How Can I make a Random Picker actually Decide Randomly(math.random problems)?

So I use math.random to pick out one player from the entire server to be chosen as a monster. Simple, right? However, the problem is that sometimes that same player gets picked again. He can be picked up to 10 times in a row before the picker chooses another person, which is a huge problem. How can I go about making a truly random picker, and make sure that the person who was just picked cannot be chosen again until at least 2 rounds later?

My current script (functional, but problem is stated above):

-- this function is fired every time a new round starts.
function chooseBeast()
	local plrs = game.Players:GetPlayers()
	local eligibleplrs = {}
	for _,v in pairs(plrs) do
		if v:FindFirstChild("AFK") and v.AFK.Value == false then
			table.insert(eligibleplrs, v)
		end
	end
	local randteam = eligibleplrs[math.random(1, #eligibleplrs)] --<- choose monster HERE --
end
-- this is a simplified version of my script btw, above this comment is where my problem arises.

while wait(120) do
	resetEverything()
	-- intermission
	wait(30)
	chooseBeast()
	LoadMap(math.random(1, 10)
end

You can change the seed of math.random by doing math.randomseed(number). For the best results, the number should be something that is always different, such as the return value of tick() or time()

Or you can stop using math.random at all and use the Random class