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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 like New York Lotto. From the image shown from New York Lottery for the said game, the odds of winning the jackpot are 1 in 45,057,474. Let us confirm if this is really the odds. Probability = favorable combination / total possible combinations = 1 / 45,057,474 Odds= favorable combination/ (total possible combinations - favorable combinations)= 1 / (45,057,474- 1)= 1/ 45,057,473 From our computation, we found out that 1 in 45,057,474 refers to the probability instead of the odds. Are you still not convinced that you must look closely at the information you read from some state lotteries? Look at this example for Texas Lottery Lotto Texas whose total possible combinations are 25,827,165. We once again see that the title for the column is Odds, and the values under it follow the accepted configuration for odds. We can compute for the odds and probability. Probability = favorable combination / total possible combinations = 1 / 25,827,165 Odds = favorable combination/ (total possible combinations - favorable combinations) = 1 / (25,827,165- 1) = 1/ 25,827,164 Therefore, 1: 25,827,165 does not refer to the odds or to the probability. This coincides with the observation of Lawrence Fulton, Francis A. Méndez Mediavilla, Nathaniel Bastian, and Rasim Muzaffer Musal who prepared the manuscript entitled “Confusion Between Odds and Probability, a Pandemic?” This manuscript appeared in the November 2012 edition of the Journal of Statistics Education. Let me quote the exact statement, which is The figure presented as odds is indeed not odds.Source: Confusion Between Odds and Probability, a Pandemic? This document talks about the common confusion from using the words odds and probability. The goal of this work coincides with the aim of this article. It points out this issue of emphasizing the importance and the responsibility of meticulously disseminating information. It further supports the results of our computation and analysis that the value for odds to win the jackpot in Lotto Texas is not really the odds. The document also presented proof that the Texas Powerball incorrectly calculated odds and incorrectly reported probability as odds. Our examples here are only a few. You could see a lot of misinterpretation and misrepresentation across many state lottery websites. Thus, do not be a victim of this confusion pandemic. Always remember, odds and probability are not mathematically equivalent. Consider this as a reminder that you must double-check the information about odds and probability. After all, you need to make the best decision out of accurate data from mathematical analysis.
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Winning The Lottery vs. Getting Struck By Lightning
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อัปเดตล่าสุดเมื่อวันที่ 2 มกราคม 2021 การชนะลอตเตอรีเทียบกับสายฟ้าเป็นเส้นยอดนิยมที่ผู้คนพยายามกีดกันไม่ให้ผู้อื่นเล่นลอตเตอรี สำหรับฉันฉันถามสิ่งนี้: คุณอยากถูกฟ้าผ่าตายหรือคุณอยากถูกลอตเตอรี? ทุกอย่างขึ้นอยู่กับตัวเลือกของคุณไม่ใช่เหรอ? หากคุณต้องการถูกฟ้าผ่าให้ออกไปข้างนอกและหาที่หลบใต้ต้นไม้ต้นเดียวในทุ่ง เป็นทางเลือกของคุณ ดังนั้นโอกาสที่จะถูกไฟฟ้าดูดจะเป็นไปในความโปรดปรานของคุณอย่างแน่นอน แต่คุณไม่ต้องการทำเช่นนั้น เพราะมันไม่สนุก. อย่างถูกต้อง? แต่พยายามหลีกเลี่ยงโดยการเข้าบ้านตีกอล์ฟในวันอื่นอาศัยอยู่ในสถานที่ที่มีโอกาสถูกฟ้าผ่าน้อยกว่า ดังนั้นความน่าจะเป็นจึงกลายเป็นศูนย์หรือเป็นไปไม่ได้อย่างแท้จริง ในทำนองเดียวกันมีบางสิ่งที่มีแนวโน้มที่จะเกิดขึ้นกับคุณมากกว่าการชนะลอตเตอรี และเช่นเดียวกับสายฟ้าฟาดกับลอตเตอรีผู้คนพยายามทำให้ลอตเตอรีตกอยู่ในสภาพที่ไม่ดี ลองพูดคุยเกี่ยวกับสถานการณ์เหล่านี้และดูว่าลอตเตอรีเป็นสิ่งเลวร้ายที่บางคนอยากจะเชื่อหรือไม่ หากคุณยึดติดที่สุดฉันจะให้ลิงก์ไปยังหน้าที่เกี่ยวข้องเพื่อเพิ่มโอกาสในการชนะลอตเตอรีเพื่อให้คุณมีโอกาสและคณิตศาสตร์อยู่เคียงข้างคุณ หวยฟ้าผ่าฉลาม ฯลฯ โอกาสในการชนะ UK Euromillions คือ 1 ใน 139.8 ล้าน โอกาสในการชนะ UK Lotto คือหนึ่งใน 45 ล้าน อัตราต่อรองจะแย่ลงมากเมื่อคุณเล่น Mega Millions สหรัฐด้วยอัตราต่อรอง 1 ถึง 302.5 ล้าน น่าเสียดายที่การถูกฟ้าผ่ามีโอกาสมากกว่าการถูกล็อตเตอรี่ โอกาสในการถูกโจมตีตลอดชีวิตคือ 1 ใน 3,000 ข้อเท็จจริงเกี่ยวกับฟ้าผ่า National Geographic ในสถานการณ์ "ชนะลอตเตอรีกับฟ้าผ่า" อัตราต่อรองยังคงสนับสนุนการใช้ไฟฟ้าอย่างต่อเนื่อง แต่สายฟ้าไม่ใช่ข้อโต้แย้งเดียวที่กลุ่มต่อต้านลอตเตอรีใช้เพื่อกีดกันชุมชนเกม มีเหตุการณ์อื่น ๆ อีกสองสามอย่างที่มีแนวโน้มที่จะเกิดขึ้นมากกว่าที่คุณเคยถูกลอตเตอรี เหตุการณ์ที่ดูเหมือนสุ่มเหล่านี้มีตั้งแต่การออกเดทกับนางแบบไปจนถึงการเป็นดาราภาพยนตร์หรือแม้แต่นักบุญ และรายการต่อไป: อลันแฮร์ริสนักดาราศาสตร์กล่าวว่าอุกกาบาตสามารถสร้างความเสียหายได้มากพอที่จะดึงโลกจำนวนมากออกมา อัตราต่อรองคือ 1 ใน 700,000 ฝันร้ายของขากรรไกรของเราอาจไม่ไกลนักเมื่อเทียบกับการชนะลอตเตอรี Kevin Breuninger ของ CNBC ระบุว่า "โอกาสที่จะถูกฆ่าจากการโจมตีของฉลามคือ 1 ใน 3.7 ล้าน" ดังนั้นโปรดใช้ความระมัดระวังเมื่อคุณออกไปในมหาสมุทรโปรดจำไว้ว่ามีเพียงฉลามที่โชคดีเพียงตัวเดียว (หรือในกรณีนี้อาจจะโชคไม่ดี) เท่านั้นที่จำเป็น Gregory Baer ผู้แต่ง Life: The Odds กล่าวว่าโอกาสในการเป็นนักบุญมีประมาณ 1 ใน 20 ล้านคน นี่เป็นเพราะความจริงที่ว่าจากประชากร 100 พันล้านคนที่เคยมีอยู่มีเพียง 5,000 คนเท่านั้นที่ได้รับการยอมรับ อย่างไรก็ตาม 1 ใน 20 ล้านดีกว่า 1 ใน 300 ล้านคุณไม่คิดเหรอ? วิธีเล่นอัตราต่อรองของคุณ (ผิดน้อยกว่า) จัดการกับมัน คุณจะไม่มีวันชนะลอตเตอรีหากคุณไม่ซื้อตั๋ว ในทำนองเดียวกันคุณไม่น่าจะถูกฟ้าผ่าเมื่อคุณอยู่ในบ้านในช่วงพายุฝนฟ้าคะนอง คุณต้องการที่จะถูกฆ่าโดยฉลามหรือไม่? ไปว่ายน้ำในมหาสมุทร หากคุณไม่ได้ฝึกฝนอย่างมืออาชีพในฐานะนักดำน้ำคุณอาจไม่อยากทำเช่นนี้ คุณชอบ? ความจริงก็คือโอกาสที่จะตายจากฉลามนั้นเป็นศูนย์อย่างแท้จริงเมื่อคุณอาศัยอยู่ในชนบทมาตลอดชีวิต คุณต้องการเป็นนักบุญหรือไม่? อย่าถามฉัน แต่คุณสามารถถามพระของคุณได้ หากคุณไม่ปฏิบัติตามก็จะไม่เกิดขึ้น ต้องการพบกับซูเปอร์โมเดลหรือไม่? ฉันสามารถแนะนำหนึ่งหรือสองสิ่งได้ แต่ถ้าคุณไม่ถามซูเปอร์โมเดลก็จะไม่เกิดขึ้น แล้วภัยพิบัติจากอุกกาบาตล่ะ? คุณสามารถทำบางอย่างเพื่อป้องกันได้ กดดันรัฐบาลให้สนับสนุนโครงการที่สามารถป้องกันผลกระทบจากดาวเคราะห์น้อย ในคำพูดของอลันแฮร์ริส: เราใช้จ่ายเงินหลายพันล้านไปกับการโจมตีของผู้ก่อการร้าย แต่แทบไม่มีอะไรที่จะป้องกันผลกระทบจากดาวเคราะห์น้อยได้ อย่างไรก็ตามในทุกวิธีที่เราสามารถตายจากเหตุการณ์ทางดาราศาสตร์ผลกระทบของดาวเคราะห์น้อยเป็นทั้งเหตุการณ์ที่น่าจะเป็นไปได้สูงสุดและเป็นเหตุการณ์เดียวที่เราสามารถป้องกันได้ นักดาราศาสตร์อลันแฮร์ริสนิตยสาร Discover คุณสามารถทำเรื่องโง่ ๆ ในชีวิตและได้รับสิ่งที่คุณต้องการให้เกิดขึ้นกับคุณ อย่างที่บอกห้ามดื่มขณะขับรถ แท้จริงมันเป็นทางเลือกของคุณที่กำหนดชะตากรรมของคุณ ในฐานะคนที่มีสามัญสำนึกคุณสามารถดำเนินการกับสิ่งต่างๆอย่างมีเหตุผลและทำผิดพลาดน้อยลง คนชนะลอตเตอรีโชคดีที่การถูกลอตเตอรี่ไม่ใช่โอกาสที่เลวร้ายที่สุดในโลกนี้ คุณมีแนวโน้มที่จะเล่นลอตเตอรีมากกว่าใคร ๆ ในการเลือกแขนแข่งขัน NCAA ที่สมบูรณ์แบบตามที่ Jonathan Mattingly ครูคณิตศาสตร์ของ Duke กล่าว ฉันรู้ว่า. การชนะลอตเตอรีไม่ใช่เรื่องง่าย แต่มีโอกาสหนึ่งใน 300 ล้านคนจึงถูกล็อตเตอรี่ มันให้อะไร? คุณจะเล่นหวยหรือไม่? หรือคุณควรหยุดและรอให้ฟ้าผ่า? ขึ้นอยู่กับคุณ เป็นทางเลือกของคุณที่สำคัญ หากคุณเลือกเล่นลอตเตอรีคุณอาจถามว่า "มีวิธีใดในการปรับปรุงอัตราต่อรองของคุณหรือไม่" ใช่. คุณสามารถใช้คณิตศาสตร์เพื่อทราบทางเลือกที่เป็นไปได้ทั้งหมดและตัดสินใจเลือกอย่างชาญฉลาด และการใช้เครื่องคำนวณ Lotterycodex จะช่วยให้คุณเป็นผู้เล่นล็อตโต้ที่ชาญฉลาดได้อย่างแน่นอน คุณสามารถทำตามเคล็ดลับลอตเตอรีและใช้กลยุทธ์ทางคณิตศาสตร์ที่สามารถช่วยให้คุณเลือกได้อย่างชาญฉลาด และโชคดีสำหรับคุณที่มีวันเดือนปีเกิดพิเศษเป็นเลขวิเศษของคุณ คุณไม่จำเป็นต้องหลีกเลี่ยงเลข 13 เพียงเพราะเป็นเลขอาภัพ และเราไม่จำเป็นต้องเสียเงินไปกับหวยขยะหลายร้อยใบ เคล็ดลับในการชนะลอตเตอรีคืออะไร? เคล็ดลับอยู่ที่พลังของคณิตศาสตร์เชิงผสมและทฤษฎีความน่าจะเป็น หากคุณไม่เริ่มออกแบบและใช้คณิตศาสตร์ให้เป็นประโยชน์การชนะลอตเตอรีและการติดสายฟ้ายังคงมีโอกาสไม่เท่ากัน และในขณะที่พวกเราส่วนใหญ่กลัวคณิตศาสตร์ในโรงเรียนมัธยม แต่ความจริงก็คือเขาเป็นเพื่อนที่ดีที่สุดของคุณในการปรับปรุงกลยุทธ์เกมของคุณ มีบางวิธีในการชนะลอตเตอรีเพื่อประโยชน์ของคุณและพยายามที่จะชนะลอตเตอรีทางคณิตศาสตร์ซึ่งรวมถึงการเลือกลอตเตอรีที่ชนะง่ายกว่า (หมายความว่ามีอัตราต่อรองโดยรวมที่ดีกว่าสำหรับคุณในฐานะผู้เล่น) โดยใช้อัตราต่อรองแทนสถิติ และใช้แผนเกมลอตเตอรีที่มั่นคง ความจริงก็คือไม่มีเคล็ดลับ วิธีเดียวที่คุณจะเพิ่มโอกาสในการชนะลอตเตอรีได้คือการหาตัวเลือกที่เป็นไปได้ทั้งหมดและตัดสินใจอย่างชาญฉลาด ไม่ใช่เรื่องง่ายที่จะชนะ แต่คุณสามารถทำตามคำแนะนำฟรีของเราและใช้เครื่องคำนวณลอตเตอรีเพื่อดูตัวเลือกทั้งหมดและตัดสินใจได้อย่างถูกต้อง ใครจะรู้? มันสามารถช่วยให้คุณตีทองแทนสายฟ้าและทำให้คุณถูกลอตเตอรี! อย่าลืม - ประเด็นเบื้องหลังการพนันและลอตเตอรีคือการสนุก! ตั๋วสามารถเข้าถึงได้มากแน่นอนว่าโอกาสในการถูกลอตเตอรีนั้นเป็นเรื่องดาราศาสตร์ แต่การชนะเป็นเพียงผลพลอยได้จากการได้รับรางวัล เล่นหวยให้สนุก และส่วนหนึ่งของความบันเทิงคือรายได้ส่วนใหญ่ไปที่โครงการการศึกษาและสาธารณสุขของรัฐบาล หากคุณไม่เล่นลอตเตอรีเพราะคุณมีแนวโน้มที่จะถูกฟ้าผ่ามากกว่าที่คุณจะชนะแจ็คพอตแสดงว่าคุณคิดถูกแล้ว คุณคิดถูกถ้าคุณทำเงินมันคือสิ่งที่คุณสนใจ แต่ถ้าคุณมองจากมุมที่ใหญ่กว่านี้คุณอาจจะรู้ว่าการเล่นหวยไม่ได้แย่ในที่สุด และคุณจะไม่เสียชีวิตจากการเล่นหวย ถ้าคุณโชคดีล่ะ? มันน่าทึ่ง. แต่ลองนึกถึงชั่วโมงแห่งจินตนาการเกี่ยวกับสิ่งที่คุณสามารถทำกับ "อะไรก็ได้ถ้าคุณชนะ" นี้ ไม่สนุกเหรอ? ในระดับที่สูงขึ้นให้นึกถึงผู้ด้อยโอกาสในสังคม แล้วถามตัวเองว่าถ้าทุกคนเลิกเล่นหวยเพียงเพราะฟ้าผ่าดีกว่า? บทความอื่น ๆ เพื่อสำรวจ:
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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 win than a lottery that draws 7 balls, but a pick 5 game is even better. It is that simple. Together, these two factors determine the odds of winning a specific lottery. The table below shows the odds for different types of lotteries: With these odds, it is easy to see that the best way to win a lottery is to choose one with the lowest odds. Based on the table above, the 5/20 offers better odds. Another variable that you should consider is the extra ball. The extra ball is called by different names, including “bonus ball,” “power ball,” “lucky star ball,” and others. The extra balls may be drawn from the same drum or come from a different drum. The Irish lottery and the Australian Tattslotto draw from the same drum as the main numbers. On the other hand, the U.S. Powerball and the Euro Millions used a different drum for the extra balls. Drawing extra balls from a different drum makes it more difficult to win the game. For instance, the U.S. Powerball 5/69 has odds of 1:11 million without the extra ball. To win the Powerball jackpot, you also need to choose the red Powerball correctly. This ball is drawn from a second drum containing 26 balls and increases the odds to 1:292 million. The table below shows the odds for winning the most popular lotteries in the world: With a 5/20 lottery, the Trinidad/Tobago Cash Pot has a favorable odds of 1 to 15,504. The Italian Superenalotto 6/90 has an infinitesimal 1:622,614,630. Players consider the large jackpot lotteries as a prime motivation to keep on playing. It is also important to consider reasonable chances of winning whenever you play the lottery. That is just a simple example to prove that calculation is important in playing the lottery. Now let’s go to a more advanced method. How NOT to be mathematically wrong Besides choosing the lottery with better odds, we can be more granular on a mathematical strategy. That’s how Lotterycodex helps to go deep into a more advanced application of mathematics in lottery games. Specifically, we talk about combinatorial math and probability theory. Now, it’s very important to understand that mathematically, there’s no way you can increase your probability. We don’t have the power to manipulate the underlying probability. And there’s no way you can beat the odds of the lottery. No one can! So if that’s the case, then how can we use math to improve our playing strategy? The answer is simple: “know the best choice and be wrong less.” A true mathematical strategy is all about calculating all the possible choices and making an intelligent choice that will provide you with the best ratio of success to failure. So a mathematical strategy is all about making an intelligent choice and being wrong less. There are several things that we keep repeating about probability and the lottery. One of these is that any combination has the same probability of being drawn as any other combination. We don’t know what combination will be drawn beforehand, but we know that it can be any of the possible combinations. As such, each combination has an equal chance of winning. If we take a combination like 5-10-15-20-25-30, it has exactly one chance of winning out of all the possible combinations. If all combinations have the same probability, then there should be nothing wrong with choosing to play numbers like 1-2-3-4-5-6 or 5-10-15-20-25-30. However, these combinations and others like them very rarely get drawn. It is easy to say that players have a gut feel about not playing these combinations. However, gut feel or intuition does not have a place in playing the lottery. These groups of combinations, along with others that have non-random patterns, are considered “unusual,” “coincidences,” and “rare” events. We avoid these numbers because they appear to be not random enough. However, we still expect them to occur at some point. The law of truly large numbers states that even the most unlikely combination will happen if given enough draws. To better understand the concept of combinations that seldom occur, as against a more likely combination, let’s look at patterns of numbers. Lucky numbers using odd-even analysis Again, we ask the question, does one combination have a better odd than another? For instance, if we compare a combination of 6-even-zero-odd-numbers against 3-odd-3-even, we should see something interesting. In a 6/49 system, the following are the comparison between a 6-even (no odd numbers) combination and a 3-odd-3-even combination: The probabilities above show that 3-odd-3-even combinations are drawn around 333 times in 1,000 draws, while a 6-even combination with no odd numbers is drawn only nine times in 1,000 draws. If all combinations have the same chances of being drawn, how do we explain the above difference in odds? The simplest explanation is that there is a difference in definitions between the “odds” and the “probability.” Probability is the measurement of the likelihood that an event will occur so we express the formula in the following way: The odds on the other hand refer to the ratio of success to failure and we use this formula instead: In a 6/49 system, a single combination has a 1 in 13,983,816 chance. There are 4,655,200 ways to combine 3-odd-3-even combinations. So out of 3 games, you get one opportunity to match the winning combination against two ways you will not. In simple terms, if you play 100 times, you get 33 opportunities to win the jackpot against having 66 ways you will not. Compare this with the odds of a 6-even combination with only 1 opportunity to match the winning combination against 100 ways you will not. This means that you have less opportunity to match the winning numbers and more chances of losing. If you want to improve your odds, you should choose a combination from a group that provides you with a better ratio of success to failure. Meaning, look for more opportunities to win with less chance of losing. 6-even-combination3-odd-3-even-combination134,596 ways to win4,655,200 ways to win13,849,220 ways to fail9,328,616 ways to failJust 1 opportunity to win in every 100 attempts that you playGet 33 opportunities to win in every 100 attempts that you playLOW RATIO OF SUCCESSHIGH RATIO OF SUCCESSNot a smart choiceAn intelligent choice RememberYour goal is to win the lottery, and the first thing you should know before you play is to know the ratio of success to failure and choose the best one. You cannot change the underlying probability and you cannot beat the lottery’s odds, but as a lotto player, you have the power to know and make the right choice. Even choosing not to play is a strategy by itself. When choosing combinations, always look for the number of ways you win and the number of ways you will fail. To get the bigger picture of why you should choose 3-odd 3-even combinations, let’s look at the whole odd-even scheme. In a 6/49 lottery, there are the set of odd and the set of even numbers: Odd numbers = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49 Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48 We can create different mixes of numbers from the above sets to come up with different combinatorial patterns. We then compute the probabilities based on their patterns. The table above shows that the balanced mix of 3-odd-3-even numbers has the best probability of being drawn. The worst patterns are the 6-odd and the 6-even combination. RememberChoosing a 3-odd-3-even combination instead of 6-even (e.g., 2-4-6-8-10-12) WILL NOT increase your chances of winning because all combinations have the same probability. The reason you shouldn’t choose 2-4-6-8-10-12 is that the 0-odd-6-even pattern has fewer ways to win and have more ways to fail. You should choose 3-odd-3-even because it gives you the best ratio of success to failure. This probability study reflects the overall performance of all the lottery systems in the world regardless of the format. Whether your game is a 6/49 game, or 6/45, or 5/69, or 5/50 game. Probability theory behaves the same way across all lottery games. Take a look at the results of the Australian Saturday Lotto from January 7, 2006 to February 1, 2020: Other lotteries closely follow the above graph for actual lottery results. As expected, the results closely match that of the expected values. We recommend that when you play your lucky numbers, make sure to balance your odd and even numbers to get a better ratio of success to failure. Lucky numbers using low-high analysis Much like what we did with the odd-even combination, we compare different high and low combinations. Although it seems obvious where this is headed, going through the exercise clears up the matter. Using the 6/49 lottery system, we can divide the numbers between high and low, as follows: Low numbers = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 High numbers = 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 See the table below for the possible combinatorial patterns and their probability. I’ve added a column for the approximate occurrence of the combinations for every 100 draws. Recommended to use for your lucky numbers Middle patterns (OK but not recommended) Worst patterns (Avoid) If using any lucky numbers in your strategy, make sure to have a balanced low and high numbers to get a better ratio of success to failure. RememberChoosing a 3-low-3-high combination instead of a 6-low combination (e.g., 1-2-3-4-5-12) WILL NOT increase your chances of winning because all combinations are equally likely. You should avoid 1-2-3-4-5-6 because a 6-low-0-high pattern has fewer ways to win and more ways to fail. I recommend choosing 3-low-3-high because it offers the best ratio of success to failure. As usual, the results of the actual draws is very close to the high-low analysis. Below are the results of lotteries sorted according to their high-low combinations. The actual lottery results validated the predicted results. It only shows that probability theory can actually predict the likely outcome of any lottery draw based on the law of large numbers. The power of the Lotterycodex calculator Finally, here’s the Lotterycodex calculator as a superior type of lottery wheel. The Lotterycodex is the only lottery calculator that combines combinatorics and probability theory in a single calculation. Meaning, it performs as a lottery wheel and can separate the good, the bad, the worst, and the best combinations with probability analysis. This feature provides lotto players with a complete picture of how the whole lottery game works according to the law of large numbers. In the earlier topics, we have discussed odd-even in one analysis. And we presented the patterns of low-high numbers in a separate analysis. The problem with these two separate analyses is the existence of “contradicting conclusions.” For example, according to the odd-even analysis, 1-2-3-4-5-6 is among the best combinations because of its balanced composition of 3-odd-3-even numbers. On the other hand, according to the low-high analysis, 1-2-3-4-5-6 is one of the worst combinations. There’s a need to solve this contradiction. The best solution here is to combine the two strategies into one combinatorial/probability equation to produce a single conclusive analysis. Lotterycodex wheel is designed to combine odd-even and low-high in one combinatorial design. For example, in a 4/20 lottery game, the high and low numbers are: LOW1,2,3,4,5,6,7,8,9,10HIGH11,12,13,14,15,16,17,18,19,20 Further dividing the sets into odd and even numbers:  ODDEVENLOW1,3,5,7,92,4,6,8,10HIGH11,13,15,17,1912,14,16,18,20 These sets are the basis of the Lotterycodex Combinatorial Design: We can use these sets to analyze a group of combinations according to their composition. For instance, one pattern can be a 2-low-odd, 1-high-odd,…