Minnesota Lottery and the Mathematical Strategy for Winning Games
Minnesotans win, says Minnesota Lottery as it breaks down its sales proceeds. The state lottery has given $3.25 billion and more to programs benefiting Minnesotans.
It is great to know that the dollars you spend on lottery games go to beneficial causes.
Yet, wouldn’t it be great to win the jackpot or at least get something valuable from your lottery spending?
After all, your goal for every ticket you buy is to win the jackpot more than to give to charity.
Random lotto draws have an underlying probability that is hard to beat.
This means you need a precise game plan to follow to circumvent this.
If you agree, then the details below can help you accurately strategize your lottery games.
How to play Minnesota Lottery better?
“You can’t win if you don’t play. But what are the chances of winning?” also says Minnesota Lottery (see “About the Lottery” page on its website). Thus, let us start our discussion with these statements.
One needs to buy at least a ticket to get a chance to win. When buying a ticket, you first mark the numbers on a playslip to create a combination.
Some people just rely on luck when they play the lottery. Some use special dates and birthdays to create lottery combinations. Others just randomly mark numbers on the playslip.
Incidentally, there are thousands and millions of combinations to choose from. A lotto jackpot contender is free to play any combination he wants to use. Yet, an ardent player will settle on a combination that offers the best chances of winning.
Yet, with lotteries, expect to experience more losses than wins. Out of 20 attempts, you might not even have a single moment of victory. A strategy will help minimize the number of times you lose and maximize your chances of winning.
Buy, what exact strategy should you use? I daresay a mathematical lottery game strategy.
However, let me remind you at this point that there are many mathematical concepts we can use to play lotteries. It is important that we choose the most appropriate concept that can give better winning chances.
Different players use different strategies for playing, including those we mentioned above. To have a precise strategy to play the Minnesota Lottery draw games better, you need something that can bring you close to the jackpot.
Perhaps the most common strategy that many players use in creating combinations is the use of 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 not too popular during draws. Then, players may decide which of these hot and cold numbers they will add in their combinations.
This method could be valid only if we are talking about the 100 draws of a lottery game. Incidentally, lottery games have more than just 100 draws. With more draws, these hot and cold numbers become null.
There are mathematical laws that govern the world of lotteries. One of them is the law of large numbers. LLN explains why these hot and cold numbers cease to exist with the number of draws reaching infinity.
With a significant increase in the number of draws, all balls in the number field will have similar frequencies. Thus, there will be no more hot and cold numbers. So, what mathematical strategy should you use then?
This computer-simulated image of 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.
Statistics may apply to an extent, but probability offers a much more appropriate method of playing.
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 10 balls, and these balls vary only in colors of blue, green, yellow, and red.
Blue balls are for out of the country destinations. Green balls are places from the southern part of the country.
Yellow balls are for destinations in the northern part of the country. Red balls are for destinations within their province and adjacent provinces.
For their next trip, they invited their siblings to go with them.
Their siblings can use statistical sampling to make a guess on which destination they will go. This applies when they do not know how many balls are in each of the 4 colors.
If they know the number of balls for each color, the siblings have a better idea where they might go.
If there are 2 red balls in the box, then they would know that there is a 20% chance they will travel within the province.
Four green balls will give them 40% chances to visit the south. If there are 3 yellow balls, they have 30% chances of traveling to the north. One red ball gives them 10% of traveling abroad.
Statistical sampling applies when we do not know some more crucial information like the number of balls in every color. Probability calculations apply when you know the important details.
Lotteries are random, but deterministic. With lotteries that have finite characteristics, the more appropriate tool to use is probability.
Statistics would not work as effectively as you want it to because of the limited sample. Remember that you only consider a few draws out of the infinite number of lottery draws.
I do not force you to abandon the use of statistics, especially if this is what you have been using in the past. However, the mathematical lotto strategy is one where you have to make a sensible decision.
Would you insist on using hot and cold numbers now that you know this method is inappropriate? When playing lottery games, always remember that there are many possible choices to choose from.
A precise mathematical strategy based on probability will help you make the best among these choices.
Which ratio do you consider when strategizing your games?
Now, let us agree at this point that lottery games are random. The probability that controls the games is impossible to beat.
The strategy a player must develop will not exactly show him how to predict the next winning combinations. No one and nothing could foresee the results of random lottery games.
Nonetheless, developing and following a strategy will help you know your options and choose the best among them. The discussion below will help gather useful information for creating your very own lotto game strategy.
The finite characteristics of lottery games make it possible to perform mathematical computations and analysis.
For instance, we can compute for the total number of possible combinations in a 6/42 game by using the formula
Substitute 6 to r and 42 to n to get 5,245,786 total possible combinations.
The total number of possible combinations allows discerning players to also determine their probability of winning. This involves using the formula below.
Probability in tells you how likely an event will occur from the number of 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 to win 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 to win from 20-21-22-23-24-25 is also 1 in 5,245,786. This is also the winning probability you have from 37-38-39-40-41-42. Playing for these three combinations will give you the winning probability 3 in 5,245,786.
Notice that every combination has an equal probability. Therefore, some people do not mind which number they use. In their minds, putting any numbers together is fine because any combination they choose has only one probability.
I just mentioned that the mathematical lotto strategy involves knowing your possible choices and choosing which the best is. If you will consider only the probability, how can you choose the best if you know that all combinations have the same probability?
Therefore, you need to consider another mathematical concept to show you what other viable choices there are. This time, analyze the lottery game through odds.
The formula for odds is
Odds in a lottery are the possibility of your combination appearing instead of the other combinations. You compare the favorable combinations with unfavorable combinations. Thus, odds also refer to the ratio of success to failure.
RememberThe ratio of success to failure directs you to the best combinations that will help you achieve the goal to win the lottery. Since the lottery has underlying probability, no one can change or control, a perceptive player may use this ratio to know his options and to choose the best. It is up to his discernment what option to use and what action to take best.
Probability treats every combination the same, in a way that they each provide one winning possibility to a player. Thus, it makes no difference which combination you choose.
Meanwhile, odds let you have more options to choose from. Odds, along with combinatorial mathematics, make you see the number of ways to win and compare it with the number of times to lose.
Odds allow you to discover the use of basic combinatorial groups in a lottery game.
Basic combinatorial groups, how can they help you play better?
If you consider only the probability, you can see the lottery in such a limited way of either winning or losing.
With odds, you can see a wider view of the lottery landscape. It could give you a more detailed picture of the game by dividing the total number of combinations into basic combinatorial groups.
To understand what these groups are, you first need to understand what numbers and combinations are.
A lottery game’s finite characteristic involves how many numbers you should pick from the number of balls in a game (number field). A 6/42 game, for example, has 1-42 balls from which you can select 6 numbers.
In a lottery draw for 6/42, every ball in the drum denotes every number from 1 to 42. 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 placed together 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. These attributes make a certain combination and combinatorial group distinctive.
The unique odd-even or low-high attributes of combinatorial groups give them unequal ratios of success to failure. This inequality is what you can take advantage of when devising a mathematical strategy.
You will logically choose the combination that gives more ways to win and fewer ways to lose.
RememberEither a 3-low-2-high or 5-high combination will give you the same winning probability. However, a 3-low-2-high combination has a better ratio of success to failure than a 5-high combination. As a perceptive player, you will not choose 5-high over 3-low-2-high because it has more ways of losing and fewer ways of winning.
See the following example.
Abby has 2 favorite combinations when playing Northstar Cash. These are 6-8-18-24-30 and 15-16-17-18-19-20. Using the information from the table above, which do you think gives Abby the best shot at winning the jackpot?
6-8-18-24-30 contains all even numbers. The table above shows that this pattern offers 3,003 ways of winning and 166,908 ways to fail.
15-16-17-18-19-20 has 3 odd and 2 even numbers. Based on the information above, this pattern has 58,800 ways to win and 111,111 ways to fail.
Thus, 15-16-17-18-19-20 can provide Abby with the best shot at winning the jackpot. This combination contains the best ratio of success to failure. It has more ways to win and fewer ways to fail than the 6-8-18-24-30 with a 5-even pattern.
A note on combinatorial analysisThe numbers on lottery balls are only “symbols” just like “animals” or “fruits”, or pretty much anything that you can count. We refer to numbers as odd, even, low and high numbers, not as a strategy but as a model in performing mathematical calculations.Combinatorial mathematics involves counting and grouping things like numbers in the lottery. In other situations, it can also be other objects like gadgets, coins, pens, etc. Through the knowledge of combinatorial mathematics, you can optimize your ability to choose and decide what would be best for the circumstances.This is the fundamental concept behind Lotterycodex. It involves applying “combinatorial and probability theory” for classifying combinations as good, bad, worst, and best. Thus, you can make decisions based on combinations offering the best ratio of success to failure.
Here is another sample scenario where the knowledge of combinatorial mathematics serves a valuable purpose in lottery games.
Adam is an avid Gopher 5 player. While his enthusiasm for the game does not wane despite his losses, he wants to know how he could play better.
He, therefore, did some reading on the internet and luckily discovered about basic combinatorial analysis.
He realized that all those years and dollars he spent on 25-30-37-42-43 might have been a waste of effort. According to the low-high analysis of this combination, it contains all high numbers.
From the table above, this combination has 33,649 ways to win and 1,500,290 ways to fail. Instead of sticking to this combination, Adam could tweak the numbers so it may contain 3 low and 2 high numbers.
In this way, he could have the best ratio of success to failure: 512,072 ways to win and 1,021,867 ways to fail.
Basic combinatorial analysis lets you see how combinations will perform in the succeeding draws. Based on the ratio of combinations, you could come up with decisions on which combinations are worth your money.
You could also decide to change your long-time combinations if you think it is necessary. Basic combinatorial groups empower you in your decision-making by showing you what options you have.
Through the information on the ratios of combinations, you could make well-informed decision and strategy when playing Minnesota lottery games.
Take note that basic combinatorial groups are also present in Lotto America and Lucky for Life. Make sure not to miss the opportunity and decide wisely based on accurate mathematical information.
Keep reading below to know the basic combinatorial groups in details. Although two or more games may have similar combinatorial groups, remember that the ratio could vary.
So, let’s discover about the combinatorial groups for Northstar Cash first.
Northstar Cash and its basic combinatorial groups
Northstar Cash, as described on the Minnesota Lottery website, is the luckiest game. One play costs $1, and it gives you the chance to win at least $25,000.
It is a 5/31 game, so you must pick 5 numbers from 1 to 31 to make a combination. You need to match at least 3 numbers to win, but winning the jackpot remains the goal.
Minnesota Lottery holds daily draws for this game. You could buy a ticket with multi-draws of up to 14, but make sure that the combination you have for these 14 consecutive games has the best ratio to offer.
So, how do you ensure this?
This game has the odd and even number sets
Odd = 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31
Even = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30
Like what you have read earlier, using the combination formula gives this game 169,911 possible combinations.
There are 6 basic combinatorial groups for this game. The 5-even group only has 3,003 possible combinations out of 169,911 so it could occur only twice in every 100 draws.
With estimated occurrences slightly higher than 5-even is the 5-odd group with 4,368 possible combinations. Either of these groups is the worst pattern you could use. 5-even has the ratio of 1 to 56, while 5-odd offers the ratio of 1 to 38.
1-odd-4-even has 21,840 possible combinations so you could lose 148,071 ways with this pattern. Meanwhile, 4-odd-1-even has 27,300 possible combinations so you will have 142,611 ways to lose when you use this pattern.
Either pattern may offer higher ratios than 5-even and 5-odd, but they are not yet the best choices for playing Northstar Cash. A better choice is a 2-odd-3-even pattern.
It has 54,600 ways to win and 115,311 ways to lose. Thus, the ratio of success to failure it offers is 1 to 2.
You could make 58,800 combinations with 3 odd and 2 even numbers, so there are 111,111 ways you might lose with it. The ratio is also 1 to 2.
Notice that 3-odd-2-even and 2-odd-3-even groups share a similar ratio (rounded off values). Thus, which do you think is the better pattern to use?
Keep in mind the purpose we have for analyzing basic combinatorial groups. We are looking for a pattern that has fewer ways of losing and more ways to win.
Between the 3-odd-2-even and 2-odd-3-even, the latter meets our requirements. It offers 4,200 more ways to win and 4,200 fewer ways to lose, in terms of their possible combinations.
The better choice is easier to pick when comparing 5-even ans 3-odd-2-even. As we have said earlier, the best choice in a 5/31 game is 3-odd-2-even. The worst is 5-even.
The best choice has almost 20 times more ways to win than the worst choice. It could also give you 55,979 fewer ways to lose. The best ratio is almost 18 times better than the worst ratio.
Of course, we only just tackled the odd-even composition. Lotto game numbers could also be low or high.
The Northstar Cash has the low and high sets
Low = 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
High = 17,18,19,20,21,22,23,24,25,26,27,28,29,30,31
Players could also create combinations with varying compositions of low and high numbers.
There are also 6 groups here with different low-high compositions.
The worst choice with the lowest ratio of success to failure is 5-high. Out of every 100 draws, this pattern can give only 2 opportunities to match the winning combination.
With slightly higher number of occurrences, but still a bad choice is 5-low. With 4,368 possible combinations, it could still make you lose 165,543 times.
There are two middle choices of low-high patterns in this game. A player could create combinations with 1 low and 4 high numbers. He could have 21,840 ways and lose 148,071.
If you want 5,460 more ways to win and 17,472 lesser ways to lose than 1-low-4-high, use the 4-low-1-high pattern. It also has three more occurrences in 100 draws.
The 2-low-3-high pattern offers 54,600 ways to win and 115,311 ways to lose. This pattern offers a ratio that is 16 times better than that of the worst pattern of 5-high.
If you want to be closest to winning the jackpot among all patterns in most draws, use a 3-low-2-high combination. You can play with 58,800 combinations with this pattern.
This is 20 times higher than the number of possible combinations you can create with 5-high pattern. A 3-low-2-high pattern will also give you 33 times fewer ways to lose out of 100 draws than 5-high.
RememberIt does not matter whether you have a 5-even or a 3-odd-2-even combination when it comes to probability. You have the same probability of winning from either of them. Yet, it makes a difference when you choose 3-odd-2-even over 5-high when you consider the ratio of success to failure. You have 213,656 ways to lose with the 3-odd-2-even and 318,444 ways to lose with 5-odd.
How will you then apply this knowledge to real life-lotto games?
When you decide to play the Northstar Cash and before visiting the retailer to buy tickets, already make a game plan.
Decide on the combination you want to use, especially if you will pay for 14 advanced plays.
Let us assume your choice of combination is 17-18-21-29-30.
Analyzing the odd-even composition of this combination will show this offers the best ratio. Yet, before you spend money on at least one game, do not forget its low-high composition.
It might have the best odd-even pattern, but it has the worst low-high ratio since all are high numbers. It is at this point where you could make a decision based on what the table above suggests. You may replace some numbers so that it could follow the best pattern of 3-low-2-high.
A player who knows about basic combinatorial groups knows that he can decide however he wants to play. However, logic dictates that the best way to play is to pick combinations offering the best ratio of success to failure. These combinations will help him be less wrong in most draws while giving more chances to match the winning combination.
Hence, it is helpful for players to know basic combinatorial groups that also apply to other games like Gopher 5.
The basic combinatorial groups in Gopher 5
Minnesota Lottery also offers Gopher 5. It is a 5/47 lotto draw game where you should pick 5 numbers from 1 to 47 to play a combination for $1.
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. Regardless of you choose single or multi-draw plays, always use combinations worth spending money on.
Once more, basic combinatorial analysis will help to achieve this goal. Keep reading to know how.
This game’s 1-47 balls can be divided into odd or even groups.
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
Even = 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46
Players could choose from 1,533,939 possible combinations out of these numbers. These combinations may follow the following patterns.
The question is which pattern should they choose if they want to be close as possible to the jackpot?
Out of the 1,533,939, there are 33,649 combinations containing all even numbers. While some people might prefer this pattern for reasons like uniformity, it could only take you far from the jackpot. It can make you lose in 1,500,290 ways.
You may also follow the 5-odd pattern, but this will also not be of much help in winning. With only 42,504 ways to win, you have 1,491,435 ways to fail from it.
Considerably, the middle choices are 1-odd-4-even and 4-odd-1-even. There are 212,520 combinations with 1-odd-4-even pattern. Thus, you may lose in 1,321,419 ways.
The 4-odd-1-even has more ways to win at 244,398. Yet, it still has 1,289,541 ways to lose. A good choice of pattern is 2-odd-3-even. With 488,796 possible combinations to make, your ways to fail are 1,045,143.
Ultimately, your best choice of pattern is 3-odd-2-even with 512,072 ways to win and 1,021,867 ways to fail. It has 12 times more ways to win than 5-even; twice as many ways to win than 1-odd-4-even and 4-odd-1-even.
2-odd-3-even might have a comparable ratio of success to failure to 3-odd-2-even, but the latter offers 23,276 more ways to win and fewer ways to lose.
To make the selection among these patterns easier, you simply refer to the table above. The best choice of combination in Minnesota Lottery Gopher 5 contains 3 odd, 2 even numbers.
This gives 33 opportunities to match the winning combination in 100 draws. 3-odd-2-even combinations offer 15 times more ways to win and 478,423 fewer ways to lose than the 5-even combinations.
For a complete approach in choosing combinations for Gopher 5, you must also consider their low-high composition.
To get the low and high numbers in a lottery game, just divide the number field into two. The upper half will comprise the low set, and the lower half numbers are for the high set.
In Minnesota Gopher 5, these 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
High = 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47
From these low and high numbers, you may create and play for combinations following any of the patterns shown in the table below. Your decision will ensue, but it is always best to know the options before making a decision.
Would you play…