Number of times heads occurs in a row

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#1

How would you find the number of times a coin flips heads in a row given that landing heads occurs with probability p and tails is (1-p)? Also you can’t have an upper bound on the max number of heads in a row

I’m not looking for a recursive solution nor one that involves loops etc
I want it to be an O(1) math function or something similar

I’m not looking for the probability of landing heads N times, I’m looking for if I were to start flipping coins right now, how many times would I get heads in a row (so using math.random)

#2

My memory of probability is a bit shaky but I believe than p(heads)^n will give you your total probability. We have a 50% chance of landing a head (p = 0.5), so if we wanted the probability of landing 5 heads in a row, it would be 0.5^5 = 0.03125

So you can compare this by doing something like math.random < (0.5^n)

#3

Just realised I interpreted your question a little wrong - I’ll see if I can thing of anything for your case

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#4

Something like this should work:

function log(num, base)
	return math.log(num) / math.log(base) 
end

function numHeads(headsProbability)
	local probResult = math.random()
	local heads = math.floor(log(1/(1 - probResult), 1/headsProbability))
	return heads
end
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