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

Hey for anyone wondering; I did eventually find a way to do this, and in such a manner as I think its worth sharing with other people.

I basically went with mostly OOP, I created a class called the GameController and another class for matches.

The matches class holds the information like the match time, the game mode, the current map, etc. The GameController class holds all the functions that actually start the game (Like choosing the map, teleporting the players, updating the intermission sequences, etc).

Then I required them into a server script and ran a bit of code like this:

while true do 
    gameController:StartIntermission() 
    gameController:StartGame()
    wait()
end

Its super clean and works really well, Im thinking about finishing it and open sourcing it for my buddies. If I ever do, I'll try and remember to post it here for other people to learn. Cheers.