Not a new strategy, but it's slightly different to MrBuu423's and [HG] JuIcY [Bandit Killer]'s, and I've completed 4/20s nearly 10 times with it now.

share link: http://gtm.steamproxy.vip/sharedfiles/filedetails/?id=324229302

Update: 20/12/2014
While surfing youtube I discovered a video earlier than mine that used a very similar method to mine (keeping the right door open) but was a couple of days earlier than mine. In their video they check the right light constantly but talk about making a video where they won't check the right light until they have to, same as my method, however I don't know if they ever went that step.

In this video (which I think was my 7th or so time completing 4/20s, I had 18% power by 5am)
It was also one of the more clutch 4/20 wins.

https://www.youtube.com/watch?v=vDsf7atFnPk
http://www.twitch.tv/dragondave17/c/5259884
http://www.twitch.tv/dragondave17/b/576183305 (direct video, 2 weeks expiry)

There's no need to check the right light at all until Chica is about to leave the East Hall Corner or the camera feed goes out, which means you can focus entirely on Bonnie and slowing down Foxy by spamming the camera feed, so my cycle is:

Check left light - check East Hall Corner (4B) x2

You can check the status of Foxy whenever Chicka is at the right blind spot, or if you feel it's necessary by closing the right door, looking at Pirate Cove then back at 4B before closing the camera.

When Chicka is in East Hall Corner or the camera feed goes out, I switch to only checking the camera feed once and checking both lights, because you need to be quick if Chicka and Bonnie decide to attack at the same time.

Also checking the cam feed twice is about the time it takes to move a 20 AI animatronic away from the blind spots, so it means you only have to flash the light once usually and they are gone, meaning you can keep the doors closed for a minimal time conserving more power.

If you can do this quickly enough, you can get Freddy mostly stun-locked in 4B and he will stay there a long time, try it out. Otherwise, checking the right lights is definitely a good idea.
You start off with the short cycle, switch to MrBuus whenever Chicka is in position, and then switch to Bigbugs when Foxy is in his frozen sideways sprint (you don't see the latter part in this video though as Foxy doesn't move).

You don't need to check on Foxy everytime you close the door on Chicka though, it depends on how far along Foxy is. If Foxy is in his sideways running pose, switching to Bigbug's cycle is a good idea as that cycle allows frequent Cove checks at cost of power and increased risk from Bonnie.


On the video:
The video definitely isn't perfect play and definitely wasn't my best 4/20s run, I make a ton of mistakes in it (nerves & shakes) that could've ended the run, but even then, I come by with 18% 5am power and succeed. The general idea is it should be easy to improve on the video even if you make a lot of mistakes. It was the one I was going to upload anyway, and it had an interesting finish on it. One of the times towards the end when I closed the left door, I should've closed the right door as well and used the period of safety to check Foxy, since you get a little power to burn with this method (you can also close both doors even when Bonnie isn't there to check).

The win rate with this method is still pretty close to 100% for me, as long as I don't make any glaring mistakes.

This is simple, for extra difficulty, play the game and never ever use the door lights. Story mode and 6th night should be doable, so if you want to pull off the truly impossible, you could attempt 4/20s without using door lights.

Here's my first attempt at no door lights challenge in story mode (replay from my stream).

Nights 2-3
https://www.youtube.com/watch?v=aqoDPiUbX2U

Nights 4-5
https://www.youtube.com/watch?v=OtnU2hkCygU

Another attempt, with music (no helpful kitchen audio cues)
https://www.youtube.com/watch?v=dzpCKONBbk8
https://www.youtube.com/watch?v=MExfXoMtd0w
https://www.youtube.com/watch?v=MJzJEca_Ads
https://www.youtube.com/watch?v=_OBJwDzhJ2k

http://www.twitch.tv/dragondave17/c/5273536 (highlight, night 2 onwards)

Nights 1-5
http://www.twitch.tv/dragondave17/b/576921991 (full, expires in 2 weeks)

Q. Why doesn't Freddy kill you?
A. Freddy can't enter while you're looking at east hall corner, which includes flipping the cams up and down, as long as you keep them on east hall corner while the door is open

Q. Why doesn't Foxy kill you?
A. Foxy doesn't attack if you check (any) cameras consistently, it doesn't have to be Pirate Cove. At most Foxy should attack once, always sometime after 2am. If he attacks twice, you are dead by the other methods anyway which don't give you more than 10% spare power by 5am usually (the second attack removes 6% power, and you need an absolute minimum of 4.5% power to survive), you can get just enough power to survive two attacks and make the night with this method but it's recommended to conserve power by only letting him attack once at most instead.