What’s The Deal With State Lottery Odds Table?
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Last updated on February 8, 2021 Probability and odds are two related concepts, but they are not mathematically equivalent. Therefore, discussing probability and odds must include their difference in meaning and in scale. Some think it matters not what term is used, as long as you get the gist. However, it could lead to flawed decision making and incorrect estimates of chance if the exact term gets jumbled in a wrong context. Distinguishing probability from odds The inappropriate swapping of the terms “probability” and “odds” is widespread in many state lottery websites. If you lack the insight to perceive this, you might end up making the wrong decisions when playing. It is, therefore, necessary to know the difference between the two related mathematical concepts. In lottery games, for example, knowing the difference between probability and odds could help you decide which combination to play. Disclaimer: I am not saying that the computations of odds and probabilities on state lottery websites are wrong. The purpose of this article is to simply set a clear definition and context for probability and odds. Probability refers to the ratio of the number of times an outcome could occur compared to the number of all possible outcomes. In our previous posts, we use the formula below for probability. In a lottery game, the probability of winning offered by one combination you mark on your playslip is one over the total number of possible combinations. For example, you bought a ticket for a 6/47 game for the combination 1-2-3-4-5-6. In order to bring home the jackpot, you need to exactly match the winning combination. A 6/47 game has a total possible combinations of 10,737,573. Therefore, the probability is 1/10,737,573. A common way of expressing probability in spoken language is x in y. Hence, the probability to win in a 6/47 game with 1-2-3-4-5-6 combination is 1 in 10,737,573. Odds also refer to a ratio. This time, however, it is the ratio of favorable outcomes compared to unfavorable outcomes. Odds compare the number of ways an event can occur with the number of ways the event cannot occur. We have been using the formula below to compute for odds. We aptly refer to odds as the ratio of success to failure because the odds favoring your winning the lottery is the number of success over the number of failures. Using the formulas for odds, we can compute for the odds as 1/ (10,737,573 – 1) or 1/10,737,572. In our other posts, we express odds or ratio of success to failure as x to y. Hence, the odds for winning in a 6/47 lotto game with the combination 1-2-3-4-5-6 is 1 to 10,737,572. Others also denote odds as x: y so we can also write 1 to 10,737,572 as 1: 10,737,572. This is just for the jackpot prize. We may also calculate the second division prize for matching 5 out of 6 balls. C(6,5)= Number of ways to match 5 balls (6 ways to happen) C(41,1) = The sixth ball must be one of the remaining 41 balls that were not drawn (41 ways this can happen) (6 * 41)  = 246 ways you can match 5 of 6 We have to minus the 246 from the total number of combinations. Therefore, there are 10,737,327 ways to fail. 10,737,573 - 246 = 10,737,327 With this, the expression of odds should be: Odds (5 of 6) = 246 / 10,737,327 or Odds (5 of 6) = 1 : 43,648 Clearly, it shouldn’t be 1 : 43,649 as shown in the Official Michigan Lotto 47 odds table shown below. The same can be said for other minor prize divisions. Confusing information about odds and probability in lotteries is widespread. In the following discussion, you will see that there are only at least two state lotteries that hit the correct mark in declaring the probability of winning for the games they offer. Apparently, 10 other state lotteries do not show the correct information that players need to know. These are only a few examples, but expect to see more lotteries with confusing odds and probability details. Make sure that you have the proper knowledge to distinguish odds from probability and vice versa. This way, you will be prepared to realize for yourself what you must do when you see the inaccurate information. Massachusetts Lottery There are only at least two state lotteries that provide information to their players based on how we recognize and use probability and odds. Among them is Massachusetts Lottery. This is a table for 6/69 Megabucks Doubler of Massachusetts Lottery. The information provided by the Massachusetts Lottery to its patrons coincides with how we explain probability and odds to discerning readers. You see from the table above that the probability to win the jackpot by matching 6 out of 6 numbers is 1 in 13,983,816. This is also how Massachusetts Lottery provided players with the crucial probability information for its other draw games. Expect to see a similar representation of probability for Mass Cash, Lucky for Life, Powerball and Mega Millions. The probability to win the jackpot in Mass Cash is 1 in 324,632. In Lucky for Life, you could win $7,000 a WEEK for LIFE! by matching the 5 numbers and the Lucky Balls at a probability of  1 in 30,821,472. Confusion could arise looking at the winning odds from Powerball website and the winning probability from Massachusetts Powerball web page. The Powerball website notes that the odds to win the grand prize are 1 in 292,201,338. The probability of winning the game from the Massachusetts webpage aligns more with our understanding of probability. The “1 in 292,201,338” is not the odds, but the probability to win. A similar situation exists for Mega Millions. The Massachusetts web page for Mega Million depicts the probability to win this game as 1 in 302,575,350. Massachusetts is not alone in presenting probability this way. There is also Pennsylvania Lottery. Pennsylvania Lottery Pennsylvania Lottery, meanwhile, does not claim outright that the information it provides is odds or probability. See the image below to see what I mean. Instead of stating directly whether it is odds or probability, Pennsylvania Lottery uses “chances of winning”. Incidentally, probability also refers to the number reflecting the chance that a particular event will occur. It is also valid to call probability as chance. Hence, the way Pennsylvania Lottery presented chances of winning is the same as saying probability of winning. From the information in the table, the probability or chance to win the jackpot in the Pennsylvania Lottery Treasure Hunt is 1 in 142,506. You could also view similar presentation of probability for Pennsylvania Lottery’s other draw games like Cash4Life, Cash 5, Powerball and Mega Millions. It is unfortunate that other state lotteries do not have the same manner of imparting knowledge to its regulars on probability and odds. In this day and age of technology, one must be insightful when reading and accepting any presented information. This will help eliminate chances of deciding incorrectly. Ohio Lottery Take, for instance, this table for Ohio Lottery Classic Lotto. Notice that this Classic Lotto from Ohio Lottery and the Megabucks Doubler from Massachusetts Lottery are both 6/49 games. The table above shows that the supposed odds for winning the jackpot in Ohio Lottery Classic Lotto are 1 in 13,983,816. An observant reader will immediately question whether or not the information is valid. Either the title for the column is incorrect or the respective entries for odds are inaccurate. It is important that you establish an accurate interpretation of data based on your knowledge about odds and probability. Do not accept what you read as it is. Don’t you think that perhaps the column should be named “Probability” instead of “Odds”? Let me explain. A 6/49 game has a total possible combination of 13,983,816. Therefore, if it is really the odds, it should have contained 1 to 13,983,815 instead of 1 in 13,983,816. This 1 in 13,983,816 is a more appropriate as the probability to win, instead of odds. Let me show you other examples of confusing odds tables. More perplexing odds tables The Virginia Lottery Cash 5 is a 5/41 game. The total possible combination in this game is 749,398. Applying what we learned about probability and the formula above, the probability to win Cash 5 is 1 in 749,398. Using the formula above for odds, we could get 1 to 749,397 as the odds to win in Cash 5. Thus, do not feel confused when you visit the web page for Virginia Lottery Cash 5. You know better than to immediately believe that the odds of winning the jackpot are 1 in 749,398. Our next figure is for California Lottery Fantasy 5. A 5/39 game like this has the total possible combinations of 575,757. If we do the simple computation, we could get Probability = favorable combination / total possible combinations = 1 / 575,757 Odds = favorable combination/ (total possible combinations - favorable combinations) = 1 / (575,757 - 1) = 1/ 575,756 Thus, what interpretation can you give for the odds information in the table above? Is 1 in 575,757 probability or odds? Next, we look at the of Lotto 6/42 from Louisiana Lottery. It claims that the odds to win the cash jackpot in Louisiana Lottery Lotto are 1 in 5,245,786. A 6/42 like this has the total possible combinations of 5,245,786. Let me show you the simple math computations for probability and odds. Probability = favorable combination / total possible combinations = 1 / 5,245,786 Odds = favorable combination/ (total possible combinations - favorable combinations) = 1 / (5,245,786- 1) = 1/ 5,245,785 Therefore, the 1 in 5,245,785 from the table above is not the odds, but the probability. Let as look now at this table for Hoosier Lottery Lotto 6/46 and see if the information is correct. In a 6/46 game, the total number of possible combinations is 9,366,819. Probability = favorable combination / total possible combinations = 1 / 9,366,819 Odds= favorable combination/ (total possible combinations - favorable combinations)= 1 / (9,366,819- 1)= 1/ 9,366,818 Would you believe what the table says that the odds to win the jackpot are 1 in 9,366,819? It really helps to first confirm if the information you read is correct or not. Our next example of confusing odds table is from Minnesota Lottery Northstar Cash. This is a 5/31 game that has 169,911 total possible combinations. Let us see if the information of odds from the table is acceptable. Probability = favorable combination / total possible combinations = 1 / 169,911 Odds= favorable combination/ (total possible combinations - favorable combinations)= 1 / (169,911 - 1)= 1/ 169,910 Do you just accept that the odds of winning the jackpot for Northstar Cash are 1 in 169,911? A 6/47 game like the Classic Lotto 47 from Michigan Lottery has the total possible combinations of 10,737,573. Looking at the values underneath the Odds column of the table above could make you get more confused. Sure, the title of the column is Odds. The succeeding entries even follow the depiction x: y that we mentioned above as applicable for odds. Yet, are the numerical values acceptable? Probability = favorable combination / total possible combinations = 1 / 10,737,573 Odds= favorable combination/ (total possible combinations - favorable combinations)= 1 / (10,737,573- 1)= 1/ 10,737,572 Our computations show that 1: 10,737,573 are not the odds for winning the jackpot in Classic Lotto 47. It is also not even the probability for the same game. A similar game is this Jumbo Bucks Lotto from Georgia Lottery. See the image below. Although different in the way of writing the figures, the values in this table from Georgia Lottery also do not conform to the values we have gathered from our odds computation. It is more appropriate to say that 1: 10,737,573 is the probability to win the jackpot rather than the odds. There are 45,057,474 total possible combinations in a 6/59 game…
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How To Use Lucky Numbers To Win The Lottery
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Last updated on January 2, 2021 It is not easy to disprove superstitions without first learning why coincidences or lucky numbers occur in the lottery. Someone sent me an email and said this: My Uncle won the lottery several times (no jackpot, though) in the ’90s, and he claimed that luck plays an important role. I don’t know, but I am trying my lucky numbers in the lottery, yet it seems that I am not as lucky as my Uncle. Surprisingly we hear the news of players winning the jackpot twice or even more. Can you explain why sometimes the lottery favors few players? I would agree if someone claimed that he had won the lottery because of luck. That’s because in a random event where you don’t know what’s going to happen next and you win, what else can you call that but “luck” indeed. However, striking luck twice or several times is said to be unusual in a sense. Even if the odds of winning the lottery are seemingly improbable, some people achieve a continuous winning streak. For example, a man won the Illinois lottery twice., Every once in awhile, we hear unusual stories of lucky lotto players such as the Colorado man who won the Powerball jackpot twice on the same day. Such an occurrence happened not just once. A Newark man and a woman in Virginia experienced this too on different occasions., So why do all these happen in a truly random, fair, and unbiased lottery game? The answer is the law of truly large numbers or LTLN. Good luck, bad luck, and the law of truly large numbers Being lucky can be ascribed to randomness. When many people pooled their bets together to have fun at the lottery, someone at one point had to be lucky. And although improbable, someone who got lucky yesterday might be the same person who may get lucky again tomorrow. That may sound extremely unusual, but mathematicians don’t look at it that way. The law of truly large numbers takes effect in a random event, whether we like it or not. The law of truly large numbers states that given abundant opportunities (hence the term truly large numbers), even unusual events and strange coincidences are expected to occur. Mathematicians will be surprised if we don’t see unusual stories like these in the news., , This particular law in mathematics applies to lotteries and all extraordinary events and coincidences in every aspect of life. In the lottery, this mathematical law can be observed very quickly. First, many countries worldwide operate lottery games. All these draws happening worldwide quickly add up to already abundant opportunities. At any given time, an unexpected and unusual story can happen at any place around the world. History has proven that the vast amount of lottery draws taking place every day allows for such unnatural occurrences to exist. From the perspective of lucky people, the inverse can happen too. These unusual events are NOT always pleasant news. For example, in 1980, Maureen Wilcox bought tickets for the Massachusetts State Lottery and the Rhode Island Lottery. Both tickets had the winning numbers. Unfortunately, her ticket for the Rhode Island Lottery matched the Massachusetts Lottery winning combination, and vice versa. Wilcox’s story takes away: do not play two different lotteries at the same time on the same day. Interestingly, some events can be so bizarre and fascinating that one would think such seemingly improbable things aren’t real. For example, mathematicians use the same law to explain why we hear stories of lotto players who have won using tarot cards. Or a pet owner got his winning numbers from his pet chicken, who accidentally walked on a calculator. Likewise, the same law answers why a Loughton man’s vivid lottery dream came true., ,, If you hear a story about a palm reader or a paranormal psychic who helped someone win the lottery, don’t be surprised at all. However, please don’t believe that palm-reading, psychic reading, and other supernatural tools work as a strategy to win the lottery. The unusual lottery winning stories you hear in the news does not affirm the effectiveness of their methods. These supernatural beliefs don’t apply to any random game, let alone the lottery. The law of truly large numbers is truly fascinating and adds color to our everyday lives. These are the stories that the mainstream media likes to cover and sometimes exaggerate. In September of 2009, the Bulgarian national lottery was shaken after the same six numbers (4, 15, 23, 24, 35, and 42) were drawn in two consecutive draws. This event created a media storm and led the Bulgarian authorities to order an immediate investigation. Should we be surprised by this incident? True, it’s freakishly unusual and improbable, but it can happen according to the law of truly large numbers. David J. Hand, an emeritus professor of mathematics and senior research investigator at Imperial College London, said this: Sometimes, though, when there are really many opportunities, it can look as if there are only relatively few. This misperception leads us to grossly underestimate the probability of an event: we think something is incredibly unlikely, when it’s actually very likely, perhaps almost certain.David J. Hand Life is full of surprises. The lottery is not exempted from that powerful force of nature. How to be lucky using the law of large numbers You cannot change or manipulate your chances of winning the lottery because the underlying probability never changes. You also cannot beat the odds —no one can. However, there’s a way to play the lottery and get the best shot possible. How? Buy more tickets. However, buying more tickets is useless if you’re making the wrong choices.To get the best chance possible, we need to add another strategy—making intelligent choices. That’s how math can help. We can line up all your options and make intelligent choices to make sure you are not mathematically wrong most of the time. How NOT to be mathematically wrong in the lottery Earlier, we discussed that some people are “lucky” or “unlucky” because all lotteries are bound to behave according to “the law of truly large numbers.” So, here’s another question that you might ask: can you force luck on your side? Lucky for you, yes. It may sound absurd, but you can—mathematically. How? To borrow a line from a multi-awarded Bob Dylan song: The answer my friend is blowing in the wind. I’ll explain why in a little while. But let me give you a more concrete example. To be lucky, you have to follow another law in mathematics called the law of large numbers or LLN. Just to be clear, LTLN is different from LLN. While the law of truly large numbers (or LTLN) explains why unusual events occur and why some people are lucky, the law of large numbers (or LLN), on the other hand, defines the conclusion of the lottery based on a large number of draws. Theoretically, you can force luck on your side if you follow the conclusion. That means you are intelligently playing the lottery with the best ratio of success to failure by following the general trend (I”ll give you lots of examples below). The depth of this strategy can be difficult to grasp at first. But, if you try your best to understand how it works, you’ll discover a powerful strategy for playing the lottery that only mathematics can provide. Here’s a related article that might interest you: Using Birth Dates in PLaying the Lottery? Here’s What Math Says. Fortunately, you don’t need to know mathematics to implement a mathematical strategy. This lottery calculator will do ALL the heavy lifting for you. There, now you’re getting closer to being confidently lucky! Before we continue further, let me state a little caveat. Being lucky and the illusion of control Making an intelligent choice is a pretty straightforward statement. However, probability theory is one of the most misunderstood fields in mathematics. We need to thresh out this issue carefully and in the right perspective. To say that you can force luck on your side doesn’t mean you have the power to control the outcome of any lottery draw. The concept is very far from that. Have you heard of the term “illusion of control?”, An illusion of control is a dangerous belief to have for yourself. Some people believe that just because they have a strategy to win, they also think they’re in control of the lottery draws. Let me tell you right off the bat that you can’t win the lottery more frequently. Some lotto gurus may try to convince you that you can win small prizes more often. On the other hand, I would suggest that you run away from these people as fast as possible. I have already debunked this issue in my earlier article: The Truth About Winning Small Prizes in the Lottery Here’s the truth: forcing luck to your favor is not equivalent to making money in the lottery. The truth is that the expected value of each ticket is always negative.In other words, the lottery can neither be a source of income nor a substitute for a real job. The lottery’s real objective is to have fun, and the fun begins at the number-selection process. When you use the power of calculation, you can never be mathematically wrong based on the law of large numbers. I recommend that you explore the fascinating world of math so you can fully appreciate how it is applied in the lottery setting. While the Lotterycodex calculator does all the hard work, it’s still best that you know how it works. So, let’s move on and explain how math works in the lottery. First, we will discuss the simplest strategy then proceed to a more advanced option. The simplest one is your choice of the lottery. The lottery game you choose can hugely influence your luck. Your choice of a lottery game can influence your luck When it comes to making choices, you have the power to calculate your advantage. For example, if choosing between the 6/42 and 6/49 games, the smart player would opt for 6/42. That’s the point of calculating the odds. You know that you are “not mathematically wrong” when it’s time to make a crucial decision. Choosing the right game entails comparing the odds between the two lotteries and playing the one that offers an easier opportunity to win. This explains why our forefathers were far luckier than us. Prior to 1992, Lotto America offered odds of 1 in 18.6 million chances (1 in 18,643,560) for its 7/40 game format. By the time the Powerball replaced Lotto America in 1992, players had to deal with the increase in odds of 1 to 55 million. So, lottery players during the Lotto America era benefitted from three times better odds than when Powerball was introduced. Powerball had undergone major changes in its draw format several times since it started. The game tremendously increased the odds from 1:55 million odds in 1992 to the current odds of 1:292 million. Comparatively, lottery players in the olden days had much better chances of winning the lottery. But don’t despair; there is still hope of winning in the modern lottery systems. Players nowadays have hundreds of lottery games to choose from. Powerball is not the only game you can play. You can easily try your luck with other lottery games that have better odds. How can we explain this from a mathematical point of view? There are two factors to consider: the number field and the pick size. To choose which lottery to play, bear in mind that it is easier to win a game with a smaller number field. A lottery with 49 balls is easier to win than a lottery with 59 balls. Similarly, a lottery with 42 numbers is easier to win than a lottery with a 49 number field. Additionally, a pick size of 6 balls is easier to…