17 September, 2009

Lottery coincidence ?

This week exactly the same lottery numbers came up two weeks running. Click here for the story. Just how unlikely an event is that? One in 14 million (assuming it is the standard  6 out of 49 type of lottery) most people would answer. And very considerably higher if the balls had been retrieved in the same order. In fact, this figure applies to what would be the probablity of this lottery on this particular occasion coming up with the same numbers two weeks running. In fact, there are lotteries in many countries round the world and some countries have several draws a week. So there are several hundred lotteries somewhere in the world each week.Multiplied by 52 weeks a year, this comes out to several tens of thousands of lotteries each year. Then over the period that lotteries have existed, the probability that such an event could happen becomes far more realistic. I should add that the lottery that hit the headlines was in Bulgaria. Coincidences do happen and the probability of this particular one is nowhere near as slim as a first look would have us believe. But it would have been more credible if there had already been cases of five of the six numbers comming up in consecutive weeks. Maybe they have, has anyone collected any statistics on this?

Another explanation of course is that someone had tampered with the lottery balls, perhaps by adding weights to certain balls. Why do that, if it will mean the same numbers coming up week after week and sharing the winnings with people who play lottery numbers by "form". More likely is that anyone who had doctored the balls had simply left the doctored balls in the machine. So a good place to start looking would be the person or persons who won the previous week.An idea to look into if the same numbers come up again next week.

While I am on the subject of lotteries, just a few words on strategy.Mathematics tells us that there is no point in poring over tables of previous winning lottery numbers. I am also reminded of an Andy Capp cartoon strip, in which Flo (Andy's long-suffering wife) pointed out that the bookmaker always went on more expensive holidays than Andy and Flo ever did. So, in the long term, the organiser is the winner in any lottery. Mathematically, the expectation (figure obtained by multiplying potential winnings by probability) must be lower than the stake, since the lottery organiser takes a cut before distributing the winnings. But that is not always the case. From time to time there is a "rollover", when there has been no jackpot winner for several weeks and the stakes are combined. In that case, the expectation suddenly becomes much higher. Someone else has also pointed out that many people tend to play similar numbers (dates, or by studying "form"), so if you avoid such numbers you would share with few people if you ever did win. 
Finally, as the advert says, 100% of winners have played. The lottery enables people to play an imperceptible proportion of their income in the hope that they may one day win. So in fact, the transaction is simply to buy a dream. If you ever win, that is a bonus.

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