Efrat asks: How is it possible that theoretically each of the numbers drawn in the lottery has an equal chance of being selected, while in reality this is not the case and there are numbers that repeat themselves much more than others (for example: 3 and 8 are chosen much more than 36, according to data I read on the net).
Sorry Efrat: It seems that the statistics have changed in the time since you sent the question and until I checked. The data does not provide confirmation that 3 and 8 are more lucky numbers in the lotto than the other 35 of their brothers in the group of natural numbers up to 37. According to the Lottery website, in the last two years in Israel the winning numbers with the highest frequency are 1, 32 and 33. The number 3 only came up 13 times in the last year and number 8 was drawn 19 times compared to 24 appearances of 33 in the same period of time.
But the real bewilderment is the very interest in "hot numbers", the lottery is based on a random draw of 6 numbers from 1 to 37. Twice a week the balls bearing the numbers are shuffled again and past results have no effect on the chance of a number in the next draw. And yet, Efrat is not only looking for templates in the past, but even the Lottery website proudly displays a page "Statistical information” which allows the bettor to know, for example, how many times the number 7 has come up since September 2005 until the writing of these lines (263 times for those who really like unnecessary trivia). Randomness is a difficult concept to digest. Ages of evolution have shaped the mind to look for patterns and regularities and games of chance undermine the way we perceive and interpret the world. Monitoring of roulette gamblers revealed that after a sequence of 6 repetitions on the same color (red or black) over 80% of the players will bet on the opposite color even though the game wheel does not remember the previous results and the players themselves would not sit around it if they did not believe that the casino provides them with random roulette. This type of error, i.e. expecting the next random event to bring our sample closer to equilibrium is called The gambler's fallacy (gambler's fallacy) and it is widespread and rooted in our intuition. In the state of Maryland in the USA, for many years, a lottery has been operating in which a 3-digit number (from 0 to 999) is won every day. It turns out that the day after a certain number is won, the frequency of betting on it drops by about 2 times and remains lower than expected for about two months. There are those who claim that our tendency to the "gambler's fallacy" stems from the fact that the way we predict events based on early observations is adapted to small and closed samples. If we look at the students leaving the class after the bell rings and it appears that the first 5 to leave are boys, it makes sense to bet that a student and not a student will be number 6 simply because after some of the boys left, the relative share of girls among those remaining in the class increased. The gambler's fallacy, according to this view, is simply a fallout from common situations such as lotteries where the cards are reshuffled after each bet. A second type of mistake is assuming a "hot hand" - the customer's term from the world of basketball where players and coaches tend to assume that the one who scored several shots in a row will also score the next shot and therefore it is better to hand him the ball. In a large-scale study that examined the preferences of Danish lottery bettors, it became clear that 21% of them are prone to the "gambler's fallacy", while 6% tend to lay down a "warm hand" and bet on numbers that have been drawn in the recent past. The two failures seem to be opposites but it turns out that the same people tend to fail at both. Immediately after a winning number the "gambler's fallacy" is evident and the bets on it drop sharply out of the mistaken expectation that the sample will "correct itself" but if the same number comes up several times in a row the gamblers go to the hot hand fallacy as if their confidence in the randomness of the lottery is shaken. It seems that our lottery company tries to encourage such mistakes in the statistical information it shares: the lottery encourages the hot hand fallacy on the page called "Hot Numbers" where an orange flame is drawn next to numbers that have come up many times in the lottery and the gambler's fallacy on the "Hot Numbers" page where less drawn numbers are decorated with a blue flame . What is the lottery's interest in making these statistics available? Studies show that both those who fall into the "gambler's fallacy" and those who assume a "hot hand" tend to gamble more than those who have a good understanding of the principles of probability. Those who bother to find out the results of past lotteries and base their lottery guesses on the basis of this information fill more columns and flow more money to the organizers than just gamblers.
Apparently, Efrat, every combination of numbers in the lottery carries with it the same chance of winning, but not every combination carries the same profit expectancy: since the prize is divided among the guessers, you should choose a combination that, if it does happen, will leave you alone with the entire pot.
The lottery that floods us with barren information about the results of lotteries 10 and 15 years ago keeps to itself the really interesting information: which numbers and combinations are liked by gamblers. And yet there were those who found lines resembling the typical lottery column by examining the common denominator of the lotteries in which many guessers shared the first prize and in contrast combinations of numbers that left the prize for the next lottery.
Many bettors include in the bet important dates such as birthdays and weddings because there are at most 31 days in a month but 37 numbers to choose from, so high numbers will be neglected compared to the low ones. In the UK, where the form contains 49 numbers to choose from, it was found that about half of the winning orphan raffles contained at least 3 numbers outside the realm of guessing by date enthusiasts. Last Saturday night the lottery was held without a big win and I bet that the 2 consecutive numbers 33 and 34 that came up in the lottery are responsible for that. Even those who try to fill in a "random" column unwittingly create patterns that are far from random: such a person tends to move the pencil over the center of the form and spread the guesses "fairly" over it. In such columns, there are almost no consecutive numbers, even though the probability of a pair of consecutive numbers in a six is about 60%, and in particular, those filling in trying to reproduce randomness avoid numbers that are one above the other on the form and they miss the numbers at the ends of the row. It turns out that combinations of numbers sitting on the form in such a way that bettors perceive as "random" that is, spread in a way that does not disadvantage any side of the table of numbers yield a large number of partners for the prize. Particularly popular numbers among diviners are 7 and its multiples, 9, 11 and the mystical numbers 12 and 13.
But Efrat, even the lottery column with the best chance of escaping the crowd carries with it a chance of less than 1 to 2 million to win the big prize. It's hard to grasp how small this chance is and one can only explain the ear with analogies: there is a greater chance that a person you choose at random from among the country's residents will be a former Chief of Staff than to win the lottery and the chance of a young and healthy person dying on the day he fills out the form is significantly higher than his chance of winning. Why then is the strange game so popular all over the world? This puzzle will have its own column.
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More of the topic in Hayadan:
7 תגובות
Every period (up to two months) there are certain numbers that come out more than the others, then they stop coming out with high odds, and there are other numbers that come out more, it is not understood how this happens, maybe it has to do with the order of putting the balls into the mixer...
My name is Noah. But I'm not comfortable with the article.
There is obvious cheating in the lottery if there is information about the weight of the balls before the draw, then there is control over the exit/emission of the ball by the machine. Before all the above calculations, it is advisable to demand from the lottery company that they perform draws manually and not by computer, for example a person with a face covering who does not see the tax ball is drawn and thus there is no way to control which ball comes out.
Since the balls are checked for their weight - lottery - and deviations cause a ball or a complete set to be changed - it is likely that a change can be seen in a certain deviation of results. It is worth a computer test in groups of 50 draws or any number between 50-150 draws - and try to "feel" the replacement of the set of balls. Bring me a computer person skilled in Excel and a macro in Excel and we can prepare an amazing article.
"The Oded method" or, as it is officially called, the martingale, operates in the biggest bet of all: in the economy.
Many central banks have set themselves an inflation target of 2% without explaining why. In my opinion, the explanation is simple: such inflation erodes half (0.4999) of the value of money during one generation (35 years)... a number too precise to be coincidental.
The "Oded" method will not work, because when you reach the really big numbers, let's say 1,048,576 US dollars, the croupier will point out that there is an upper limit for gambling and he does not agree to cross it.
Beyond that, it's hard and long work to earn a single $. If you are in Las Vegas, and pay $200 for your room, you will have to work more than two days straight to recoup your investment.
"The Oded method" named after the guy who discovered it for us, says that we will choose a color, red or black in roulette, and put a dollar on it. If we won, we will take the dollar and put another. We lost, women 2 dollars, 4, 8, 16.. At some point it has to come out red, right? So when it comes out we earn a dollar and we can start the process over, thus accumulating a small treasure for us after a long period of time.
Question: Will the Oded method work? And if not why?