Ohio Lottery
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…
Ohio Lottery And The Power Of Mathematical Gaming
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Last updated on January 6, 2021 The Ohio Lottery distributes over $5.7 million in prizes every day. If you want to claim your possible share of this pot money, you have to be in it to win it. Do not simply play using your lucky numbers. Do you want to be one of its 350,000+ daily winners? Then prepare the best game plan. Learn about how to use the power of math to achieve success, even if you hate math. Let’s start. Don’t use statistics to analyze lotto game It is hard to say when people started using statistics as a strategy. Supporters of this method analyze the lotto results from a specific duration (such as the previous 100 draws). This method supposedly allows them to determine the hot, cold, and warm numbers. From their observations, they predict which numbers will soon win. It is possible that what they analyze from the past 100 draws is correct, but this strategy has loopholes. One loophole is that 100 draws are not sufficient sample data to analyze, given that there are thousands to millions of possible combinations in a particular lotto game. Their observation from 100 draws will definitely change with a substantial increase in the number of draws. When trying to answer a problem, the first thing to do is analyze its nature and the available data to pick the most appropriate method to deal with it. Suppose we have a box containing 20 balls you can’t see. The only information you know is that there are yellow, cyan, green, and gray marbles. You do not know how many balls there are for each color. We can say that any question you ask is statistical. Thus, we could only surmise the composition of the balls in the box through sampling. If we know how many balls there are for each color, such as 6 yellow, 6 cyan, 5 gray, and 3 green; thus, we could ask probabilistic questions. In the same manner, we know how many numbers there are in a particular lotto game. Thus, the lottery is probabilistic instead of statistical. For example, the 6/49 lotto has 49 balls, and the 5/45 lotto has 45 balls. Instead of a statistical question, we could ask a probabilistic question. What is the probability that tomorrow’s draw results are 1-2-3-4-5-6? Or what is the probability that the winning combination has 3-low-odd and 3-low-even numbers? Probability theory is the one that will help you become a better lottery player. But aside from probability theory, other mathematical concepts can improve probability analysis, such as combinatorics and the law of large numbers. With the lottery being random and having a finite number set (per specific game), we have adequate knowledge to calculate the probability of combinations and get the best possible shot to win the game. This truly random nature of the lottery guarantees the precision of any performed mathematical calculation, based on the law of large numbers. Probability, together with combinatorics, will provide you with an accurate prediction so you will not shoot your arrow without a precise aim. This is the same image you have seen in our previous article, A Visual Analysis of a Truly Random Lottery with a Deterministic Outcome. You could revisit and reread this post to understand more about computer simulations to analyze the lottery’s randomness. Now, to ease your worries about some mathematical names and concepts I just mentioned, let me first provide you with their brief description. You will learn more about them as we continue our discussion. Probability describes how likely an event (a combination in terms of the lottery) will occur.Combinatorics is the field of mathematics used as a primary basis of lottery mathematics.Law of large numbers or LLN states that with adequate trials, the actual results always converge on the expected theoretical outcomes. Read The Winning Lottery Formula Based on Combinatorics and Probability to access more information. Get a calculator to get you going in the right direction To increase your chances of winning a game in the Ohio lottery, the only logical way is to buy more lottery tickets (of different combinations). This refers to the covering principle that eliminates concerns on hot and cold numbers or lucky and unlucky numbers. Covering helps you trap the winning numbers. Choose as many numbers as you can and play every unique combination from your selection. To take advantage of this covering strategy, you will need to use a computer program more commonly known as a lottery wheel. There are many kinds of lottery wheels, and each has its own advantages and disadvantages. Below are some of them. Full Wheel enables you to select more numbers. Choosing System 7 allows you to select 7 numbers. In a pick-5 lotto game, for instance, picking 7 numbers will create 21 possible combinations. The disadvantage of full wheels is the high cost of playing. Picking more numbers results in more combinations. More combinations mean buying more tickets to maximize your covering. If you pick 10 numbers, the total combinations will be 252. If you have 12 numbers, there will be 792 combinations.The minimal-type wheel or abbreviated wheel offers an economical solution but provides what seems to be consolation prizes. Satisfy a particular condition, and you have a guaranteed win from a minimum number of tickets. For instance, your selection contains all the winning numbers; you win a small amount. However, the trade-off here is the decreased probability of winning the jackpot. It moves you away from achieving your primary goal, which is to hit the jackpot. If neither type of wheels work, what you need is a lottery wheel that uses probability and combinatorics. This wheel is the Lotterycodex calculator. Through this new lottery wheel, you can play at a minimal cost while playing with a better success to failure ratio of winning the grand prize (not just the consolation prize). I will give you examples of how the calculator analyzes the games in the Ohio lottery. But before that, you should first know the difference between numbers and combinations. Know the difference between numbers and combinations The first thing a player must know is the difference between a number and a combination to play the lottery. The image below shows this. Each ball in a lottery drum denotes each number in a particular lottery game. The combination is the set of numbers you will choose to play. For example, in a 6/49 game, there are 49 numbers to choose from (1-49) to create your combination of 6 numbers. This knowledge of numbers and combination is the basic foundation for learning about their probability and odds that affect your chances of winning the jackpot. Now that you know the difference let’s go deeper into the discussion of probability theory. Let’s begin with the notorious 1-2-3-4-5-6 combination. The 1-2-3-4-5-6 combination has the same winning probability as any other one Each number and combination has the same probability of being drawn in the game. According to the law of large numbers, every number will converge in the same probability value when there is a huge draw size. There will also be just one winning combination after the draw. Thus, there is only one way of winning the jackpot. To express this mathematically, we use the probability formula shown below. In a classic 6/49 game, the combination 1-2-3-4-5-6 has an equal probability of getting drawn as the rest of 13,983,815 combinations. The same principle applies to Lucky for Life 5/48 and the Rolling Cash 5/39 games. Knowing this, you might be ready to believe that there really is no other way to win except to pray harder for your lucky stars to shine brightly and grant your wish. However, while there is really nothing bad about praying, it is better to combine mathematical strategy with your unwavering faith. So a mathematical strategy involves understanding the type of combination in a lottery game. Combinations are not created equally. That said, let’s discuss now how your choice of combination could make or break your success. The ratio of success to failure A combination has composition. You can describe it according to the characteristics of the numbers it contains. Look at the examples in the image below. This composition of every combination is what you should take advantage of. From our discussion above, you know that every number and every combination has the same probability. But probability differs from odds. Knowing the difference lets you understand the game better and devise a good game plan. From earlier discussion, probability measures how likely something is to happen. In a lottery, the probability is equal to the number of times a certain combination will get drawn divided by the total number of combinations. Odds refer to the number an event will occur over the number an event will not occur. In the lottery, “odds” are the ratio of success to failure. The formula in the image below best represents this. Let us say you will play in the classic 6/49 game. You will most likely not feel confident to play the combination 1-2-3-4-5-6, although you know that this has the same probability as other combinations. This is your logic telling you to be wary. Yet, if you fully understand the lottery’s mathematical laws, you know that such straight and sequential combinations are improbable events that might happen. In a 6/49 game, you know that a combinatorial pattern could have all six numbers as odd or even. It can have 1-odd and 5-even numbers or 5-odd and 1-even. You can also pick 4-odd and 2-even numbers or 2-odd and 4-even numbers. A combination may also have 3-odd and 3-even numbers. Using probability theory, we can distinguish which group of combinations is the best and the worst. Let us analyze the image above. This applies to 6/49 games like the Classic Lotto of Ohio Lottery. Out of the 13,983,816 total combinations in a 6/49 game, the 6-odd combinations can give you 177,100 ways to win and 13,806,716 ways to fail. The probability of this combination (computing using the probability formula) is 0.012665 (rounded off). Thus, the expected occurrence of a 6-odd combination in every 100 draws of a 6/49 game is 1. This means that this type of combination will only occur once every 100 draws. The same process applies when you want to determine the probability and estimated occurrence in 100 draws of other patterns. Therefore, the combination with the highest estimated occurrence in 100 draws is one with 3-odd and 3-even numbers in its composition. Between a 6-odd and 3-odd-3-even combination, you are better off playing for the latter. Making a 4-odd-2-even pattern with 1,275,120 possible combinations has the expected occurrence of 25 in every 100 draws. Hence, this is the second to the best pattern you can use when choosing numbers to form a combination. For the 3-odd-3-even combinations, there are 4,655,200 ways to win and 9,328,616 ways you could lose. The 6-odd combination offers 177,100 ways of winning and 13,806,716 ways of losing. You clearly have fewer ways of losing with a balanced combination of 3-odd-3-even than all 6 odd numbers. This should make us realize that while we have no power in controlling the probability of winning, we can choose an action that will give us the best ratio of success to failure. Use this knowledge to choose combinations that will help you win and keep you from wasting money. To develop a mathematical strategy for playing the lottery, you must choose the best ratio of success to failure. Thus, math is the only means that can show you what your options are. This is far more reliable than the lucky numbers on your astrological predictions or the supposed hot and cold numbers from past draw results. The image above summarizes the best and the worst choices you can make when playing a 6/49 lottery game. RememberAvoiding combinations such as 1-2-3-4-5-6 and choosing 3-low-3-high (e.g., 2-13-24-37-35-46) WILL NOT increase your chances of winning because all…