I was recently reading some news about a German 13 years-old kid having recalculated the odds of an impact occurring between Earth and the Apophis asteroid. NASA had initially estimated a 1 in 45,000 probability for the asteroid to hit the Earth but apparently they ignored the possibility for the Apophis to hit one of the 40,000 objects orbiting Earth that would put it onto a new trajectory leading straight to us. When factoring this new parameter into the equation the odds suddenly increased to 1 in 450 (and this is exactly what the guy from Germany did).
Now, if you come to think about the odds: 1 in 450 for you winning the lottery looks really, really crappy. On the other hand, a 1 in 450 probability for an asteroid smashing into Earth is disturbingly high. As I quite absently thought about it for a few seconds I suddenly remembered a great article I had read a few years back about the lottery and probabilities. As soon as I had the opportunity I searched the net and managed to locate it on www.fravia.com, a great site to always "go hunting for treasures". I reproduce it below hoping the guy that put it together, +Atheist, won't mind my attempt to spread it. You don't have to take it at face value, just think about it by yourself.
Most people don't have any hope of coming to grips with a near-vanishing probability like 0.0000000715. With such a small value "number numbness" comes into play. Does anyone understand how little chance he has of winning big in a lottery? Private and state lottery corporations, which annually part gullible idiots from trillions of their (almost always meager) earnings all over the world, certainly hope not. Attempts to explain the fantastically small probability of winning a lottery often meet with the objection: "But what if I'm the one?". It would be fair to respond: "Don't worry, you won't be". The probability you have is mathematically zero, yet the bait dangles before millions of gullible people who never fail to buy their weekly ticket. Let's demonstrate the odds with a popular form of lottery that allows the player to select six numbers between 1 and 49 inclusive. The price of a couple of dollars seems good value if it means a real chance at winning several million dollars. Imagine being a mere six numbers away from a new life. Six little numbers! Alas, the dream is an empty one. The real chance of winning a six-number lottery, if you buy one ticket, is 1 in 13.983.816. Hope you know some math, if not: learn. 49*48*47*46*45*44 is MORE than enough, (10.068.347.520) because it treats different orderings of the SAME six-number combinations as being different. But for lottery purposes the ORDER of appearance of the numbers is irrelevant. Since there are 6 ways to choose the first number, there are five to choose the second, four for the third and so on... So there are 6*5*4*3*2*1 ways (in fact 720) to ORDER six numbers. So 10.068.347.520/720 works out to 13.983.816. To express this as a probability, divide 1 by 13.983.816. You'll get something like 0.0000000715. This is an extremely small number, for all practical purposes it IS zero (ask a mathematician if you don't believe me. De facto you have the same chance of winning this lottery whether either you play or not. In case you still don't think that this number is HOPELESS (the "But what if I'm the one?" syndrome), think about lightning. Say lightning kills between 200 and 300 peoples in Europe every year. Say we have 250.000.000 people here. Let's say we get 250 kills every year. Divide: you get a probability of 0.000001 (one chance in 1 million). This is a small number, yet MUCH greater that the lottery chance. Therefore you are a GREAT deal more likely to be killed by a lightning sometime in 1998 than you are to win the next 6-49 lottery you play (that chance, after all is 1 in 14 millions). So instead of playing lottery you'd better be very careful when the clouds are really dark. Of course what I said about lotteries holds true for gambling as well. In all games of chance, even clever people may fall prey to a curious belief (you probably too, my reader, carry on). Roulette wheels, cards and slot machines foretell the future. How else can you explain the common belief in the so-called law of averages? In gambling and lotteries, the desire to win focuses undue attention on statistical anomalies such as runs of good and bad luck. When gamblers experience a thrilling sequence of wins they say they are having a "hot streak" and fear that their luck will "change". On the other hand, when they have been losing heavily, they are sustained by the belief that their luck is about to "turn". The longer they wait, they believe, the more "likely" it becomes that the next roll of the dice will favor their bet. Therefore, somehow the dice 'must know' what has been going on... Even in the seemingly more innocuous lotteries, the same behaviour may emerge. Many lotto players have no other game plan but to wait for the big win that will jump-start their lives. This dream of winning may sustain them in some sense, but it also erodes their ability to formulate and pursue their own goals. They pay double for the dream: they lose money and they lose opportunities. This suits well the society we live in, which is sporting more and more lotteries ("scratch" numbers; "duo" numbers and the whole series of 6 out of 36 etc ... have you noticed that they are growing and spreading without pause? By the way: the first "internationale" lotteries, for "internationale" gullible idiots are doing well too... more and more 'german state lotteries' are luring the zombies nowadays). As usual, the only thing that the society will do is NOT to help people understand reality, but to betray them selling these wishes without any substance in order to get their meager earnings. Anyway +ORC was - as always - right: "neminem pecunia divitem fecit"... the obsession for such an insignificant (and useless) target: "let's make lotta money", an obsession that this awful and doomed society continuously pumps inside our ears and our eyes, let people forget that there is a LIFE to enjoy, full of free beautiful things, like for instance poetry, love, knowledge gathering and cracking. The Internet we live in has added a lot to this list, and will give us whatever we may need... if we will be able to keep it free from the commercial vultures. Have a look at the SOFTWARE for lotteries-addicts and you'll see hundred and one way to keep track of past numbers, i.e. numbers that have won past lotteries and numbers that are "due", because they may not have appeared recently. This needs urgent reverse-engineering. The host of strategies developed for picking numbers have no more chance of success than the standard practice of using your birth date. Once more: to expect past numbers to predict future ones is an utter waste of time. Try to free your mind from petty thoughts: the combination 1, 2, 3, 4, 5, 6 (which many people would judge a sure loser) is just as likely to win as 3, 11, 21, 25, 32 and 40 (a combination of currently 'due' numbers from an 'expert trend chart' from a bogus software that gullible people can 'buy' in order to 'win'). So the probability of anyone of the 49 numbers to be 'chosen' (if the lottery itself is not a bogus one) is always exactly 1/49. There is a particular (non mathematical) reason that most people believe that 1, 2, 3, 4, 5 and 6 is not as likely to occur: It is memorable. The sequence 3, 11, 21, 25, 32 and 40 is not. Not surprisingly, most winning lottery numbers have this non-memorable quality. After all, only a tiny fraction of all six-number combinations has anything memorable or remarkable about it. The ordinary slave concludes in effect, that memorable numbers are not 'good bets' for lottery plays, because memorable number sequences never seem to win. Our cracking session is not yet finished: The real lottery winners are (of course) the lottery corporations themselves. The money that does NOT go to prizes and overhead (about a third of the revenues AT LEAST) is pocketed by the State. Lotteries are politically popular becuse both politicians and a large segment of the electorate love them. They work like a voluntary tax, whose contributions are levied by people on themselves! And many can ill afford to pay it. At the beginning of this century the first socialist newspapers (when socialists still meant people that wanted and tried to change the society) did usually publish the lotto results with a proviso: 'Only idiots waste money on this'. A nice, if a little didactic, warning for their popular readerships. Socialists are all dead, could not survive today, in a world so deteriorated. And the "working classes" read Murdoch's toilet paper and waste money on lotto every week. Back to our reality cracking. You can easily figure out your expected winnings in a six-number lottery. Simply multiply the amount you may lose (your actual bet) by the probability of losing. Subtract the second number from the first to get your 'expected' winnings (in the statistical sense). For example, suppose you buy a $ 1 ticket in a six-number lottery with a current jackpot of $ 1 million. Now follow: if you win the lottery (you won't of course), you win $ 999.999 or $ 1 million minus the cost of the ticket. If you lose, you lose $ 1. Moltiply by the respective probabilities: $ 999.999 * 0.000000013 - $ 1 * 0.999999987 This gives about MINUS 98.7 cents. So, this is your expected winning. Every time you play your money will be eroded at a rate of $ 0.987 per play. That's what gamblers call a sucker bet. Let's visit now the roulette table and our old deep (and stupid) belief that there exist a "law of averages". The roulette table takes on average 5 5/9 percent for the house every play. (Check if you don't believe me). From all roulette games, the take for the house is slow, steady and statistically inexorable. If the gamblers do not notice the continued drain on their pockets, it is because they are lost in the gullible dream of instant money... well people don't notice the continued drain on their pockets when they visit Disneyland either. Say you are playing RED on a roulette table, say the ball lands on BLACK seven times in a row. "Now, you say to yourself, now the ball will ALMOST CERTAINLY land on a RED number... it's the law of the averages!". This is unfortunately NOT true, whatever you may believe. It is NOT true that the longer you wait for a certain random event, the more likely it becomes. It is NOT true. In fact it is quite WRONG. The reason so many people believe this has to do with the confusion (nurtured by all sort of gambling crooks) between the probability of a run and the probability of a single event in that run. The situation is the same flipping a coin. Like the lottery balls and the roulette wheel, the coin knows nothing at all about past history. Its probability to fall seven times head is (.5) at the seventh power, or .0078. This is a number that still differs from virtual zero. Sooner or later it will happen. Not frequent, but in the realm of the truly possible. The chance of winning your lottery are on the contrary the same as to see a flipping coin falling head 24 times consecutively. You will never see it, unless you spend an infinite life flipping coins. Back to our roulette and the seven BLACK in a row. So, you now want to play RED, don't you? What you THINK you are betting on, is that a long run of black must, sooner or later, end. That is a safe bet, but that is NOT what you are betting on. You are betting simply, that the NEXT run will be RED. This is the (statistical AND mathematical) simple truth. Short runs are frequent, very long runs are infrequent, but there is NO upper limit to how long a run may be. If you could play for ever and you would have infinite capital you would experience all possible run lengths. But if you have finite time and finite capital you'll soon or later (remember the ZERO on the roulette table!) lose the last bet and go home broke. Incidentally, that's also one of the reasons most casinos generally apply a house limit on all bets. Suckers should have NO statistical chance whatsoever."
by +Atheist
17 February 1998
http://www.searchlores.org/realicra/ath_sta1.htm
Now, if you come to think about the odds: 1 in 450 for you winning the lottery looks really, really crappy. On the other hand, a 1 in 450 probability for an asteroid smashing into Earth is disturbingly high. As I quite absently thought about it for a few seconds I suddenly remembered a great article I had read a few years back about the lottery and probabilities. As soon as I had the opportunity I searched the net and managed to locate it on www.fravia.com, a great site to always "go hunting for treasures". I reproduce it below hoping the guy that put it together, +Atheist, won't mind my attempt to spread it. You don't have to take it at face value, just think about it by yourself.
Most people don't have any hope of coming to grips with a near-vanishing probability like 0.0000000715. With such a small value "number numbness" comes into play. Does anyone understand how little chance he has of winning big in a lottery? Private and state lottery corporations, which annually part gullible idiots from trillions of their (almost always meager) earnings all over the world, certainly hope not. Attempts to explain the fantastically small probability of winning a lottery often meet with the objection: "But what if I'm the one?". It would be fair to respond: "Don't worry, you won't be". The probability you have is mathematically zero, yet the bait dangles before millions of gullible people who never fail to buy their weekly ticket. Let's demonstrate the odds with a popular form of lottery that allows the player to select six numbers between 1 and 49 inclusive. The price of a couple of dollars seems good value if it means a real chance at winning several million dollars. Imagine being a mere six numbers away from a new life. Six little numbers! Alas, the dream is an empty one. The real chance of winning a six-number lottery, if you buy one ticket, is 1 in 13.983.816. Hope you know some math, if not: learn. 49*48*47*46*45*44 is MORE than enough, (10.068.347.520) because it treats different orderings of the SAME six-number combinations as being different. But for lottery purposes the ORDER of appearance of the numbers is irrelevant. Since there are 6 ways to choose the first number, there are five to choose the second, four for the third and so on... So there are 6*5*4*3*2*1 ways (in fact 720) to ORDER six numbers. So 10.068.347.520/720 works out to 13.983.816. To express this as a probability, divide 1 by 13.983.816. You'll get something like 0.0000000715. This is an extremely small number, for all practical purposes it IS zero (ask a mathematician if you don't believe me. De facto you have the same chance of winning this lottery whether either you play or not. In case you still don't think that this number is HOPELESS (the "But what if I'm the one?" syndrome), think about lightning. Say lightning kills between 200 and 300 peoples in Europe every year. Say we have 250.000.000 people here. Let's say we get 250 kills every year. Divide: you get a probability of 0.000001 (one chance in 1 million). This is a small number, yet MUCH greater that the lottery chance. Therefore you are a GREAT deal more likely to be killed by a lightning sometime in 1998 than you are to win the next 6-49 lottery you play (that chance, after all is 1 in 14 millions). So instead of playing lottery you'd better be very careful when the clouds are really dark. Of course what I said about lotteries holds true for gambling as well. In all games of chance, even clever people may fall prey to a curious belief (you probably too, my reader, carry on). Roulette wheels, cards and slot machines foretell the future. How else can you explain the common belief in the so-called law of averages? In gambling and lotteries, the desire to win focuses undue attention on statistical anomalies such as runs of good and bad luck. When gamblers experience a thrilling sequence of wins they say they are having a "hot streak" and fear that their luck will "change". On the other hand, when they have been losing heavily, they are sustained by the belief that their luck is about to "turn". The longer they wait, they believe, the more "likely" it becomes that the next roll of the dice will favor their bet. Therefore, somehow the dice 'must know' what has been going on... Even in the seemingly more innocuous lotteries, the same behaviour may emerge. Many lotto players have no other game plan but to wait for the big win that will jump-start their lives. This dream of winning may sustain them in some sense, but it also erodes their ability to formulate and pursue their own goals. They pay double for the dream: they lose money and they lose opportunities. This suits well the society we live in, which is sporting more and more lotteries ("scratch" numbers; "duo" numbers and the whole series of 6 out of 36 etc ... have you noticed that they are growing and spreading without pause? By the way: the first "internationale" lotteries, for "internationale" gullible idiots are doing well too... more and more 'german state lotteries' are luring the zombies nowadays). As usual, the only thing that the society will do is NOT to help people understand reality, but to betray them selling these wishes without any substance in order to get their meager earnings. Anyway +ORC was - as always - right: "neminem pecunia divitem fecit"... the obsession for such an insignificant (and useless) target: "let's make lotta money", an obsession that this awful and doomed society continuously pumps inside our ears and our eyes, let people forget that there is a LIFE to enjoy, full of free beautiful things, like for instance poetry, love, knowledge gathering and cracking. The Internet we live in has added a lot to this list, and will give us whatever we may need... if we will be able to keep it free from the commercial vultures. Have a look at the SOFTWARE for lotteries-addicts and you'll see hundred and one way to keep track of past numbers, i.e. numbers that have won past lotteries and numbers that are "due", because they may not have appeared recently. This needs urgent reverse-engineering. The host of strategies developed for picking numbers have no more chance of success than the standard practice of using your birth date. Once more: to expect past numbers to predict future ones is an utter waste of time. Try to free your mind from petty thoughts: the combination 1, 2, 3, 4, 5, 6 (which many people would judge a sure loser) is just as likely to win as 3, 11, 21, 25, 32 and 40 (a combination of currently 'due' numbers from an 'expert trend chart' from a bogus software that gullible people can 'buy' in order to 'win'). So the probability of anyone of the 49 numbers to be 'chosen' (if the lottery itself is not a bogus one) is always exactly 1/49. There is a particular (non mathematical) reason that most people believe that 1, 2, 3, 4, 5 and 6 is not as likely to occur: It is memorable. The sequence 3, 11, 21, 25, 32 and 40 is not. Not surprisingly, most winning lottery numbers have this non-memorable quality. After all, only a tiny fraction of all six-number combinations has anything memorable or remarkable about it. The ordinary slave concludes in effect, that memorable numbers are not 'good bets' for lottery plays, because memorable number sequences never seem to win. Our cracking session is not yet finished: The real lottery winners are (of course) the lottery corporations themselves. The money that does NOT go to prizes and overhead (about a third of the revenues AT LEAST) is pocketed by the State. Lotteries are politically popular becuse both politicians and a large segment of the electorate love them. They work like a voluntary tax, whose contributions are levied by people on themselves! And many can ill afford to pay it. At the beginning of this century the first socialist newspapers (when socialists still meant people that wanted and tried to change the society) did usually publish the lotto results with a proviso: 'Only idiots waste money on this'. A nice, if a little didactic, warning for their popular readerships. Socialists are all dead, could not survive today, in a world so deteriorated. And the "working classes" read Murdoch's toilet paper and waste money on lotto every week. Back to our reality cracking. You can easily figure out your expected winnings in a six-number lottery. Simply multiply the amount you may lose (your actual bet) by the probability of losing. Subtract the second number from the first to get your 'expected' winnings (in the statistical sense). For example, suppose you buy a $ 1 ticket in a six-number lottery with a current jackpot of $ 1 million. Now follow: if you win the lottery (you won't of course), you win $ 999.999 or $ 1 million minus the cost of the ticket. If you lose, you lose $ 1. Moltiply by the respective probabilities: $ 999.999 * 0.000000013 - $ 1 * 0.999999987 This gives about MINUS 98.7 cents. So, this is your expected winning. Every time you play your money will be eroded at a rate of $ 0.987 per play. That's what gamblers call a sucker bet. Let's visit now the roulette table and our old deep (and stupid) belief that there exist a "law of averages". The roulette table takes on average 5 5/9 percent for the house every play. (Check if you don't believe me). From all roulette games, the take for the house is slow, steady and statistically inexorable. If the gamblers do not notice the continued drain on their pockets, it is because they are lost in the gullible dream of instant money... well people don't notice the continued drain on their pockets when they visit Disneyland either. Say you are playing RED on a roulette table, say the ball lands on BLACK seven times in a row. "Now, you say to yourself, now the ball will ALMOST CERTAINLY land on a RED number... it's the law of the averages!". This is unfortunately NOT true, whatever you may believe. It is NOT true that the longer you wait for a certain random event, the more likely it becomes. It is NOT true. In fact it is quite WRONG. The reason so many people believe this has to do with the confusion (nurtured by all sort of gambling crooks) between the probability of a run and the probability of a single event in that run. The situation is the same flipping a coin. Like the lottery balls and the roulette wheel, the coin knows nothing at all about past history. Its probability to fall seven times head is (.5) at the seventh power, or .0078. This is a number that still differs from virtual zero. Sooner or later it will happen. Not frequent, but in the realm of the truly possible. The chance of winning your lottery are on the contrary the same as to see a flipping coin falling head 24 times consecutively. You will never see it, unless you spend an infinite life flipping coins. Back to our roulette and the seven BLACK in a row. So, you now want to play RED, don't you? What you THINK you are betting on, is that a long run of black must, sooner or later, end. That is a safe bet, but that is NOT what you are betting on. You are betting simply, that the NEXT run will be RED. This is the (statistical AND mathematical) simple truth. Short runs are frequent, very long runs are infrequent, but there is NO upper limit to how long a run may be. If you could play for ever and you would have infinite capital you would experience all possible run lengths. But if you have finite time and finite capital you'll soon or later (remember the ZERO on the roulette table!) lose the last bet and go home broke. Incidentally, that's also one of the reasons most casinos generally apply a house limit on all bets. Suckers should have NO statistical chance whatsoever."
by +Atheist
17 February 1998
http://www.searchlores.org/realicra/ath_sta1.htm
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