What's a good way to keep a game looping through rounds/matches ?

I've made dozens of round based games before. What I usually do is make a bunch of functions each with it's own purpose (e.g the intermission or choosing specific maps).

function Intermission() --Intermission function
	for i = 30,0,-1 do --We run a loop 30 times and each time it runs it subtracts "i" by 1.
		print(i) --Print i
		wait(1) --wait a second
	end
end

function ChooseMap() --Choose map function
	local Maps = game:GetService("ReplicatedStorage"):GetChildren() --We get the children of the replicated storage (assuming its all maps, if not make a separate folder within replicated storage and get the children from there)
	local ChosenMap = Maps[math.random(1,#Maps) --We index the Maps table from a random number between 1 to the number of maps in the table.
	
	print(ChosenMap.Name.." is the chosen map!") --We print that its the chosen map.
	
	local Map = ChosenMap:Clone() --We clone it
	Map.Name = "Map" --We name it map for future reference
	Map.Parent = workspace --We parent it to the workspace.
end

function RunGame()
	local Map = workspace.Map --We grab the map and since it was named map beforehand its easier to get
	for i,v in pairs(game:GetService("Players"):GetPlayers()) do --We loop through the players
		if v.Character and v.Character.Humanoid.Health > 0 then --Run a simple conditional statement to see if the character of the specific player exists and if they're still alive
			Character.HumanoidRootPart.CFrame = Map.Spawns[i].CFrame + Vector3.new(0,3,0) --If thats the case then we modify the cframe of their humanoidrootpart to a spawn in the map and add Vector3.new() to ensure that they don't get stuck in the spawn.
		end
	end
end

while true do -- A while true do loop in which we run all three of these functions, and since when you run a function it yields the code we can easily do all three one by one.
	Intermission()
	ChooseMap()
	RunGame()
end

Considering you're attempting to check if the game is reaching its win/lose conditions, I usually make a loop for the game timer and have a loop that runs each second that checks if any of the players are alive and I use a conditional statement to check.

function RunGame()
	local IngamePlayers = {}

	local Map = workspace.Map --We grab the map and since it was named map beforehand its easier to get
	for i,v in pairs(game:GetService("Players"):GetPlayers()) do --We loop through the players
		if v.Character and v.Character.Humanoid.Health > 0 then --Run a simple conditional statement to see if the character of the specific player exists and if they're still alive
			Character.HumanoidRootPart.CFrame = Map.Spawns[i].CFrame + Vector3.new(0,3,0) --If thats the case then we modify the cframe of their humanoidrootpart to a spawn in the map and add Vector3.new() to ensure that they don't get stuck in the spawn.

			table.insert(IngamePlayers,i) --We insert them into the table
		end
	end

	for time = 100,0,-1 do
		print(i)

		for index,plr in pairs(IngamePlayers) do
			if plr then --if the player exists
				local char= plr.Character
				if char.Humanoid.Health > 100 then --If they are alive
					--We do nothing.
				else
					table.remove(IngamePlayers,index) --remove them since theyre dead.
				end
			else
				table.remove(IngamePlayers,index) --remove them from the table since they probably left the game. 		
			end
		end
		
		if #IngamePlayers == 1 then
			print(IngamePlayers[1].Name.." has won!")
		elseif #IngamePlayers == 0 then
			print("everyone died! no one wins!")
		elseif i == 0 then
			print("ran out of time! no one wins!")
		end

		wait(1) --We do this every second.
	end
end