The Intermission function does not update on the GUI when I run the script. Can someone help me?

local players = game:GetService("Players")

local function Intermission(player)

local BeginningText = game.Players.player.PlayerGui.ScreenGui

game.StarterGui.ScreenGui.Enabled = true
		
	wait(1)
	BeginningText.TextLabel.Text = "Beginning In 4"
	wait(1)
	 BeginningText.TextLabel.Text = "Beginning In 3"
	wait(1)
	 BeginningText.TextLabel.Text = "Beginning In 2"
	wait(1)
	 BeginningText.TextLabel.Text = "Beginning In 1"
	wait(1)
	 BeginningText.TextLabel.Text = "Beginning In 0"
end

	local function playerwait(player)
		  if #players:GetPlayers() > 2 then 
        game.StarterGui.WaitingForPlayer.Enabled = false

		wait(1)
		
		Intermission(player)
    end
		end
		
game.Players.PlayerAdded:Connect(playerwait)

The problem is that at the start, you've defined BeginningText as game.Players.player.PlayerGui.ScreenGui. I think this is the issue. Try doing instead game.StarterGui.ScreenGui - or is this running separately on each client rather than the whole server? You haven't provided any background information for us to help you with ;-;