Mathematics behind Lottery

Everybody likes to be rich. But rather than working hard to achieve it, we tend to look for shortcuts. This is the reason for all the get-rich-quick scams that are abundant today. There are people who have lost their whole possessions seeking these fortunes. Unfortunately, people have a hard time gasping the harsh truth. There are no shortcuts to success. One famous quick-rich scam is the lottery. Our effort is to educate you about the impossible odds you have to beat to win the jackpot, through an understanding of probability and possibility.

Imagine you flipping a coin. What are the possible outcomes? It can either fall with head or tails at top. Or it can roll towards a sewer and disappear. If you flip the coin outside, even a bird can swoop in and swallow the coin before landing. All of these are POSSIBILITIES. But their occurrences are negligible (rare). So we consider only landing head or tail. If the coin is an unbiased coin (equal chance to land either side), the PROBABILITY of landing Head is ½ or 50%, and landing Tail is 50%. Similarly, getting 1 on a six sided dice throw has a probability of 1/6 or 16.6%. Now that we have an idea of probability and possibility, Let us dive into our lottery business. Imagine you have two coins. What is the possibility of both of them landing Head on two flips? To understand this, let us draw a diagram illustrating all the possible outcomes.

As you can see, there are 4 possible outcomes, and getting both heads is one of them. So the probability of getting two heads is ¼ or 25%. Similarly, one can express getting 10 consecutive Heads as

So what are the odds of you winning the lottery? A typical lottery has 6 numbers picked, each from a pool of 0 to 9 numbers. That means probability of your number combination being picked is

This is an insanely small probability! To compare this with usual occurring, the chances of you meeting a Fatal accident in Sri Lanka is 0.15%, which is 10000 times more likely! Yet you don’t bet on meeting with an accident, do you? Add the English letter to this equation, and the probability gets even lower. Some lotteries have a different method, where 6 numbers are chosen from a single pool of 80 numbers. Here, the winning probability of Jackpot is

So why do people buy lotteries with these odds. There are few psychological phenomenon at play here. First one is overestimation of own odds. Our brains are not accustomed to very large numbers, or very small numbers. We can distinguish difference between 10,100 and 1000. But we cannot easily comprehend between million and billion. To give you an idea between million and billion, consider this. 1 million seconds is little more than 11 days. 1 billion seconds equals 31.75 YEARS!

Another reason for buying lottery is near miss effect. When the winning numbers are closer to your numbers, you think that you’ll win next time. But there is no relationship between this week’s winning numbers and next week’s winning numbers. Also, there is a phenomenon known as gamblers fallacy. Simply put, if this week did not have a winner, we think next week’s chances of having a winner are higher. This is also false. Next week’s draw is independent from this week. Finally, there is the availability bias. By showing previous winners on TV, Lottery companies make you believe that you can win. But you don’t see the millions of people who didn’t win on TV, do you?

So how do you increase your chances of winning lottery? As a start, rather than buying a ticket every day, collect money and buy a lot of ticket on a single day. Also, join with some friends and pool your money to buy lots of lotteries. Here, even though you have to share your winnings, you can increase your chances of winning. But remember, even after all these tricks, your chance of winning is still very low. Your money and time is better utilized at something useful, and you can surely win a fortune then. All the world’s current billionaires have struggled at their beginnings, and none of them have won a lottery. Just think on that.

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