How do I prevent RemoteEvent:FireAllClients() from firing more than once?

I have a script that adds to a counter that all players have by 1 for every round. However, this counter adds more than once sometimes, varying from 1 to however many players there are in the game.

How do I prevent from FireAllClients from firing more than once?

Server-side (the for loop that awards wins)

for _, player in pairs(activePlayers) do
        if player then
            if gameresult == "RunnerWin" and player == runner then
                awardWins(player)
                awardPoints(player, 15)
                print(gameresult)
            elseif gameresult == "PlayersWin" and player ~= runner then
                awardWins(player)
                awardPoints(player, 10)
                print(gameresult)
            else
                print("no one wins")
            end
            event:FireAllClients("RoundEnd", 1)
        end 
    end

Local-side

local replicatedstorage = game:GetService("ReplicatedStorage")
local event = replicatedstorage:WaitForChild("RemoteEvent")
local player = game.Players.LocalPlayer

event.OnClientEvent:connect(function( ... )
    local args = { ... }
    if args[1] == "RoundEnd" then
        local trails = player:FindFirstChild("Trails")
        if trails then
            local pCounter = trails:FindFirstChild("Counters")

            if pCounter then
                local counters = pCounter:GetChildren()
                for _, c in pairs(counters) do
                    if c:IsA("IntValue") then
                        c.Value = c.Value + args[2]
                        print("CAPS LOCK ON! I FIRED ONCE")
                    end
                end
            end
        end
    end
end)