You must be one in 14 million to win the lottery jackpot

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

29 June 2008

There is Sh20 million to be won but no one seems to have enough luck to take it. It started with only Sh2 million in 2002 and over the years, the prize money has increased gradually every week to hit the maximum allowed by the rules of the game.

This is the story of the TOTO 6/49 lottery operated by First Lotto Ltd. Is there something fishy going on or are Kenyans just simply unlucky? According to a company official, about 20,000 tickets are sold every week each playing an average of three games each. Are these enough to guarantee that the jackpot will be won?

The game is easy to play: for only Sh20, you can play one game by selecting any six numbers from 1 to 49. During the draw, 49 balls labelled 1 to 49 are put in a box and mixed. Then six balls are picked at random, one at a time and these become the winning numbers.

So what are the chances of getting the correct numbers?

Suppose one million people are individually asked to write down any number from 1 to 49. Since all the numbers are equally likely, approximately 1,000,000 divided by 49 = 20,400 people would pick each value.

For example 20,400 people would write the number 1, another 20,400 would put down the number 2 and so on. Now, if the 20,400 who wrote “1” were then asked to select another number from 2 to 49, about 20,400 divided by 48 = 425 would pick the value 2. The division here is by 48 because there 48 numbers to choose from (2, 3, 4, 5…49).

And if the 425 who have picked 1 and 2 are asked to choose a third number from 3 to 49, only about nine would select the value 3. This means that if one million people were asked to pick three numbers from 1 to 49, only nine are likely to select 1, 2, and 3 – in that order. 9 in a million is equal to about 1 in 100,000.

Here is another way of looking at it: the likelihood of getting number 1 in the first draw is one in 49, the chance of picking 2 in the second attempt is one in 48, and in the third draw, the odds of selecting 3 are one in 47. Thus the probability of choosing the numbers 1, 2, and 3 is one in 49 x 48 x 47, that is, one in 110,544.

However, in the lottery, the order of the numbers does not matter; selecting 2, 1, 3 is the same as, say 3, 2, 1. Since there are six ways of arranging the three numbers 1, 2, 3, (123, 132, 213, 231, 312, and 321) the chances of getting the three correct values in any order must be one chance in 18,424 (that is, 110,544 divided by 6).

In TOTO 6/49, players select any six numbers from 1 to 49, therefore the odds of picking the correct values and in the order they are drawn are one in 10,068,347,520 (= 49 x 48 x 47 x 46 x 45 x 44). But since the order does not matter, we must divide this by the number of ways of arranging six numbers.

There is an elegant mathematical technique of calculating the number of ways of arranging a given number of items. It is called the factorial and for three items we multiply 3 x 2 x 1 = 6. For six items the answer is 6 x 5 x 4 x 3 x 2 x 1 = is 720.

Therefore, the probability of winning the jackpot is 10,068,347,520 divided by 720. The result is one in 13,983,816 or approximately one in 14 million. That is a very slim chance, but we must bear in mind that one is asked to put in only Sh20 and stands to win a minimum of Sh2 million.

In short, participants get a one in 14 million chance to multiply their money 100,000 times. It’s not a bad bet if you ask me but how does it compare with other countries?

In the UK for example, the National Lottery operates a similar game with tickets going for one pound and a minimum jackpot of two million pounds. Here, players get an opportunity to multiply their money by one million – much better than their Kenyan counterparts.

Nonetheless, the reason the TOTO6/49 jackpot hasn’t been won in a period of six years is not that Kenyans are unlucky: It is that they haven’t been told about the game.

That is, there isn’t enough publicity done for the lottery. Sh20 million is the largest prize money in the history of the country and it is surprising that many people still don’t know about the game.

If First Loto Ltd invested more in publicity, greater numbers people would play and the jackpot would be taken in a short time. That would dispel the air of scepticism in the public and trigger an avalanche of participants. As they say in Hollywood, nothing succeeds like success.