Minnesota Lottery and the Mathematical Strategy
Minnesotans win, says Minnesota Lottery as it breaks down its sales proceeds. As a result, the state lottery has given $3.25 billion and more to programs benefiting Minnesotans.
Knowing that your dollars on lottery games go to beneficial causes is great.
Yet, wouldn’t it be great to win the jackpot? After all, your goal for every ticket you buy is to win the jackpot.
Random lotto draws have an underlying probability that is hard to beat. Therefore, you need a precise game plan to get the best shot possible according to probability. The details below can help you accurately strategize your lottery games in Minnesota.
The Best Lotto Game in Minnesota Lottery
Minnesota Lottery claims Northstar is its most winnable game. On average, there is one jackpot winner each week for this game.
Allow me to explain why Northstar Cash achieved its title as the luckiest Minnesota Lottery draw game.
Generally, a game with the smallest pick size, number field, and no extra ball gives the best odds of winning.
The table above shows that all draw games require a pick size of 5. Northstar Cash has the smallest number field with no extra ball resulting in the least possible combinations.
The probability of winning in Northstar is 1 in 169,911, making it the easiest lotto game to win a jackpot prize.
Minnesota Lottery Gopher 5 has 47 balls, so the number of possible combinations is 1,533,939. Therefore, Northstar Cash is nine times better if the probability of winning here is 1 in 1,533,939.
Games with extra balls drawn from a separate drum are much harder to win. For example, Lotto America offers a probability of 1 in 25,989,600. Thus, Minnesota Lottery Northstar Cash is 153 times better.
Winning in Minnesota Lucky for Life has a probability of 1 in 30,821,472. Northstar Cash makes it easier to win the jackpot by 181 times.
The probability of winning in Powerball is 1 in 292,201,338. Thus, winning the jackpot here is 1,720 times more difficult than in Northstar Cash.
And with a probability of 1 in 302,575,350 to win a jackpot in Mega Millions, Northstar Cash then offers 1,781 times better chances.
The decision to play is yours alone. You could choose which game to play, no matter how hard it is to win the jackpot. Understand the principles that make the game work to create a strategy for playing.
How To Play Minnesota Lottery According to Math
“You can’t win if you don’t play,” says Minnesota Lottery. One needs to buy at least a ticket to get a chance to win. Some people rely on luck when they play the lottery. Some use special dates and birthdays to create lottery combinations. Others randomly mark numbers on the playslip.
There are millions of combinations to choose from. A player is free to play any combination he wants to use.
With the negative expected value of the lottery games, expect to experience more losses than wins. For example, out of 20 attempts, you might not even have a moment of victory. However, a mathematical strategy will help minimize the number of times you lose and maximize your shots of winning. See How to Win the Lottery According to Math.
However, it would be best if you were careful with your strategy. And NO, there are better tools than statistics for you.
Let me explain.
The most common strategy many players use in creating combinations is hot and cold numbers. They derive these figures by analyzing statistics of the previous jackpot winning numbers of, say, 100 draws.
Hot numbers are those that get drawn frequently. Cold numbers are those that are rare during draws. Then, players may decide which of these hot and cold numbers they will add to their combinations.
This method doesn’t work. Incidentally, these hot and cold numbers will converge in the same expected value with more draws.
There are mathematical laws that govern lottery events. One of them is the law of large numbers or LLN. The LLN explains why these hot and cold numbers don’t exist when the number of draws gets larger and larger.
With a significant increase in the number of draws, all balls in the number field will catch up with almost similar frequencies. Thus, there will be no hot and cold numbers.
So when hot and cold numbers don’t work, what does?
Let’s take a look at this image below:
This computer-simulated image of the lottery’s randomness suggests there are ideas you can take advantage of. This way, you will be less wrong in most of the games you play. See also this article.
You don’t need statistics to get the right thing.
Let me first give you a scenario to illustrate this.
Jared and Sally have a bucket list of places they want to see. They decide on their next destination by drawing balls from a box. The box contains ten balls, and these balls vary only in colors blue, green, yellow, and red.
Blue balls = out-of-the-country destinations.
Green balls = southern part of the country.
Yellow balls = northern part of the country.
Red balls = adjacent provinces.
For their next trip, they invited their siblings to go with them.
Their siblings can use statistical sampling to guess which destination they will go to. This applies when they do not know the composition of the balls.
Suppose they know the number of balls for each color. In that case, the siblings can avoid statistical sampling altogether and use probability theory instead to understand better where they might go.
If two red balls are in the box, they would know there is a 20% chance they will travel within the province.
Four green balls will give them a 40% chance to visit the south. If there are three yellow balls, they have a 30% chance of traveling to the north. Traveling abroad is 10% because there’s only one red ball.
When information is limited, you resort to statistical sampling. But when data is adequate, you use probability theory.
Since a lottery game is finite, you don’t need statistics. Instead, the more appropriate tool to use is probability theory because we have adequate information on the composition of the game.
When playing lottery games, always remember that there are many possible choices. A precise mathematical strategy based on probability theory will help you get the best shot possible.
Play with the Right Ratio
No one could foresee the results of random lottery games.
Nonetheless, the finite characteristic of lottery games makes it possible to perform mathematical computations and analyses.
For instance, using the formula, we can compute the total number of possible combinations in a 6/42 game.
Substitute 6 to r and 42 to n to get 5,245,786 possible combinations.
Then if we want to calculate the probability of winning the jackpot, we use this formula below:
Probability tells you how likely an event will occur from the possible outcomes.
When you play the 6/42 lottery, you pay for a combination you want to use, like 6–7–8–9–10–11. To win the lottery, your combination must exactly match the winning combination. Therefore, your probability of winning with 6–7–8–9–10–11 is 1 in 5,245,786.
You can only increase your chances of winning when you spend more money on other combinations. For instance, you also play for the combinations 20–21–22–23–24–25 and 37–38–39–40–41–42.
The probability of winning from 20–21–22–23–24–25 is also 1 in 5,245,786. Therefore, playing for all three combinations will give you the winning probability of 3 in 5,245,786.
Notice that every combination has an equal probability. Therefore, some people are okay with which number they use. In their minds, putting any numbers together is fine because any combination they choose has the same probability.
Well, you need to consider another mathematical concept. This time, we can calculate the odds. But, unfortunately, odds and probability are two different terms and are not mathematically equivalent.
The formula for odds is
With odds, you measure the ratio of success to failure. Using the concept of odds, we can compare two combinatorial groups with varying odds. It can help us choose numbers easily based on the group with more favorable shots.
For example, we can divide the number field into low and high sets.
Low numbers = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
High numbers = {17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}
The 1–2–3–4–5 combination belongs to the 5-low-0-high group.
There are 4,368 ways to combine numbers without high numbers. So, if you play 1–2–3–4–5, you get 165,543 ways not to match the winning combinations.
Therefore, the ratio becomes 1 to 38. That means you get one favorable shot in approximately 39 attempts.
I don’t suggest that lotto players play 1–2–3–4–5 or any combinations with no high numbers, as this ratio reflects.
Remember that a true random lotto game must distribute numbers across the number field. So a winning combination with low numbers is very rare.
You can make a better game by balancing low and high numbers. Pick numbers across the number field to get the best shot possible.
And here’s why.
There are 58,800 ways to combine 3-low-2-high numbers. This group has 111,111 ways to avoid matching the winning combinations. Therefore, you get 35 favorable opportunities to match the winning combination out of 100 attempts. The ratio is about 1 to 2. Therefore, you get one favorable shot in approximately three attempts.
Noticeably, the Northstar Cash is dominated by two groups which are the 3-low-2-high and the 2-low-3-high groups. And these two groups will continue to dominate as more Northstar Cash draws occur.
Measuring the ratio is very useful for lotto players. And this is how we explain why 1–2–3–4–5 is not the most sensible decision you can make to play Northstar Cash or any Minnesota Lottery games.
Remember:
All combinations have the same probability because there’s only one way to win the jackpot. We use the ratio as a basis for getting the best shot possible because a truly random game distributes the probability across the number field. Therefore, the majority of the winning numbers will have a balanced composition of odd/even and low/high numbers.
Combinatorial Groups in the Lottery
Considering only the probability of a combination, you can see the lottery in such a limited way.
With odds, you can see a wider view of the lottery landscape. It could give you a more detailed picture of the game.
First, you need to understand what numbers and combinations are.
A 6/42 game, for example, has 1–42 balls from which you can select six numbers.
In a 6/42 lottery draw, all the balls share the same shape, texture, weight, and size, so there is no partiality for favoring one ball over the others.
Understand that a number will only manifest its significance when picked with other numbers to form a combination. When put together, these numbers give the combination its distinctive composition.
In a lottery game, numbers could be odd or even and low or high. In addition, these attributes can describe the composition of a combination.
Thus, each combinatorial group has a different composition and may hold a certain ratio that may differ.
Logically, choosing the combination that gives more favorable shots and fewer ways to lose would be best.
See the following example:
A 3-odd-2-even or 5-even combination will give you the same winning probability. However, if you choose the 5-even combination, know that this composition only occurs approximately twice in 114 draws. As a lotto player, you want something better.
A note on combinatorial analysis: The numbers on lottery balls are only “symbols.” Balls can also be represented using animals, fruits, or anything you can group. This article uses odd, even, low, and high numbers for mathematical calculations. Combinatorial mathematics involves counting and grouping things like numbers in the lottery. Through the knowledge of combinatorial mathematics, you can optimize your ability to choose and decide what would be best for the circumstances.
This combinatorial grouping is the fundamental concept behind Lotterycodex. Lotterycodex applies probability theory to separate the good from the bad and the best from the worst.
Lotterycodex - Advanced Combinatorial Analysis
Basic combinatorial analysis shows you why composition matters. Yet, as basic as it is, some contradictions might confuse players.
For example, odd-even analysis supports that 1–2–3–4–5 is ideal. Yet, the low-high analysis will disprove this, revealing that 1–2–3–4–5 has the worst ratio of success to failure.
To remove the contradiction between the two analyses, we combine the odd-even and low-high analyses into one combinatorial design called Lotterycodex.
Allow me to illustrate and explain how Lotterycodex works.
Notice from our discussion on basic combinatorial groups that the best choices are patterns with a balanced composition. However, this time, instead of dealing with two separate analyses, we combine odd-even and low-high numbers into one combinatorial design.
I want to show you how this Lotterycodex combinatorial analysis works in my free guide: The Winning Lottery Formula Based on Combinatorics and Probability Theory.
Let’s study the draw games of the Minnesota Lottery using the Lotterycodex method.
Northstar Cash
Northstar Cash is the luckiest game, as described on the Minnesota Lottery website. One play costs $1, allowing you to win at least $25,000.
It is a 5/31 game, so you pick five numbers from 1 to 31 to make a combination. You need to match at least three numbers to win something.
Minnesota Lottery holds daily draws for this game. You could buy a ticket with multi-draws of up to 14.
An example for Northstar Cash is 17–18–21–29–30. Based on the advanced combinatorial design table above, it is easy to see that this combination has no balance.
Below is a summary of Lotterycodex analysis on in Northstar Cash 5/31 game.
In a 5/31 game, there are 56 Lotterycodex patterns. Patterns #1, #2, and #3 are the best patterns you can use. Meanwhile, there are 22 middle patterns and 31 worst patterns.
Here’s how these Lotterycodex patterns will likely perform in 2000 and 5000 draws.
Using pattern #1, you could expect that it will occur 148 times in 2,000 draws. This means that this pattern offers a ratio of 1 to 14. For every 15 attempts, you get one favorable opportunity to match the winning combination.
Using a middle pattern like pattern #5, you could expect a frequency of 74 times in 2,000 draws. The ratio it offers is, therefore, 1 to 27. It will take you 28 attempts before getting a favorable shot.
Meanwhile, pattern #29 is the worst pattern to use when playing Northstar Cash. With this pattern, the ratio it offers is 1 to 111. You need to play in 112 games to have one favorable shot.
Many players have likely been using any middle and the worst patterns without awareness. Thus, they have been spending a lot of money, playing religiously in every draw, and waiting a long time to get one good shot.
With these Lotterycodex patterns, you gain the awareness and the details to keep you from playing mindlessly.
Gopher 5
Gopher 5 is a 5/47 lotto draw game where you pick five numbers from 1 to 47.
The starting jackpot is $100,000. Minnesota Lottery hold draws for Gopher 5 every Monday, Wednesday, and Friday. Multi-draw tickets are also available for up to 14 draws.
Lotterycodex analyzes the Minnesota Lottery Gopher 5 using the following sets of numbers.
The above table will produce combinatorial patterns that will allow you to see how Gopher 5 works in many draws. Please refer to this partial list of Lotterycodex patterns below:
For pattern #35, the estimated frequency is only 16 times in 2,000 draws. Therefore, with a ratio of 1 to 25, you need 26 attempts to get one favorable opportunity.
There is pattern #11 with an estimated occurrence of 57 in 2,000 draws. This can give a ratio of 1 to 35, so 36 attempts are necessary before you can get one good shot.
There is also pattern #1, whose estimated occurrences in 2,000 draws are 136. The ratio it offers is 1 to 15. Therefore, it is pattern #1 that will give you less chance to fail and more good shots at winning.
In a 5/47 game like the Gopher 5, there are also 56 Lotterycodex patterns, and only patterns #1, #2, and #3 will give you more good shots.
Lotto America
It was in 1988 when the Multi-State Lottery Association originally launched Lotto America—the original game required picking seven numbers from 1 to 40. Then, West Virginia, Rhode Island, Oregon, Missouri, Kansas, Iowa, and Washington, DC, participated.
Nine more state lotteries later followed. Finally, however, Lotto America reached its final draw on April 18, 1992. The following day, MSL began the new multi-jurisdictional draw game of Powerball.
In October 2017, after a 25-year hiatus, players started playing the new Lotto America game. Aside from Minnesota, 12 other states and jurisdictions offer Lotto America.
This new version now requires players to choose five numbers from 1 to 52 and a Star Ball from 1 to 10. One play is worth $1. In addition, players may opt for an additional stake from the All-Star Bonus on non-jackpot prizes.
The jackpot for Lotto America starts at $2 million. It increases by at least $50,000 if nobody wins on the last draw. There are two weekly draws for this game, Wednesdays and Saturdays.
Although there is an extra ball in this game, you may still use combinatorial analysis for a 5/52 game. After all, matching five numbers could let you win $20,000.
The sets of numbers below are what we use to study Lotto America using a Lotterycodex calculator.
A 5/52 game has 56 Lotterycodex patterns; only patterns #1, #2, #3, and #4 are the best.
Some players mindlessly stick to their special and lucky numbers, believing they will someday win. But unfortunately, they are unaware that their combination might have one of the worst patterns.
Suppose it is pattern #53. This pattern will give you one good shot after 2000 draws. After that, it is like waiting for an eternity for some phenomenon to happen.
A combination might also have a middle pattern like pattern #17. Therefore, you must play for 55 draws before getting that one good shot. If Minnesota’s Lotto America has two draws per week, 55 attempts would mean playing twice a week for 28 weeks or seven months. And all you get is just one good shot.
You can see what is likely to happen through combinatorics and probability theory. Lotterycodex will tell you to focus on pattern #1. With a ratio of 1 to 15, you might only need 16 attempts to have one good shot at winning.
This means playing Minnesota Lottery regularly for eight weeks or two months. A doubter might say this is still a long wait. Naturally, however, would you prefer to wait two months or seven months?
The answer all depends on your preferences and circumstances. Still, knowing all available options gives you the edge in choosing the best.
Lucky For Life
Lucky for Life is a lottery draw game available in many US states and jurisdictions. Aside from Minnesota Lottery, 25 other state lotteries and the District of Columbia also offer “The Game of a Lifetime.”
In a 5/48 game, you choose five numbers from 1 to 48 and then a Lucky Ball from 1 to 18. One play costs $2 for a chance to win the jackpot of $1,000 a day for life. There are two draws per week for this game, Mondays and Thursdays.
Matching just the five numbers will help you win $25,000 a year for life, which is already awesome.
Let us see the benefits of using Lotterycodex in the Minnesota Lucky for Life.
Out of these sets, we get a total of 56 Lotterycodex patterns. Below is a partial list of these patterns and their expected frequencies.
A player will save time waiting in line to buy a ticket that belongs to pattern #41. Occurring just 7 in 2,000 draws, you would need to play 287 times only to get one favorable shot.
287 attempts may convert to 144 weeks or 36 months, or three years. Imagine the time you could waste if you are unaware that your combination has the worst ratio.
Fortunately, a precise mathematical method could direct you to the patterns with the best shot at winning. Patterns #1, #2, #3, and #4 are the best.
Probability Theory and The Law of Large Numbers
The best combinatorial group dominates!
This means that the dominant combinatorial group will continue to dominate as the number of draws gets larger and larger.
Let me show you that pattern #1 will dominate the Northstar Cash draws.
Pattern #38:
= 0.0057677255 x 2,000
= occurs about 12 times in 2000 draws
Pattern #20:
= 0.0184567215 x 2,000
= occurs about 37 times in 2000 draws.
Pattern #1:
= 0.0738268858 x 2,000
= Occurs about 148 times in 2000 draws.
Our computations above reveal that in 2,000 draws, pattern #1 has roughly 148 occurrences. This is four times more occurrences than pattern #20 and 12 times more frequent than pattern #38.
This is the same trend you can expect after 5,000 draws.
Pattern #38:
= 0.0057677255 x 5,000
= Occurs about 29 times in 5000 draws
Pattern #20:
= 0.0184567215 x 5,000
= Occurs about 92 times in 5000 draws
Pattern #1:
= 0.0738268858 x 5,000
= Occurs about 369 times in 5000 draws
The calculation above reinforces the idea of focusing on pattern #1. The table below is a partial list of patterns for Gopher 5.
Pattern #35:
= 0.0078881885 x 2,000
= Occurs about 16 times in 2000 draws
Pattern #26:
= 0.0154895338 x 2,000
= Occurs about 31 times in 2000 draws
Pattern #1:
= 0.0681539488 x 2,000
= Occurs about 136 times in 2000 draws
The table above shows that pattern #1 has the most favorable ratio. This makes pattern #1 the most dominant pattern as more draws occur.
Let’s check Lotto America.
Pattern #35:
= 0.0035764306 x 2,000
= Occurs about seven times in 2000 draws
Pattern #26:
= 0.0185974390 x 2,000
= Occurs about 37 times in 2000 draws
Pattern #1:
= 0.0659363745 x 2,000
= Occurs about 132 times in 2000 draws
The calculations above tell you that pattern #1 will always dominate the game as more draws occur. It’s a mathematical certainty.
A combinatorial calculation can be very overwhelming. But you can use a Lotterycodex calculator to conveniently and accurately study your lottery game.
Are Quick Pick and Superstitions Helpful to Lotto Players?
Players can mark the Quick Pick option on the playslip. Then, the computer will randomly pick numbers to print on your ticket. It’s very convenient for players.
Superstitions also make playing convenient. For example, you ordered a Chinese takeout with a fortune cookie. Then, you could use the numbers you see from the fortune cookie.
Many players might choose these playing methods because they learned about some winners’ success stories. One example is Charles Jackson, who won the Powerball jackpot of $344M thanks to a fortune cookie.
Yet, can you believe that the same fortune would come unto you when you follow the same game plan?
Quick-pick numbers that a computer selects pay no attention to the ratio of success to failure.
You need to play better lotto games.
There are some superstitions that you could follow along with the application of combinatorial analysis. One is buying tickets from a store people believe to be lucky. One example is Cub Foods (Bloomington), which some Northstar Cash players regard as the luckiest retailer.
Do not simply think you could win or lose, so you face the risk and play randomly. Instead, always put the ratio of success to failure into perspective and guide you in making the best decisions.
Playing lotteries is simple. Just create a combination from the number pool and buy at least one ticket. Yet, there can be millions of combinations in one game. Out of these combinations, you must be clever to choose the best one.
Strange Combinations and Coincidences in Lotteries
There are strange combinations that win in lottery games. And some might be coincidences too. And this is not at all unusual. So a truly random lottery must allow all these unusual combinations to win.
As weird as it might seem, many players play lottery games using the non-random combinations from the table above.
Many players prefer combinations with consecutive patterns like 1–2–3–4–5, 5–10–15–20–25, and 1–2–3–11–12, probably because of aesthetic appeal.
Some players follow inconspicuous patterns. One example is 4–6–9–13–18, whose pattern (intervals of 2, 3, 4, and 5) in between numbers will let you think for a while.
These non-random combinations could be interesting to look at on a lottery ticket. Yet, they are only the combinations an intuitive player would use with considering combinatorial analysis.
For instance, 1–2–3–4–5 has the best odd-even but worst low-high ratios. This analysis also applies to 1–2–3–11–12.
You could read stories where players use strange combinations and win the jackpot. Yet, these instances rarely happen. They only happen because many draws are already held, which paved the way for the combination to win.
These unusual winning events adhere to the law of truly large numbers. This law states that many events allow coincidences, strange happenings, and unusual events to occur.
As a lottery player, you must buy tickets to play and win. Yet, you should select combinations in different ways. You should decide wisely according to probability theory.
Play Responsibly, Decide Wisely
Lottery games are entertaining. Like movies and arcades, you must spend money to participate in the games.
Losing a few bucks might not be a big deal for some people, but others take lottery games seriously. They allow at least $100 on lottery tickets but often use ineffective playing methods.
To have the best time playing the Minnesota Lottery game, you must play responsibly and decide wisely. Here are some tips and reminders to accomplish this.
Optimize your lottery budget.
Playing solo means getting all the jackpot money for yourself if you win. Yet, you might not buy as many tickets as you like because of a limited budget. More tickets mean more chances of winning.
Thus, you could start a small lotto syndicate with relatives and friends or join a bigger, more established syndicate. A syndicate is a group of lotto players who pool money to buy more tickets. Members share accordingly whatever prize they win.
Take part in lotteries with a resolve.
A resolute lotto player is determined to make the best of every game. However, even with a precise and accurate strategy, a player is bound to experience many losses. It could dishearten you but do not give up on lotteries just yet.
Know your limits.
As a lottery player, there are certain limitations that you should consider at all times. One is the budget limit. Responsible lotto gaming involves setting aside a budget and sticking to this budget to prevent possible dependence issues.
Another area for improvement is the inability to know the next winning combinations. Lottery games are random. You cannot beat the odds.
But you can choose your odds. These options include the different combinatorial patterns offering better success ratios to failure. In addition, they will help you understand the future behavior of a lottery game.
A combination with the best ratio will not guarantee you will win in the next draw. However, choosing the best ratio will let you pay with fewer losses and have more favorable shots at winning.
Remember that knowledge is power, and power comes with responsibility. So let this be a sound reminder for you to play Minnesota Lottery smartly and responsibly.
