“Anything can happen in Jersey”, is what you’d read on the website of New Jersey Lottery.

When it comes to playing lottery games, many instances of losing are likely to happen.

For positive things to happen, you must know how to play and win mathematically.

However, ensure that the mathematical principle you use is truly appropriate for playing the lotteries.

Thus, allow me to present you the information on a suitable mathematical method for playing the lottery.

Learn how you could play with fewer instances of losing and more ways of winning.

Keep on reading and discover how to have fun while playing lotteries responsibly.

In playing lotteries, always remember that you have many choices. First, there are many lottery games to choose from. New Jersey Lottery, for example, offers Jersey Cash 6, Pick-6, Cash4Life, Powerball, Mega Millions and more.

You also have many choices when it comes to which numbers to group together to form a combination. What you must remember is that your task is to choose the best among these choices.

Conversely, the best choices are not the number that will win in the next draws. The best choices are those that can minimize instances of losing and maximize your chances of winning.

When deciding on the best among your options, mathematics can be of great help. Conversely, there are many methods that lotto players use in creating their combinations. There are methods that involve mathematical principles.

Yet, as I have said in the introduction, the math principle you choose must be the ‘appropriate’ tool you can use in playing lottery games.

So, which are appropriate and which are not? Let me first give you a comparable situation.

Sofia, George and Lana are members of the same organization that would have an upcoming anniversary party. To make sure that all members will have fairly distributed tasks, the leaders prepared a box containing 18 balls of the same size, shape and texture.

The colors of the ball will determine what task a member will perform. Red is for the foods/drinks preparation. Blue is for decorating the venue. Yellow is for games and activities. Violet is for collecting sponsorships for the prizes.

If Sofia, George and Lana do not know the number of balls per color, they can just rely on statistical sampling to determine which task they will get.

Suppose they know there are 5 red balls, 4 blue balls, 5 yellow balls and 4 violet balls. They could easily know their chances for getting the task they like to perform.

This example illustrates when statistics or probability is appropriate for a certain situation.

Statistics will help if there are some things you do not know about a certain situation. Probability works when you have specific information about the critical factors.

So, which between statistics and probability can provide more help to lotto players?

One of the popular methods that lotto players use is the use of hot and cold numbers. In fact, there is a dedicated page on the New Jersey Lottery website that provides players with such numbers.

This method applies the concept of statistics. Looking at the previous draw results of, a player may see which numbers have been drawn more. However, this method only considers a few draws of about 50-100 draws.

You could actually see some hot and cold numbers in the previous 50-100 draws. Yet, this observation will change with an increase in the number of draws. Eventually, the hot and cold numbers will become insignificant.

Thus, statistics is not the most appropriate mathematical concept you could use as a tool for picking lotto numbers.

This computer-generated image shows the randomness of a lottery game. The lottery is random, but deterministic. Since players know the crucial elements of a game, they have a way to know and predict possible events through accurate mathematical calculations.

This image suggests players could use probability calculations in establishing precise conclusions based on the law of large numbers. With this, you can play without too many instances of being wrong.

This law says that with a considerable number of draws, all lottery numbers will converge around a similar frequency (of getting drawn).

Therefore, there will no longer be hot and cold numbers. Instead of statistics, probability calculations are better to use. This is because you know the number field and pick size in every New Jersey Lottery game.

Hence, the suitable mathematical ways of playing the lottery is by applying the probability theory. Yet, do not be content just with probability. Pay attention also to the ratio of success to failure.

The important ratios in lottery games

Odds and probability are interchangeably used in many real-life applications. Yet, one has to be extra mindful of when a scenario refers to odd or probability to prevent confusions and consequences.

Thus, let me show you how odds and probability differ from one another and how they can help in playing lottery games.

Probability measures the likelihood that an event will occur. In lotteries, probability is how likely you will win using the combination on your ticket against all the possible combinations.

In formula,

Therefore, every combination shares an equal probability. In a 5/45 game, for example, there are 1,221,759 possible combinations. Every one of these combinations has the probability of 1 in 1,221,759.

In order to have increased probability of winning, you need to buy more combinations or lines on the playslip. So, many players who consider only the probability might cripple their chances of winning.

Since there is one probability, they do not mind what numbers to put together. This is not a commendable method of playing. After all, probability only generally describes your likelihood of winning against all possible combinations.

Odds, on the other hand, can show you the possibility of winning using specific combinations in a lottery game.

The formula for combination is

You may actually compute for the odds in favor of you winning the lottery. You can use the odds formula to compare the number of ways to win with the number of ways to lose. Hence, odds also refer to the ratio of success to failure.

Incidentally, combinations have varying ratios of success to failure. We’ll discuss these ratios in detail in the next section.

RememberKnowing the ratio of success to failure is crucial in accomplishing your goal to win the lottery jackpot. You must additionally pick the best among these ratios. Lotteries have probability that no one can control and odds that no one can beat. Yet, a player’s smart use of his ability to discern and choose among his options can help him play the lottery better. Using the power to know and to make the correct choice will tell him the best actions to take.

Odds and probability must be used together when creating a strategy for playing the lottery. It is not enough to know you have one chance to win. It is equally crucial to know the combinations’ odds of winning so you can select the most favorable combination.

Again, it involves making the best choices among the possible. Thus, you must know first what your possible options of combinations are.

Keep reading below to discover these combinatorial options in lottery games.

It’s time to use combinatorial groups in your lottery games.

You need to acknowledge that you have many combinatorial options in lottery games. After all, a lottery game might have thousands or millions of possible combinations.

A 5/45 game has 1,221,759 possible combinations, while a 6/49 game has 13,983,816 possible combinations.

When we say lottery combinations, these are the groups of numbers on the lottery ticket you buy.

In the Jersey Cash 5 of New Jersey Lottery, a playable combination comprises 5 numbers selected from the pool of 1-45. A combination for New Jersey Pick-6 has 6 numbers chosen from 1 to 49.

All balls in a lottery drum have the same size, shape, texture and weight so no number will be preferred over the others. One number holds no significance unless it is grouped with other numbers to make a combination.

Conversely, lottery numbers could be odd or even and low or high.

These combinations differ in composition. This composition refers to how many odd or even and low or high numbers a combination contains. Therefore, combinations may be grouped according to their distinctive composition.

The odd-even and low-high compositions of combinations also give each combinatorial group its unique ratio of success to failure. A lotto player may capitalize on these unequal ratios by choosing the best.

RememberIt makes no difference in your winning probability whether you choose a 3-low-2-high or 5-high combination. Yet, it makes a difference in the ratio of success to failure if you choose 3-low-2-high instead of 5-high. The former offers more ways of winning and fewer ways of losing than the latter.

Let me show you how.

Suppose you want to play Jersey Cash 5. Your perceptive move would be to bet for a combination with 3 odd and 2 even numbers.

Such a combination can give you 33 opportunities to match the winning combination out of 100 draws. You would be smart to avoid an all even combination because you have only 2 opportunities in 100 draws.

In the same manner, also consider whether your numbers have the right quantity of low and high numbers. Odd or even numbers is common knowledge. You could distinguish an odd from an even number, even with your eyes closed.

Determining low and high numbers in a lottery game requires a bit more effort. Divide the number field into 2. The first half comprises low numbers, while the second half comprises high numbers.

In a 6/49 game like New Jersey Lottery Pick-6, the best combinations are those with the 3 odd and 3 even numbers. You have 4,655, 200 different winning combinations using this pattern. This means you have 35 times more ways to win than using a 6-even pattern.

A note on combinatorial analysisThe numbers on lottery balls are just “symbols” to discern one from the other. It could also be “animals” or “fruits”, or other representation that fits the application. In lotteries, the odd, even, low and high numbers are not the strategy. Instead, they conveniently serve as standards in mathematical calculations.We can group anything in combinatorial mathematics, such as numbers in the lottery. In other cases, we can also group fruits, gadgets, behaviors, countries, and other objects. If you know combinatorial mathematics, you have a way to optimize and make better decisions according to the circumstances.Lotterycodex works, according to this principle. It operates based on “combinatorial and probability theory”. By separating the good, bad, worst and best combinations, you will know what will provide the best ratio of success to failure.

The inequality of odds among combinatorial groups provides you with the important details for working out a mathematical strategy. New Jersey Lottery players who know and take time to know about these combinatorial groups can use this as leverage. They only need to make the most out of their ability by choosing the best.

The basic combinatorial groups in Jersey Cash 5

The New Jersey Lottery introduced Jersey Cash 5 in September 1992. It is a game where you choose 5 numbers from 1 to 45 to create a combination. You can play a game for $1 and take part in the nightly draws.

You could choose from 1,221,759 possible combinations for your game. With these many options, which would be the most favorable ones?

Let’s see.

The odds and even sets in Jersey Cash 5 are

Odd = 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45

Even = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44

1. You can create a combination containing all 5 even or odd numbers. The 5-even group gives 26,334 possible combinations while the 5-odd has 33,649 combinations. The 5-odd group has 7,315 more possible combinations than the 5-even group.

Yet, the table above shows that either group offers the lowest estimated occurrences among all the groups in this game.

2. You could also make combinations with 1-odd-4-even or 4-even-1-odd patterns. The 1-odd-4-even combinations have a probability value of 0.1377071910254; so, it may occur 14 times in 100 draws.

The 4-odd-1-even combinations share the probability value of 0.15945043171362 so they could appear 16 times in 100 draws. Either patterns are better than the 5-odd/5-even groups, but they still offer considerably bad ratios.

3. Better than the 5-odd/5-even or 1-odd-4-even/4-odd-1-even is the 2-odd-3-even pattern. It offers 194,810 more ways to win than 4-odd-1-even and 221,375 more ways to win than 1-odd-4-even.

It also offers 12 times more ways to win than 5-odd /5-even. Hence, it is a good choice of pattern to use when making combinations for Jersey Cash 5.

4. Another option to use when creating combinations is the 3-odd-2-even pattern. It offers 409,101 ways to win and 812,658 ways to fail. It also has the highest estimated occurrences of 33 in 100 draws.

Of these 4 possible options, the best and most favorable is 3-odd-2-even. Its offered ratio of success to failure is 1 to 2.

The 2-odd-3-even pattern also offers a similar ratio. Yet, you have 19,481 more ways to win when you choose 3-odd-2-even.

The ratio of success to failure offered by 3-odd-2-even is 2 times better than 4-odd-1-even. It is 3 times better than 1-odd-4-even.

In comparison, 3-odd-2-even has 18 times better ratio than 5-odd and 23 times better ratio than 5-even.

Therefore, a perceptive player will benefit most from the 3-odd-2-even pattern. This is because this pattern will give him the least chances of losing and the most opportunities of winning.

Conversely, you must not forget that your options also include low-high numbers and patterns.

In Jersey Cash 5 from New Jersey Lottery, the number field offers the low and high sets of

Low = 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23

High = 24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45

Out of these numbers, the combinations players can create may have the following patterns.

1. The 5-high pattern has 26,334 ways to win and 1,195,425 ways to fail.

2. The 5-low pattern gives 33,649 ways to win and 1,188,110 ways to lose.

3. With 1-low-4-high, you can have 168,245 opportunities to win and 1,053,514 chances to lose.

4. With 4-low-1-high, there are 194,810 ways to win and 1,026,949 ways to lose.

5. The 2-low-3-high pattern gives 389,620 ways to win and 832,139 ways to lose.

6. The 3-low-2-high provides 409,101 winning opportunities and 812,658 instances of failure.

Analyzing these 6 groups, we could categorize them into 4 options. The bad pattern choices are 1-low-4-high and 4-low-1-high. The good option is a 2-low-3-high.

Of these available patterns, you must avoid using combinations containing all 5 low numbers. It could make you lose 382,767 ways more than when you play for 3-low-2-high combinations.

Out of 100 draws, the 3-low-2-high pattern will give you 33 opportunities to match the winning combination. This is 17 times more than the winning opportunities offered by the worst choice of 5-high combinations.

Let us apply this knowledge on some examples.

1. 13-34-37-40-44

The odd-even pattern of this combination is 2-odd-3-even, which we have known to offer a good ratio of success to failure.

Its low-high combinatorial pattern is 1-low-4-high, which provides only a good ratio.

The aim of basic combinatorial analysis is to create combinations with the best possible shot at winning. Thus, this combination needs composition modification to increase your ratio of success to failure.

2. 1-4-17-19-43

We have here a 4-odd-1-even combination. This means you could have 16 opportunities to match the winning combination using this combination. You need 6 attempts to get a chance at matching the winning combination.

It has a 4-low-1-high composition, which is also a bad choice of low-high pattern. Both ratios are bad. Thus, you need to change some numbers in this combination to achieve the best winning odds.

RememberChoosing either a 5-even or a 3-odd-2-even combination does not change your probability to win. Yet, choosing a 3-odd-2-even than a 5-even combination changes your ratio of success to failure in playing lotteries. In Jersey Cash 5, you have 812,658 ways to lose with the 3-odd-2-even and 26,334 ways to lose with 5-odd. This means that 3you have 82,767 fewer ways of losing with 3-odd-2-even than with 5-even.

Through basic combinatorial analysis, you may know how close or how far you could be at winning the jackpot. You could analyze the worth of a particular combination you want to use.

You could change some numbers if you discover it has a poor ratio of success to failure.

Basic combinatorial analysis gives the advantage of choosing the best options and following a game plan based on these choices.

Luckily, you may also apply the same knowledge when playing Pick-6 from New Jersey Lottery.

The basic combinatorial groups in Pick-6

The New Jersey Lottery held the first game of Pick-6 in May 1980. With a number pool of 1-49, a player must choose 6 numbers to make a combination.

One play costs $1 for draws held on Mondays and Thursdays.

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

With these odd and even numbers, you can create and stake on any of the 13,983,816 possible combinations. There are 7 odd-even patterns you can use when making a combination, but which of these patterns should a keen player choose?

1. Using the 6-even pattern, you can make up to 134,596 combinations. This pattern will give you 13,849,220 ways to lose.

2. The 6-odd pattern offers 177,100 ways to win and 13,806,716 ways to lose. You can have 42,504 more opportunities with 6-odd than with 6-even.

Yet, it is still not a smart choice. In fact, both patterns are considerably the worst pattern choices a player can make. 3. 1-odd-5-even provides 1,062,600 possible combinations.

Thus, there will be 12,921,216 other combinations this pattern will not cover.

4. The 5-odd-1-even pattern has 1,275,120 ways to win and 12,708,696 ways to lose. It provides 212,520 more opportunities of winning than the 1-odd-5-even pattern. Still, it is only slightly better than 1-odd-5-even.

Both 1-odd-5-even and 5-odd-1-even offer bad ratios of success to failure. It means you can still make better choices.

5. 2-odd-4-even gives 3,187,800 ways of winning. You could have 1,912,680 more combinations to choose from than when you use the 5-odd-1-even pattern.

6. With 4-odd-2-even, you can have 3,491,400 ways to win and 10,492,416 ways to fail. It is better than 2-odd-4-even by providing 303,600 more ways to win. Yet, these patterns might still not give you the best possible shot at winning.

7. 3-odd-3-even has the ideal balance of odd and even numbers. It can provide 4,655,200 ways to win and 9,328,616 ways to lose. Compared to 4-odd-2-even, this pattern offers 1,163,800 more ways of winning.

The smart decision to make is one that could help a player have more chances of winning for most draws. Thus, the 3-odd-3-even pattern is the best choice to base a combination on.

It can give you 33 opportunities to match the winning combination in 100 draws. This is 32 more winning breaks than the worst choice of 6-even.

Now let us complete the basic combinatorial analysis for Pick-6 by looking at the low-high groups.

The low and high number sets in this New Jersey Lottery game are

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

You may pick 6 numbers from these sets to make a combination following any of the 7 low-high patterns below.

1. The 6-high group has 134,596 possible combinations. You surely have thousands of combinations to choose from, but their pattern might only appear once in 100 draws.

2. If you choose 6-low instead of 6-high, you may lower your chances of failing by 42,504. Still, it is not a worthy pattern to use and spend money on.

3. You may have 7 more winning opportunities in 100 draws when you play for a 1-low-5-high combination. You can also have 885,500 fewer ways of losing with this pattern compared to 6-low. Still, this is a bad pattern to choose among the 7 options.

4. The 5-low-1-high group is better than 1-low-5-high. It can reduce your possible failures by 212,520. Nevertheless, do not stop your search for the best option here.

5. You may have 1,912,680 lesser ways of losing when you choose the 2-low-4-high pattern. Yet with 23 estimated occurrences in 100 draws, you can still play better by choosing a better pattern.

6. 4-low-2-high is a better pattern than 2-low-4-high. It can reduce your ways of failing by 303,600. It can also have 2 more probable appearances in 100 draws than 2-low-4-high.

7. The remaining pattern, 3-low-3-high, has the highest possible occurrences in 100 draws. It can give you 8 more occurrences than 4-low-2-high.

Of these 7 low-high groups, the pattern providing the most favorable ratio is 3-low-3-high. Its balanced composition can give you the fewest changes of failure and the maximum shots at winning.

The ratio of success to failure a 3-low-3-high pattern offers is 1 to 2. This means that 3 attempts can give 1 opportunity to match the winning combination. This could mean playing for about 2 weeks for draws held twice a week.

Considering the number of possible combinations, the worst choice is 6-high with a ratio of 1 to 103. Thus, it would require 104 attempts for 52 weeks before you can get that opportunity to win.

Can you now see why you should carefully create your combinations and make sure they follow the best pattern? Let us use this knowledge in some examples.

1. 3-9-15-25-36-46

This combination follows the 4-odd-2-even pattern, which has the ratio of 1 to 3. Your 4 attempts could give you 1 chance at matching the winning combination.

The combination also has the 4-low-2-high pattern. This means it also has a good low-high ratio to offer.

Knowing that the best ratio of success to failure comes from a different combinatorial pattern, use this information to change your numbers.

2. 8-12-28-30-42-46

Now, this combination has 6 even numbers. This pattern may only provide you with 1 possible opportunity to win every 100 draws.

It contains 2 low and 4 high numbers. Again, the low-high ratio from this pattern is only good enough.

Through the information you can gather from basic combinatorial analysis, you can discern what your next move should be. The combination you had in mind could have the worst, bad or good ratio.

Thus, you may change some numbers before buying tickets.

This means you can play responsibly by making sure you spend money on worthwhile combinations. This strategy is better than others relying on blind luck or false beliefs on lucky numbers.

It is always great to know that you have the best options in most lottery games, including Cash4Life. Thus, if you take an interest in knowing the mathematical way of playing this game, continue reading with a passion below.

Cash4Life and its basic combinatorial groups

It was June 13, 2014 when New Jersey Lottery and New York Lottery launched Cash4Life. It is the first “for life” draw game that offers $1,000/day for life as the jackpot prize. This game has nightly draws you can take part in for $2/play.

To play this game, choose 5 numbers from 1 to 60 and one Cash Ball from 1 to 4. If you could match all 6 numbers, you win the jackpot.

It is definitely great to win the jackpot. Yet, I know you would agree with me that winning the second prize is equally a life-changing experience.

Cash4Life involves an extra ball drawn from a separate drum. This makes the jackpot more difficult to win with an increased number of possible combinations.

Yet, if the second prize of $ 1,000/week for life can satisfy you, use basic combinatorial analysis for Cash4Life.

Let us start with the odd-even analysis.

Odd = 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59

Even = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60

Out of these odd and even numbers, the possible 5-number combinations you can create are 5,461,512.

Each of these combinations could offer a unique ratio of success to failure. This is because of their varying odd-even compositions.

As a 5/60 game, there are 6 odd-even …