probability_of_streaks.lua

-- Calculates the probability of streaks
-- author: Revolucas


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-- Only alter the variables below
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local probability = 0.5;        -- Chance of occurrence
local events = 3;               -- Number of occurrences in a row
local trials = 100;             -- Number of trials
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--/////////////////////////////////

local itr = trials/(events+1);
local last = trials - (itr-1)*(events+1) - events - 1;

local c = (1-probability)*(probability^events)
local prob = {}

for i=0,events do
    prob[i] = 0
    if (i == events) then
        prob[i] = probability^events
    end
end

for j=1,itr do
    prob[0] = prob[events] + (1-prob[0])*c;
    for i=1,events do
        prob[i] = prob[i-1] + (1-prob[i])*c;
    end
end

print("Probability of "..events.." events of probability "..probability.." in a row in "..trials.." trials = "..prob[last])
print((1/prob[last]-1).." to 1")