On The Odds Of Winning Mariba

LOOKING at the big supplement on the lavishly publicised Winna Mariba competition and the apparently generous prizes of up to N$2 million led me to wonder what the odds really are of winning not just the big prizes but even the small one of N$10.

The rules of the ‘game’ are a bit puzzling at ?rst because the writer confuses the terms ‘number’ and ‘digit’. Having sorted this out, we see that the contestant, to win the smallest prize, has to guess three numbers correctly out of seven, the seven numbers being (presumed) non-duplicate members of the set of whole number between 1 and 47 inclusive.The number of ways of choosing a sample of numbers of a given size from a given population is calculated quite easily from what in mathematics are called binomial coef?cients.In addition the contestant has to ‘guess’ a letter from the phrase Trustco Group – since there are 8 distinct letters in this phrase the chances of winning are then reduced by this factor.You can enter the competition as often as you like, but for a stake of N$4 each time! So the ‘punter’ paying in N$4 for possible winnings of N$10 is thinking of odds of 2 ? to 1 – quite modest.However, if he knew the odds of winning even this N$10 are in the region of 3700 to 1 against, he would not be so encouraged.What about the grand prize of N$1 million? Here the punter may be contemplating odds, for his N$4 investment, of 250 000 to 1 – a bit more daunting, but in fact the odds of guessing all 7 out of 7 numbers correctly, together with the right letter, come to over 500 million to 1 against.This means that if a million people enter the competition every week (all with different entries) the million-dollar prize would be awarded on average less than once every 20 years! Let us look at one more advertised special offer by this company – a computer system for N$370 per month (over 36 months).Computer equipment becomes outdated and depreciates very rapidly – say at a rate of 20% per year (being nearly worthless after 3 or 4 years).If we work out the present value (PV) function of this investment at this rate, we get about N$10 300.Since you can get a computer system of the type described currently for about N$4 000, this is another poor investment.It is to be regretted that they seem to be exploiting the lack of education or numeracy of their clients and the odds of winning its prizes, which are misleadingly advertised.Ex-Maths Teacher WindhoekHaving sorted this out, we see that the contestant, to win the smallest prize, has to guess three numbers correctly out of seven, the seven numbers being (presumed) non-duplicate members of the set of whole number between 1 and 47 inclusive.The number of ways of choosing a sample of numbers of a given size from a given population is calculated quite easily from what in mathematics are called binomial coef?cients.In addition the contestant has to ‘guess’ a letter from the phrase Trustco Group – since there are 8 distinct letters in this phrase the chances of winning are then reduced by this factor.You can enter the competition as often as you like, but for a stake of N$4 each time! So the ‘punter’ paying in N$4 for possible winnings of N$10 is thinking of odds of 2 ? to 1 – quite modest.However, if he knew the odds of winning even this N$10 are in the region of 3700 to 1 against, he would not be so encouraged.What about the grand prize of N$1 million? Here the punter may be contemplating odds, for his N$4 investment, of 250 000 to 1 – a bit more daunting, but in fact the odds of guessing all 7 out of 7 numbers correctly, together with the right letter, come to over 500 million to 1 against.This means that if a million people enter the competition every week (all with different entries) the million-dollar prize would be awarded on average less than once every 20 years! Let us look at one more advertised special offer by this company – a computer system for N$370 per month (over 36 months).Computer equipment becomes outdated and depreciates very rapidly – say at a rate of 20% per year (being nearly worthless after 3 or 4 years).If we work out the present value (PV) function of this investment at this rate, we get about N$10 300.Since you can get a computer system of the type described currently for about N$4 000, this is another poor investment.It is to be regretted that they seem to be exploiting the lack of education or numeracy of their clients and the odds of winning its prizes, which are misleadingly advertised.Ex-Maths Teacher Windhoek