When you click on youtube on embed this movie and select custom player you can set the following options

These are the parameters which can be used.

rel
Values: 0 or 1. Default is 1. Sets whether the player should load related videos once playback of the initial video starts. Related videos are displayed in the "genie menu" when the menu button is pressed. The player search functionality will be disabled if rel is set to 0.

autoplay
Values: 0 or 1. Default is 0. Sets whether or not the initial video will autoplay when the player loads.

loop
Values: 0 or 1. Default is 0. In the case of a single video player, a setting of 1 will cause the player to play the initial video again and again. In the case of a playlist player (or custom player), the player will play the entire playlist and then start again at the first video.

enablejsapi
Values: 0 or 1. Default is 0. Setting this to 1 will enable the Javascript API. For more information on the Javascript API and how to use it, see the JavaScript API documentation.

playerapiid
Value can be any alphanumeric string. This setting is used in conjunction with the JavaScript API. See the JavaScript API documentation for details.

disablekb
Values: 0 or 1. Default is 0. Setting to 1 will disable the player keyboard controls. Keyboard controls are as follows:
Spacebar: Play / Pause
Arrow Left: Restart current video
Arrow Right: Jump ahead 10% in the current video
Arrow Up: Volume up
Arrow Down: Volume Down

egm
Values: 0 or 1. Default is 0. Setting to 1 enables the "Enhanced Genie Menu". This behavior causes the genie menu (if present) to appear when the user's mouse enters the video display area, as opposed to only appearing when the menu button is pressed.

border
Values: 0 or 1. Default is 0. Setting to 1 enables a border around the entire video player. The border's primary color can be set via the color1 parameter, and a secondary color can be set by the color2 parameter.

color1, color2
Values: Any RGB value in hexadecimal format. color1 is the primary border color, and color2 is the video control bar background color and secondary border color.
 Example:
youtube.com/v/u1zgFlCw8Aw&rel=1&color1=0x2b405b&color2=0x6b8ab6&border=1&fs=1

start
Values: A positive integer. This parameter causes the player to begin playing the video at the given number of seconds from the start of the video. Note that similar to the seekTo function, the player will look for the closest keyframe to the time you specify. This means sometimes the play head may seek to just before the requested time, usually no more than ~2 seconds.

fs
Values: 0 or 1. Default is 0. Setting to 1 enables the fullscreen button. This has no effect on the Chromeless Player. Note that you must include some extra arguments to your embed code for this to work.

showsearch
Values: 0 or 1. Default is 1. Setting to 0 disables the search box from displaying when the video is minimized. Note that if the rel parameter is set to 0 then the search box will also be disabled, regardless of the value of showsearch.
 
showinfo
Values: 0 or 1. Default is 1. Setting to 0 causes the player to not display information like the video title and rating before the video starts playing.

iv_load_policy
Values: 1 or 3. Default is 1. Setting to 1 will cause video annotations to be shown by default, whereas setting to 3 will cause video annotation to not be shown by default.

cc_load_policy
Values: 1. Default is based on user preference. Setting to 1 will cause closed captions to be shown by default, even if the user has turned captions off.

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