This is a terribly unusual question. In what way “easiest to run”? Are we talking rules? Are we talking setting? Are we talking setting the atmosphere? I am just not sure what this question is getting at. So let us look at this from an entirely unusual perspective. Let me look at this from a perspective that perhaps no one else will tackle it from.
Easiest to run?
Any game that involves dice. I really do not care which one it is – if it involves dice I am more than OK to run it and consider it easy. Now why did I come up with that answer is the real question. For those of you that are regular to the blog or that may know me personally or electronically you know one of the games I love. Lords of Gossamer and Shadow is a dice-less RPG that is the “spiritual” successor to Amber RPG. You will also know that I wrote a source book for the system. All of that said I really find it a difficult and rewarding experience to run this game. It is not the easiest game to run, but a brilliant challenge.

What makes it challenging?
Often when I run a dice run system I will roll in the open. I see all the players rolls and mainly they see mine. There is an overarching set of rules that guide the results of those dice to a particular outcome. Sometimes it is pass/fail, other times in a grey zone. Mainly though the rules for the results are laid out before you though. In Lords of Gossamer and Shadow the powers and abilities of the characters are known but the direct results come from the Gamemaster. This is a large onus of responsibility and I can remember the first times I played this system wishing I had dice to hide behind.
More complications
Lords of Gossamer and Shadow is a game that results in a huge amount of learning for players and gamemasters alike. The setting is pretty much any setting with the connectivity of a plane of existence the players exist in. Preparing for this game is a unique experience and running it even more so. I have never read all of the Amber series by Roger Zelazny but am slowly making my way through them. Many of the people that run this game run it for the love of those books. I am not one of those people. I came to this system with a fresh set of eyes. It is the reason that the source material I wrote is considered an “option” because there were issues with how some of the stuff I wrote may conflict with the Amber pseudo background.
My take
All of the above is OK. I knew the system was being lifted from Amber RPG. I did not realise that the setting was congruent though. I do not mind that in the least. The makers of the game were very clear about the reasons behind their decisions. The one thing that I loved was just the pure game. I had my vision and it works. They have theirs and they work side by side. It is not the easiest game to run because the decisions of results weigh heavily on me. I do love the responsibility though and it allows a true shared story telling nature to the game.
Lords of Gossamer and Shadow is not the easiest game to run but it is the most rewarding in my opinion. Sure, I wasmeant to talk about a game that was easy to run. I flipped it and talked about one that I find the most challenging. I only did this to point out that any dice based system is an easy system. Some have complex rules, some have extensive rules, some have hardly any rules. But the fact that the onus of decision making falls to the die make them an easy system to run. I do not necessarily go in for easiest, I like challenging. Keep rolling!