Random airtime numbers can’t bust the cell phone company

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

19 October 2008

Stephen Kimani challenges the point I made a few weeks ago regarding the possibility of randomly entering a valid airtime card number in your cell phone. He observes that cards of similar denomination start with the same four digits thus he argues that the chances are not one in thirty trillion as stated in my article, adding that “I may not have the figures myself, but I tend to believe the chance should not be beyond 1 in 100,000.”

True; if knock out the first four digits of a 14-digit code, you will be left with ten digits and therefore the chances of striking a correct card number are increased from one in one hundred trillion to one in ten billion. And taking into account the limitation of three wrong trials, this goes up further to one in three billion. But this is the probability for any particular denomination of the cards.

Nonetheless, we may want to find out the potential loss that a company could suffer. The market leader has about 12 million subscribers and if all of them tried their luck at entering random scratch card numbers, chances are that none would get a valid combination!

The reason is that, with a probability of one in three billion and “only” 36 million trials (three from each subscriber), the expected successes are less than one. If you divide 36,000,000 by 3,000,000,000, you get 0.012.

What if the limitation of three trials was removed? How many times would every one have to try before we are certain that one person has entered a valid code? To get the answer, we “invert” the question a little bit and ask: How many times would each of the 12 million customers have to try to make a total of three billion attempts? The result is 3,000,000,000 divided by 12,000,000, equals 250 times.

Now how long do you think it would take to enter a 14-digit code 250 times? Suppose you can enter two digits per second; 14 would take 7 seconds. You’d also need 3s to enter the system characters (the “star-xxx-star….”) and another 10s for connecting to the network and sending the code. That is, you need 20s for each trial, or at least 83 minutes to try 250 times.

Now imagine that: If each of the 12 million customers were to try entering random airtime codes for one and a half hours, only one person would be lucky enough to get a valid entry. In reality, the system would crash in first few seconds because of overload!

If the customers did this day and night for a year, only 6,000 people would get valid codes. And what would be the total value of these codes? With 12 million subscribers who buy about Sh60 billion worth of airtime per year, my estimate is about Sh30 million…just a drop in the ocean for the cell phone company!