Last updated on January 2, 2021
“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.
It is great to know that 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 know that you have asked these questions many times. You probably even felt hopeless each time you do; you have won nothing out of your daily games.
I cannot have a definite answer to your first question, but I can present valid information in devising a strategy. Let me show you how math can be an effective strategy in winning the Massachusetts Lottery.
The right tools to use to win a Massachusetts lottery
While statistics are a mathematical concept, this is not the method that you will learn here. In fact, I will debunk the existence of hot and cold numbers, which many lotto players aim to spot when they use statistics (past game results).
Massachusetts Lottery games are random, just 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 will have the same (or almost the same) frequency of occurrence as presented in this visual analysis. The law of large numbers is behind this.
Life is a box of chocolates, and you will never know what you will get. A brown paper box contains 12 Hershey’s Kisses chocolates in milk chocolate, almonds, and chocolate truffles. Statistical sampling is a method applicable to determine how many Kisses in each flavor the box contains.
But that’s not the same case in the lottery; therefore, statistics is not the right tool to use.
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. You can compute important parameters like total combinations, the probability of a certain type of combination, and the odds of winning from a certain combination.
Therefore, instead of statistics, we can use combinatorial mathematics 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. This free guide discusses these concepts in detail.
Do not feel scared just because I mentioned some mathematical calculations when there is a lottery calculator you can use. This new tool will simplify all the crucial math concepts required to make the game better.
The key is in the ratio
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 5 numbers from 1 to 35 gives the total combination of 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.
This next formula is for odds. It is this formula that considers each combination uniquely. This is where the concept of combinatorial groups starts to matter.
There are different combinations lotto players can make in a lotto game, like the samples above. 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. This scenario considers only the probability, but not the odds, which gravely weakens your strategy for winning.
From this table above, you see there are 6 odd-even patterns for Mass Cash. Odds take into consideration the pattern of a combination.
If you play for a combination containing all 5 odd numbers, your odds are 8,568 ways to win but 316,064 ways to lose. Thus, odds give the ratio of success to failure.
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.
Odds give you hope by telling you that you need to strategically, not randomly choose the numbers on your lottery ticket.
Sadly, many players miss the opportunity that odds (or ratio of success to failure) offer because they focus only on probability.
Players, who disregard odds, could randomly pick numbers and mark 5 even numbers. The table of odd-even pattern analysis proves this is not a good idea. The 318,444 ways you can lose using this pattern is greater than the 213,656 ways of losing using a 3-odd-2-even pattern.
Focusing only on probability, you will always think there is just one way of winning, so it does not matter what numbers you select. Putting odds into consideration, you realize you must carefully pick every number to have more ways of winning and lesser ways of losing.
This strategy lets you have fewer ways of being wrong in the Massachusetts Lottery, which you can accomplish with Lotterycodex.
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.
Now let us see the ratio of success to failure in Megabucks Doubler.
To consider the ratio of success to failure in this lottery game, cautiously select low and high numbers for your combination. 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. Probability says there is one way to win. The ratio shows that choosing the best patterns gives a better winning advantage.
Knowing this, will you let a good opportunity pass by? You would definitely not. Keep reading more about choosing ideal combinations below.
What you should know about combinatorial groups
Numbers and combinations are innate in a lotto game.
Assume that in front of you, there is a jar of marbles for each number from 1 to 35. You must get 5 marbles from the jar. Each marble has the same shape, weight, and texture.
Thus, there are no biases to determine which marbles you will get when you draw one marble at a time. This explains how an individual number has no significance unless it goes with other numbers to create a combination.
Each lotto game has its pick size and number field. For example, Massachusetts Lottery Mass Cash requires you to select 5 numbers (pick size) from 1 to 35 (number field). The lotto machine will probably reject your card if you marked only 4 numbers.
In Megabucks Doubler, players choose 6 numbers from 1 to 49 to create a combination. A combination comprises 5 different numbers from 1 to 48 (plus 1 lucky ball from 1 to 18) in Lucky for Life.
From the number field of every game, there are 4 sets we can create according to the numbers’ characteristics. These are odd, even, low and high.
Refer again to the Odd-Even Patterns for Mass Cash 5/35.
Out of 1 to 35, you can make a combination containing all 5 odd numbers. You can also choose 4-odd-1-even, or 3-odd-2-even, or 2-odd-3-even, or 1-odd-4-even or 0-odd-5-even numbers. Thus, you can come up with combinations that have varying odd and even number compositions.
The unique composition of every combination produces the combinatorial groups. As explained earlier, every 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. You will choose a pattern that has more ways of winning 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 the combinatorial group that contains your 3 low and 2 high numbers. You have 516,120 fewer ways to lose using this than the 5-low combination.
RememberA 3-low-2-high or 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 ways to win 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 to fail.
From the Mass Cash ratio image above, we also paid attention to how many odd and even numbers are in the combination. In the Megabucks Doubler, the quantity of low and high numbers in the combination played a crucial role in its ratio of success to failure.
Concentrate on carefully choosing a balanced combination of odd, even, low and high numbers.
Knowing that combinatorial groups have different odds, a smart player could then form his mathematical strategy. He could map out 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.
Combinatorial groups in the Mass Cash 5/35
To play Mass Cash, pick 5 numbers from 1 to 35. Buy tickets for $1 each. The jackpot prize is $100,000.
For this Massachusetts Lottery, two of the number sets are:
Odd = 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35
Even = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34
This table shows the 6 combinatorial patterns that contain odd-even numbers for Mass Cash. While you have the freedom to choose your numbers, you surely want to spend money on tickets with numbers that can bring you closer to winning.
Thus, it is helpful selecting 3 odd and 2 even numbers on your lotto ticket. This has the most favorable ratio of success to failure among all odd-even patterns. There are 324,632 total combinations for this game.
Probability tells us that no matter what pattern we use for the game, there is only one chance to become the winner.
Yet, the ratio of success to failure gives us hope that if you use the 3-odd-3-even pattern, you could be the winner from the 34 times expected occurrence of this pattern every 100 draws.
RememberChoosing a 3-odd-2-even combination instead of a 5-even makes no difference in the probability. Yet, the 3-odd-2-even combination offers the best ratio of success to failure. This gives 213,656 ways to lose, while a 5-even combination offers 318,444 ways to lose.
We must always remember and consider the balance in your choices, so for Mass Cash, take care in choosing low and high numbers too.
Low = 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
High = 19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35
The 1-2-3-4-5-6 combination might have the highest probability in terms of odd-even analysis, but all these numbers are from the low set.
Out of 100 draws, this could only match the winning combination 3 times. There are 8,568 ways of winning, while there are 316,064 ways of losing with this pattern.
Balance in the composition is important even in Megabucks Doubler of the Massachusetts Lottery.
Combinatorial groups in the Mega Bucks 6/49
Megabucks Doubler is a 6/49 game. From 1 to 49, select 6 numbers for your combination. One wager costs $1.
Tickets with “This is a Doubler Ticket” imply that these tickets will have 2 times the non-jackpot prizes. Jackpot starts at $500,000.
The number sets for this Massachusetts Lottery game include:
Odd = 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 = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48
Your birthday is July 28, while your partner was born on December 15. Let’s say that according to your horoscope, your lucky numbers are 35 and 17.
You want to use these numbers when playing Megabucks Doubler. Let us see how this will fare.
These numbers give you the combination of 7-12-15-17-28-35. The composition of this is 4-odd-2-even. Using the table above, this pattern has a 0.25 probability value and could occur 25 times in 100 draws.
Let’s be clear first: the probability and estimated occurrence may not necessarily match the actual lottery draw. The probability is simply a mathematical guide.
4-odd-2-even pattern gives you 3,491,400 ways to win, and one of them is 7-12-15-17-28-35. Within the expected occurrence of 25 out of every 100 draws for this pattern, your number could land you the jackpot prize.
There is another factor affecting the ratio of success to failure, which is the low-high analysis.
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
Coincidentally, 7-12-15-17-28-35 is one of the 3,491,400 combinations with 4-low-2-high pattern. As the second-best combinatorial pattern for Megabucks Doubler, you have one of 4,655,200 winning ways.
However, you want to buy another ticket and use your anniversary date of January 6 instead of your horoscope number. This 1-6-7-12-15-17 follows a 6-low pattern.
The ratio is much lower for this pattern. There are 177,100 ways to win and 13,806,716 ways to lose. See the effect of low-high number choices on the odds of winning?
Let us look at Massachusetts Lottery Lucky for Life next.
Understanding the Lucky for Life game
The Lucky for Life requires you to choose 5 numbers from 1 to 48, then a lucky ball from 1 to 18. Pay $2 per ticket. The prize if you match 5 numbers and the lucky ball is $7,000 weekly for life. Match only 5 numbers, and you win $25,000 yearly for life.
Below are its number sets:
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
High = 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48
A mother of 5 children plays the Lucky for Life game using her children’s day of birth, so she marked 2-9-10-21-31. Will she have the best shot at winning at least the $25,000 yearly for life jackpot? Let’s see.
This combination has a pattern of 3-odd-2-even. From the table above, this is really a wonderful choice of numbers based on the odd-even composition. Let us see if her combination passes the low-high analysis.
2-9-10-21-31 has a 4-low-1 high pattern. This is the second to the best among the 6 combinatorial patterns. Mom’s combination is one of the 255,024 ways to win out of 1,712,304 combinations for the 5 numbers only.
Her choice of numbers surely gave her the benefit from the ratio of success to failure for choosing a good (though not the best) combination of low and high numbers. If her combination matches the winning numbers, Massachusetts Lottery will give her $25,000 every year for life.
Yet, her husband insisted that she use his birthday for the lucky ball, so she marked 18. The extra ball makes winning the jackpot more difficult. It further reduces the odds of winning because the total combinations increase to 30,821,472.
The extra ball comes from a different drum. It is your choice to play this game despite this. To know about dealing with extra balls in lotteries, please read How to Handle the Tricky Extra Ball.
Using a more 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. It has the best ratio in terms of odd-even but the worst ratio in terms of low-high.
The contradiction will inevitably lead to errors in your strategy. Thus, the solution is to combine the separate analyses into one advanced combinatorial analysis.
Instead of just focusing on the odd and even or the low and high numbers, a clever move is to bring the two methods together. You need to regroup the numbers of a given lotto game into odd-low, odd-high, even-low, and even-high sets.
This process can exhaust the energy from your brain cells, so let me illustrate this by sharing the advanced combinatorial design with you.
The table above shows the four sets of numbers for Mass Cash. The same concept applies to Megabucks Doubler and Lucky for Life of Massachusetts Lottery using different sets.
Here, you can easily see from which set a certain number is from. With 1-2-3-4-5-6, the advanced patterns clearly show that it has 3 low-odd and 3-low-even numbers. This combination only picked numbers from the two sets.
The mom player 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 only second to the best low-high pattern.
Using the advanced patterns, 2-9-10-21-31 contains 1 low-odd, 2 low-even, and 2 high odd numbers. Clearly, this is not the best combination to choose. She has to change her choices if she wants to get the best ratio.
Let’s see more of the Lotterycodex patterns for Mass Cash.
There are 56 patterns for Mass Cash. Only three can give you the best shot possible. You might not know it, but you probably have played using the worst patterns in your previous games. With the information supplied by the patterns, you could then choose only to play using any of patterns #1, #2, and #3.
From the image below, look at each pattern’s expected frequencies, so you will better understand how best and worst combinatorial patterns benefit you.
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 will spend your money on tickets using this pattern. You could waste money if you insist on using pattern #39 because it can only occur 15 times in 2000 draws.
Pattern #3 has a ratio of 1 to 133. Thus, in the 134 times you play, there is a single way to win, but 133 ways to lose.
If you only play the game once a week, this could mean that in the 134 weeks that you will play, you possibly have one week to win the jackpot. There are 52 weeks in a year, so this could mean playing for 2 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 the failure of 1 to 19. You could be the jackpot winner in one of the 20 weeks this pattern would lead you to play.
Pattern #1 makes for fewer losses and more winning opportunities. Using a mathematical strategy aims to use the best shot possible and spend money wisely.
You can picture this mathematical strategy as different routes shown by a mobile navigation app. Each combination represents each route to reach the destination. Some routes are short cuts; others will lead you to longer paths.
From the law of large numbers, the best choice is like the shortest route that can take you closer to the destination of winning the jackpot.
These unique combinatorial patterns also help time your play accordingly. From the table above on Lucky for Life, pattern #1 is among the 3 best patterns out of 56. It can occur 133 times in 2000 draws.
Be mindful, though. The approximate interval is not a precise calculation because you never know when a pattern will occur in a truly 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 15 draws. Skip playing during this interval. Save money when you skip playing so you can buy more tickets next time.
The three lottery games we discussed have thousands to millions of patterns. All these involve complex calculations. While this is intimidating, there is always an option, especially if you hate math.
Use the Lotterycodex calculator. This calculator will present the best, middle and worst patterns based on your number selection.
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 carefully select your game.
The best game to play from the Massachusetts Lottery is a subjective choice. Still, considering other factors like pick size and number field help analyze your odds of winning.
A lotto game with fewer balls, smaller pick size, and no extra number is the ideal game to play. You always have only one way of winning against the total number of combinations for the game.
With a smaller number of total combinations, you have better chances to win. In Mass Cash, you have 1 way to win against 324,632 combinations.
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. It is 5 times more challenging to match the winning combination in Lucky for Life than in Mass Cash.
Mass Cash offers better odds than Powerball, although they both 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 the prize on an ordinary day when the prize 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 in that game. Lotterycodex calculators can enhance your power to choose.
Probability and the law of large numbers
Repetition is the key to mastery, so let me reiterate the things we have discussed above.
Although the odds are hard to beat, and the probability is not something we can control, there is a way we can reap some fruits when playing the lottery. For this, we must acknowledge the randomness and finite structure of the lottery.
Ball drawing in lotteries like Massachusetts Lottery is random. Still, the law of large numbers tells that with a substantial increase in the number of draws, every ball in the lottery will have (almost) the same occurrence. Each number and combination has the same probability.
However, considering just probability is not enough for a precise mathematical strategy. Let us not forget the importance of odds or ratio of success to failure in combinatorial groups. To have the best odds, we must look at combinatorics and probability.
Every combination in the lottery contains a unique composition, such as the odd, even, low and high numbers it contains. This composition gives a combination with its specific ratio of success to failure.
Analyze how many odd or even low or high numbers you mark on your ticket. Make sure the final combination belongs to a combinatorial group that has the highest odds of winning.
Otherwise, your money will go straight to the drain since the best combinatorial group will dominate the game. This will manifest with more numbers of draws.
Look at patterns #1 and #53 of Mass Cash, for example.
Pattern #1 has a 0.0718598290 probability value, and its expected occurrence …