearly four - he even made 'friends' with the neighbour hood children and was running up and down our little cul-de-sac road with them for hours in the warm summer sun for the afternoon. It was nice. How do you think this baby was made? lmao
And generally - as a boy, he is pretty placid and cautious and a perfectionist. He wouldn't do something unless he was 100% sure he could and comfortable with it. He is very road wise, etc. So that part of it plays into our comfort levels too! ...if any of these things were different, then the situation would be too!