My better half won rupees 5000 from a kerala lottery ticket, though she was disappointed that she didn’t bag bigger prize. First prize for this ticket was 4 crore rupees. I did some number crunching for this lottery and found the following, Fig 1.
This particular lot has 45 Lakhs tickets and a total of 108921 winners, which means you have a probability of 0.02420466667 that the ticket you purchased is one among the winners.
The above table has been made based on statistical odd of winning, that is, if you want a minimum 5 tickets to win then you must at least buy 200 tickets to increase your odds of winning at least 5, Fig. 2
Digging more, I found an interesting data being shared on the official website, it's the last four digits of tickets from a total of 1,58,162 winners. If it is a perfect random distribution, each winner from 0000 to 9999 will have equal probability of winning. But there were only 6817 numbers that has appeared on that list. Number ‘3560’ has come 41 times thus far, the highest repeated number and the numbers like ‘0006’,’0009’ hasn’t come at all.
I wrote a Python code and run a simulation for 1,58,162 times, interestingly all the numbers from ‘0000’ to ‘9999’ had made its appearance at least once, making it more random than the actual draw conducted by the Lottery agency.
While running the simulation I found something very interesting, if a number hasn't been selected as winner in say first 1000 trials, then the probability of it appearing in the next trials is increased. I think it is a limitation of having software based random generator.
So the randomness or lack of it in the Kerala lottery draw maybe because of the mechanical design of the lottery selection machine.
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