Calculation issue creates lag/crashes (script timeout error)

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#1

  1. I want to calculate the requirement needed to prestige and reincarnate. Currently I am using a loop to do that when calculating multi-prestige/reincarnation

  2. It works just fine until the numbers get really big. Then the lag starts and when a player wants to prestige 1 million times, things stop working and I get the error message Script timeout: exhausted allowed execution time

  3. I have tried varies formulas to find out how to calculate the requirement without the need for a loop, but have been unsuccessful.

The original Prestige formula when a player wants to prestige just one time is:
requirement = 1000000*(currentPrestige.Value+1)

The original Reincarnation forumla when a player wants to reincarnate just one time is:
requirement = 15*(currentReincarnation.Value+1)

Here is the loop I use when a player wants to prestige multiple times at once

function module.MultiRebirthReq(plr, rebirth, num)
	local plrStats = plr:WaitForChild("PlayerStats")
	local reincarnation = plrStats.Reincarnation
	local calc = plrStats.Prestige.Value+1
	local reincarnationCalc = plrStats.Reincarnation.Value+1
	
	local requirement = 0
	

	if rebirth == "Prestige" then
	
		
		for count = 1, num do
			
			requirement = requirement+(1000000*(calc))
			calc = calc+1

		end		
		
		
		
		
	elseif rebirth == "Reincarnation" then
		for count = 1, num do
			
			requirement = requirement+(15*(reincarnationCalc))
			reincarnationCalc = reincarnationCalc+1

		end	


	end
	return requirement
end

Maybe someone here has a better understanding of math and can guide me to a more efficient formula that does not need a loop or perhaps there is a way to avoid the lag/crash/time out issue in some other way

#2

Trying to run anything more than about 10,000 times without a wait() involved is going to crash studio. Now I don’t know why you would even let people calculate prestige a million times. There are ways to calculate it without the loop, however the numbers you want to reach are beyond the normal capabilities of the Roblox engine.

#3

The game started with basic numbers and players could prestige like 10 times at once. As the game progressed, more was required.

I tried the wait() but it only ceased the error, not the breaking of the game. I know there is a way to calculate this with a formula without a loop and have tried various ways, but couldn’t figure it out.

#4

Are you wanting to achieve some form of exponential growth as a requirement for the next level or prestige, in this instance?

#5

Yes, the requirement grows with each prestige/reincarnation. I figured it out though!

It is the sum of an arithmetic sequence.

Here is what I did:

	if rebirth == "Prestige" then
	 n = currentPrestige.Value+num
	 d = 1000000
	a = 1000000
	
	totalSum =  (n/2)*(2*a+(n-1)*d)
	difference = (currentPrestige.Value/2)*(2*a+(currentPrestige.Value-1)*d)

	requirement = totalSum - difference
	
elseif rebirth == "Reincarnation" then
	
	 n = currentReincarnation.Value+num
	 d = 15
	a = 15
	
	totalSum =  (n/2)*(2*a+(n-1)*d)
	difference = (currentReincarnation.Value/2)*(2*a+(currentReincarnation.Value-1)*d)

	requirement = totalSum - difference

end