Massachusetts Lottery and the Strategy According to Math
"Oh my god, I won the Massachusetts Lottery jackpot!" A winner might exclaim after scanning his lottery ticket using the state lottery's newly launched app.
The state lottery keeps up with time and technology, but most players probably have more urgent concerns.
"When will that fortunate day come?"
"Is there a way I could win the lottery?"
I cannot have a definite answer to your first question, but for the second question, I can present valid information in devising a strategy for you.
Let me show you how math can be an effective strategy for winning the Massachusetts Lottery.
Which Massachusetts State Lottery Game Is The Best To Play?
Now, while Lotterycodex can simplify a mathematical strategy for you, know that every lotto game is unique in terms of how challenging it is to win the jackpot. Thus, to keep close to your goal of winning the jackpot, your first step is to select your game carefully.
The best game to play from the Massachusetts Lottery is a subjective choice. Still, considering other factors like pick size and number field helps analyze your odds of winning.
A lotto game with fewer balls, a smaller pick size, and no extra number is ideal.
With a smaller number of total combinations, you have better chances to win. In Mass Cash, you have one way to win against 324,632 combinations. This is the game with the most favorable odds for you.
Megabucks Doubler gives the probability of 1 way to win over 13,983,816 combinations. In Lucky for Life, you have one way to win against 1,712,304 combinations.
Megabucks Doubler makes it 43 times harder to win the jackpot than Mass Cash. Matching the winning combination in Lucky for Life is five times more challenging than in Mass Cash.
Mass Cash offers better odds than Powerball, although they have the same pick size of 5 balls. The 292,201,338 total combinations and the extra ball in Powerball make it 900 times harder to win the jackpot than in Mass Cash.
Compared to Mega Millions, Mass Cash also offers better odds. The 302,575,350 total combinations and extra ball of Mega Millions make the game 932 times harder to bring home the jackpot.
Deciding on playing a game or not may also depend on the circumstances. For example, your favorite lotto game's prize has reached over $500,000, so more players wait patiently in line to buy tickets.
Given this scenario, over one player may win and thus reduce each winner's take-home prize. It would be like playing and winning a prize on an ordinary day when it is not so immense.
Choosing which lottery game to play is your decision. Yet, before making your choice, consider all factors, especially the mathematical feasibility of winning that game. Lotterycodex calculators can enhance your power to choose.
Statistics is Not the Right Tool to Study Massachusetts Lottery
While statistics are mathematical, other methods are appropriate for studying a lottery game. I will debunk the existence of hot and cold numbers, which many lotto players aim to track when they use past draw results.
Massachusetts Lottery games are random, as the image above represents through the varied gray and white shades.
Frequently and seldom drawn numbers appear in 100 previous lotto draws. Yet, when the number of draws increases, all numbers converge in the same probability value.
Mathematically speaking, when we need to study a game with finite composition, we don't need the tools of statistics.
For example, a brown paper box contains 12 chocolates in milk, almonds, and chocolate truffles. Statistical sampling is a method that determines how many chocolates in each flavor the box contains. We use statistics because we don't know the composition of the box.
But in the lottery, our knowledge of the game is enough. Therefore any questions we ask are probability problems to solve.
In the 3 Massachusetts Lottery games, Mass Cash, Megabucks Doubler, and Lucky for Life, you know the pick size and the number of balls for selection. All these lotto games have a finite structure.
Therefore, we can use combinatorial mathematics and probability theory instead of statistics. Read this Free Guide: The Winning Lottery Formula Based on Combinatorics and Probability Theory.
It is impossible to predict the next winning combination, but combinatorics and probability will open a small window you could use to gain the best shot.
Do not feel scared just because I mentioned some mathematical concepts. There is a lottery calculator you can use. This new tool will simplify all the crucial math concepts required to improve the game.
The Ratio is the Key
Bread: butter.
Spoon: fork.
Probability: Odds.
What is the common factor among these pairs? It's love that complements one another.
Cheesy as it may sound, this is how you should apply probability and odds in the lottery.
First, let me show you the difference between probability and odds.
Probability measures the likelihood that an event will occur. Expressed in values between 0 and 1, it stands for the possibility a lotto combination will result in the draw.
In the Massachusetts State Lottery's Mass Cash game, choosing five numbers from 1 to 35 gives 324,632. There is always one winning combination in a lottery draw.
Thus, the probability of winning in the Mass Cash is 1/324,632. This is your probability regardless of which of the 324,632 combinations you use.
Now, let's talk about the odds.
This next formula is used to determine the odds. This is where the concept of combinatorial groups starts to matter. And we describe each combinatorial group based on its composition.
In simple terms, the odds refer to the success ratio to failure. The numerator represents the number of favorable shots you get, and the denominator represents the number of ways you will fail.
Your job as a smart lotto player is to ensure you get a better numerator. I like to call it a better ratio of success to failure.
Let me illustrate how the ratio works.
There are different combinations lotto players can make in a lotto game, like the samples above. For example, you can make an all-even combination like 4–16–22–28–32–48 or a consecutive combination like 1–2–3–4–5–6.
Many Massachusetts Lottery players do not think it does not matter what they pick because they only have one probability of winning regardless of their selected numbers. Unfortunately, this scenario considers only the probability but not the odds, which gravely weakens your understanding of your game.
From this table above, you see six odd-even patterns for Mass Cash.
If you play for a combination containing all five odd numbers, your odds show that you have 8,568 favorable shots and 316,064 ways you will fail. Thus, odds give you a better picture of your chances.
That said, realize that the best line should compose of 3-odd and 2-even numbers because this group will give you 110,976 favorable shots.
In simple terms, the group 3-odd-2-even will give you 34 favorable shots in every 100 draws you play. With the 5-odd line, you only get three favorable shots in 100 draws. As a smart lotto player, you don't want to spend your money in 100 draws to get only three chances of winning the jackpot.
See the difference between probability and odds?
Probability quickly dampens the mood by telling you there is just one way to win, so there seems nothing you can do.
However, the concept of odds gives you hope by telling you that you must calculate the ratio and never select numbers randomly, as most lotto players do.
Sadly, many players miss the opportunity that odds offer because they focus too much on probability.
Players could randomly pick numbers and unknowingly mark five even numbers. The 318,444 ways you lose using this pattern are greater than the 213,656 ways of losing using a 3-odd-2-even pattern.
Of course, you can't predict the lottery; therefore, the best approach to winning the lottery is to make sure you are being wrong less for most of the draws.
Focusing only on probability will make you think there is just one way of winning, so it doesn't matter what numbers you select. That's not true. Remember that you have the power to choose your odds.
Remember: Your 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 in itself.
Now let us see the ratio of success to failure in Megabucks Doubler.
This time, we will use low and high numbers as shown below:
Low = {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 = {26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49}
The table above shows that 3-low-3-high is an ideal choice because of its 4,655,200 winning opportunities.
The worst choice is a 6-low combination with 13,806,716 ways to lose. The ratio shows that choosing the best patterns gives a better winning advantage.
The Power of Combinatorial Groups
Each lotto game has its pick size and number field. For example, Massachusetts Lottery Mass Cash requires selecting five numbers from 1 to 35. The lotto machine will not accept your card if you mark only four numbers.
In Megabucks Doubler, players choose six numbers from 1 to 49 to create a combination.
In Lucky for Life, a combination comprises five numbers from 1 to 48 plus one lucky number from 1 to 18.
From the number field of every game, there are four sets we can create according to the numbers' characteristics. These are odd, even, low, and high.
You can combine all five odd numbers out of 1 to 35. You can also choose 4-odd-1-even, 3-odd-2-even, 2-odd-3-even, 1-odd-4-even, or 0-odd-5-even numbers. Thus, you can come up with combinations with varying odd and even number compositions.
The unique composition of every combination produces combinatorial groups. As explained earlier, each combinatorial group or pattern has unequal ratios of success to failure you may take advantage of.
Common sense dictates you will not choose a combinatorial group or pattern that will make you lose more. Instead, you will choose a pattern with more winning ways to offer in the Massachusetts Lottery.
The image above suggests that if you want the best shot in the Massachusetts Lucky for Life game, use three low and two high numbers.
Remember: A 3-low-2-high and a 5-low combination share an equal probability of winning. Still, the ratio of success to failure tells you that the 3-low-2-high combination offers more favorable shots than the 5-low combination. With a 5-low combination, you have more ways to lose. With a 3-low-2-high group, you have less chance of failing.
A smart player could form his mathematical strategy, knowing that combinatorial groups have different odds. Then, he could map his moves based on the combinatorial group with the best success ratio to failure.
Let us see how this works in the three Massachusetts Lottery games.
Lotterycodex — Advanced Combinatorial Design
A separate analysis of odd-even and low-high numbers could lead to confusion and contradiction, like 1–2–3–4–5–6. This is because it has the best ratio of odd-even but the worst ratio of low-high.
The solution is to combine odd-even and low-high numbers into one combinatorial design called Lotterycodex.
You need to regroup the numbers of a given lotto game into odd-low, odd-high, even-low, and even-high sets, as shown below:
The table above shows the four sets of numbers for Mass Cash. The same concept applies to Megabucks Doubler and Lucky for Life:
Here, you can easily see from which set a certain number is. For example, with 1–2–3–4–5–6, the advanced patterns clearly show that it has three low-odd and 3-low-even numbers. Unfortunately, this combination only picked numbers from two sets and lacked the required balance.
The mom of 5 in the Lucky for Life section above might also buy a Mass Cash ticket. Her combination is 2–9–10–21–31. We have determined that this combination uses the best odd-even pattern but is only second to the best low-high pattern.
Using the Lotterycodex patterns, 2–9–10–21–31 contains one low-odd, two low-even, and two high-odd numbers. This is not the best combination to choose. She has to change her choices to get the best ratio.
Let's see more of the Lotterycodex patterns for Mass Cash.
There are 56 Lotterycodex patterns for Mass Cash. Unfortunately, only three can give you the best shot possible. You might not know it, but you probably have used the worst patterns in your previous games. With the information supplied by the patterns, you could choose only to play using any patterns #1, #2, and #3.
You will better understand how the best and worst combinatorial patterns benefit you from the image below.
Now, let's look at the Lotterycodex patterns for the 6/49 game:
For a 6/49 game, the best patterns are #1, #2, and #3. The middle patterns are #4 to #20, while the worst are patterns #21 to #84.
Knowing that pattern #1 could occur 106 times out of every 2000 draws, you are better off spending your money on tickets using this pattern. On the other hand, you could save money if you insist on pattern #39 because it can only occur 15 times in 2000 draws.
Pattern #39 has a ratio of 1 to 136. Thus, in the 137 times you play, there is a single shot to win and 136 ways to fail.
If you only play the game once a week, this could mean that in the 137 weeks you play, you may have one week to win the jackpot. There are 52 weeks in a year, which could mean losing money for over two and a half years. This pattern will not give you the advantage you want to have.
Meanwhile, pattern #1 has a ratio of success to failure of 1 to 19. You get one favorable shot to become a jackpot winner in one of the 20 weeks this pattern would lead you to play.
From the law of large numbers, the best choice is the one that can take you closer to winning the jackpot.
These unique combinatorial patterns also help time your play accordingly. For example, from the table above on Lucky for Life, pattern #1 is among the three best patterns out of 56. It can occur 133 times in 2000 draws.
Be mindful, though. The approximate interval is not precise because you never know when a pattern will occur in a random lottery. But at least this approximation provides you with a general guide.
Thus, if this pattern occurred today, it might not occur again in the next draw. Yes, it may occur, but it's improbable. So skip playing during this interval. Save money when you skip playing to buy more tickets next time.
The three lottery games we discussed have very complex patterns. All these involve complex calculations. While this is intimidating, there is always an option, especially if you hate math.
You may use the Lotterycodex calculator.
This calculator will do the math for you and separate the best, middle, and worst patterns based on your number selection.
Probability and the Law of Large Numbers
Repetition is the key to mastery, so let me reiterate what we discussed above.
Although the odds are hard to beat, and the probability is not something we can control, there is a way we can play the lottery better. For this, we must acknowledge that randomness is your friend, and the finite structure of the lottery is your clue.
Ball drawing in lotteries like Massachusetts Lottery is random. Still, the law of large numbers tells us that with a substantial increase in the number of draws, every ball in the lottery will have (almost) the same occurrence. Therefore, each number and combination has the same probability.
However, remember the importance of odds or the ratio of success to failure in combinatorial groups.
Every combination in the lottery contains a unique composition, such as the odd, even, low, and high numbers. This composition gives a combination of its corresponding ratio of success to failure.
Check how many odd or even or low, or high numbers you mark on your ticket. Then, ensure the final combination belongs to a combinatorial group with the best ratio winning.
For example, look at patterns #1 and #53 of Mass Cash.
Pattern #1 has a 0.0718598290 probability value, and its expected occurrence is 144 in 2000 draws.
Expected occurrence (pattern #1)
= 0.0718598290 x 2000
= about 144 occurrences
We use the same calculation. Pattern #53 has a 0.0003881318 probability value and is expected to occur only once in 2000 draws.
Expected occurrence (pattern #53)
= 0.0003881318 x 2000
= only once
Pattern #1 is the best combinatorial group, so it dominates the game, as dictated by the law of large numbers.
With 5000 draws, you can observe the same trend.
Expected occurrence (pattern #1)
= 0.0718598290 x 5000
= about 359 occurrences
Expected occurrence (pattern #53)
= 0.0003881318 x 5000
= about twice
What should you learn from this, then? It's very simple. Make sure that your combination belongs to pattern #1 because, according to the law of large numbers, pattern #1 will always dominate the draws and will continue to dominate as the number of draws gets larger and larger.
Why You Should Play As A Lotto Syndicate
Each lotto ticket you buy gives you one chance of winning. Thus, it is logical to buy more tickets to have more chances of winning.
Since each combination has the same probability, ensure that your multiple tickets contain unique combinations. This is the covering principle that matters in lottery games.
Many players use a lottery wheel. A full wheel lets you have more combinations which could help you hit the jackpot but will hurt your budget. An abbreviated wheel is cheaper but offers fewer combinations and less chance to win the jackpot.
Lotterycodex calculator offers the benefits of these two wheels, so you can buy more to cover more. Yet, a solo player can only cover as many combinations.
This emphasizes the benefit of playing as a lotto syndicate, such as this group of MIT students. A syndicate comprises several lotto players who pool their money to cover more combinations. Still, no matter how many tickets a syndicate can buy, their pooled resources will only be useful if they choose combinations with poor odds.
Thus, a Lotterycodex calculator can also benefit lottery syndicates by directing them toward the best combinations.
Since the syndicate can purchase more lotto tickets, one of these tickets may win the jackpot or at least some smaller prizes.
The Inverse Strategy
A lottery game has more disappointments than satisfaction. You might not even win anything out of the 100 tickets you bought since beating its odds and underlying probability is impossible.
Even when you know the best combinations, losing is still inevitable. Considering the amount of money you have been losing, it is understandable you'd want to give up.
However, winning a prize is just one reward you can get from playing lottery games.
To many players, the lottery is just a game for randomly marking numbers on a ticket. They believe winning the jackpot through playing is the only way to take advantage of the lottery. This is true from the perspective of a player or lotto ticket buyer.
The lottery is an industry, and any industry consists not just of buyers. There are also sellers. By changing your perspective into that of a seller, you can get part of the lotto industry's profits.
I can give you one real-life example. In my grandmother's place, this woman asks her neighbors if they want to play the lotto. If they do, she will buy the ticket for them for a minimum charge.
Yes, she earned only a small amount from the service she offered, but she used that money to pay for her lotto ticket.
When people talk about lotteries, the first thing they think of is to participate by buying tickets. Then, they spend time and resources determining how to win that alluring pot of gold. Yet, they need to realize that they can make their pot and fill it gradually.
You can earn profits through an inverse strategy incorporated into your lotto game plan.
If you still want to focus and play better, explore more lottery tips below.
Do Not Use a Quick Pick and Superstitions Method
Call it a blunder, mistake, or superstition; there are simply many misconceptions that lotto players follow even now.
Among them is the belief that Quick Pick offers greater chances of winning. This is untrue, as you can read in my previous blog post, Top 10 Lottery Strategy Myths Debunked.
When you mark Quick Pick on your lottery ticket, you grant the machine to pick the numbers for your combination. It does the picking randomly, with no analysis for odd-even and low-high numbers.
This is the same as when you haphazardly mark the numbers on the ticket with no strategy or plan. Using Quick Pick wastes the chance to affect your odds positively.
Remember what we have discussed since the beginning, mathematical analysis is the best approach to achieving lottery success.
Let randomness focus on the lotto game and use combinatorial and probability analysis to understand how randomness works.
As this news article explains, some people got lucky when they won the lottery with Quick Pick, but choosing Quick Pick does not guarantee you are the only player with that combination.
Speaking of luck, another misconception that you ought to correct is the improper use of lucky and unlucky numbers.
Different people have different perceptions of lucky numbers. For example, some players regard birthdates or anniversary dates as their lucky numbers. Others consider the number they dreamt about as lucky.
Lucky numbers in your lotto games are fine if you correctly apply them in your lotto strategy. Always pay attention to the balance in odd, even, low, and high numbers.
Settle on a combination whose composition gives the best success and failure ratio. Again, using a Lotterycodex calculator saves you from these fallacies.
Please read: How to Win the Lottery According to Math
Strange Combinations and Coincidences
For some people, dreams convey important messages. Some have avoided life-threatening incidents because they took heed using warnings from their dream.
Similarly, other people use their dreams to determine their number selection and win the lottery. One example is the story of Terry Vigus. Such cases are considerably strange coincidences.
There are success stories of strange coincidences in the lottery.
There are combinations with noticeable patterns, just like in the table of examples above. For example, 5–10–15–20–25 has a consecutive order pattern, just like the 3–9–15–21–27 combination that made the 50 Mass Cash players lucky.
There are variations of consecutive order patterns in some non-random combinations. For example, 1–2–11–12–21–22 in the Megabucks Doubler table above has three pairs of consecutive numbers in 1–10, 11–20, and 21–30.
Non-random combinations may also contain not easily seen patterns. For example, look at the Lucky for Life examples above, like 21–23–26–31–34.
Easily noticeable or not, these rare combinations might match the lottery-winning combination. The law of truly large numbers (LTLN) makes this possible. The law states that abundant opportunities allow coincidences, unusual happenings, and outrageous events to occur.
This LTLN differs from the law of large numbers (LLN). LLN gives light to the general outcome of lotteries throughout many draws. The LTLN explains the occurrence of unusual events in random cases.
Although possible, the rare combinations' frequency of occurrence is too small, so they cannot give the best shot you need to bag the jackpot. They usually have patterns that give the worst ratio of success to failure.
You can bet on them, but they will waste money and effort. So instead, stick to the benefits offered by Lotterycodex combinatorial patterns.
While combinatorial patterns do not tell the next winning numbers, they show the future behavior of games. This is better than crossing your fingers.
Can You Predict the Next Winning Combination?
Don't bite the bait if anyone tells you he can predict the next winning combination in the lotto. Unfortunately, knowing which numbers will turn up in the next lottery draw is impossible.
The lottery has an underlying probability that no one has control over it. Still, one can make the right decision if he wants to make the most out of lottery odds. The key to a mathematical strategy needs to be corrected. You choose to play with the best shot by choosing lines with a better ratio. That's the best thing you can do and nothing more.
This is done using combinatorial patterns considering covering principle, balance selection, and probability analysis.
While it is workable to do the process manually, one miscalculation could damage your game plan.
So what's the best solution? Use a Lotterycodex calculator that conveniently analyzes your game according to the principle of combinatorial mathematics and probability theory.
Other Games You Can Play in the Massachusetts Lottery
Mass Cash, Megabucks Doubler, and Lucky for Life are just three Massachusetts Lottery games. Of course, there are other games you can play.
You may play another draw game, Keno. Here, you select the spots (1–12) and the numbers (1–80) you want to play. The wager has no fixed cost because you decide how much money to place ($1-$20). Match all 12 numbers for a possible $1,000,000 jackpot.
The Numbers Game costs $0.25 per play. Choose four numbers from 0–9.
All or Nothing is also a draw game where you pick 12 in 1–24.
Instant Games from the Massachusetts Lottery are mostly scratch cards wherein you do not need to wait for the draw. Instead, you will know if you win after scratching the cards and seeing that the images match. Each game usually has rules on the card, so read the instructions carefully.
Instant games also vary in the payout structure. For example, the Holiday Winning Blowout costs $10, and the top prize is $500. On the other hand, the $1,000,000 Money Game costs $5, and the top prize is $1 million.
Apart from drawing games and instant games, there are also Pull Tabs. If instant games require scratching, this game involves pulling tabs from the two-ply laminated paper tickets. For example, pulling the perforated windows will reveal the slot machine symbols, numbers, etc. You win a prize if the symbols on your card match.
You Have the Power to Know and Make the Right Choice
Life is about making choices. One inspirational quote from the internet says: Always choose the best choices and learn from your wrong decisions.
True enough, this quote applies not only to love, relationship, and career. It also serves as a pleasant reminder when you are spending money buying lottery tickets.
You have likely been playing the lotto for years, and the most winning you have had was the minimum payout for matching 2–3 numbers.
You sure are persistent and persevering for continuously playing despite the many losses. Yet, a different and demeaning adjective will describe you if you do not change your old ways of playing the lotto after learning the information above.
Apply what you have learned about odds and use Lotterycodex patterns to your advantage. This way, you will know the ratio of success to failure of every combination you wish to use.
