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)