Win the California Lottery According To Math
“Imagine what a buck could do.” California Lottery trademarked this slogan, which you might always remember. Your buck could make you win a jackpot, and here’s how math can help.
The Best Lottery Game in California Lottery
The best game to play might be different for everyone. This can be a subjective decision. However, mathematically speaking, the best game to play is one with the best odds of winning.
You could refer to the pick size, number field, and extra ball in a game.
California Lottery is small compared to other state lotteries because of the fewer games it offers. This makes comparing the games easier and deciding which offers the best odds.
The easiest game to win a jackpot has the smallest pick size, the least number of balls, and no extra ball from a different drum.
All the California Lottery draw games shown in the table above require a playable combination of 5 numbers. Fantasy 5 has the least number of balls and no extra ball. This makes Fantasy 5 the easiest game to win.
Other 44 states are offering the Powerball game. Nowadays, this game serves a great purpose among many players. In this article, the writer featured the game as something that eased the hopelessness of many California Lottery players amidst the Covid-19 pandemic.
In Powerball, the probability of winning the jackpot is 1 in 292,201,338. Powerball is a 5/69 game. See How to Win the Powerball.
Of the four games on the table, Mega Millions is the hardest to win. The probability of winning the jackpot (5 numbers + Mega Ball) is 1 in 302,575,350 attempts.
California Lottery draw games differ because of different pick sizes and number fields. One must understand these factors to analyze the odds and make better decisions, especially when picking numbers to play. See How to Win the Lottery According to Math.
Play the California Lottery Using the Right Tool
Lotteries are truly random. People can only guess which numbers will get drawn or what combinations will win.
Yet, this random nature over time becomes mathematically deterministic based on the law of large numbers.
This image is a computer-simulated representation of the randomness of the lottery. The gray and white dots are combinations that randomly get drawn in lottery games.
Over time, some dots will appear visibly darker than others. This image of streaks and clusters gives players ideas about being less wrong when playing lottery games.
The combination of randomness and deterministic nature leads to a probabilistic characteristic. This enables the game to behave according to the dictate of probability theory.
Don’t use statistics. Use combinatorics and probability theory
Unfortunately, many lotto players use statistics as their main strategy. It involves tracking past winning results to pinpoint hot and cold numbers.
However, these hot and cold numbers are only obvious in a few draws. With a significant increase in draws, all numbers will even out. Statistical methods, therefore, will become useless.
There are no hot and cold numbers. Therefore, statistical analysis will not work in the lottery. Since a lottery game is finite, the only tool that works is a combination of combinatorics and probability theory.
Let me give you a scenario that shows the difference between statistics and probability.
During a party game, a sealed box contains 100 blue, yellow, purple, and red balls. Each of these colors represents an amount of prize or a consequence.
Blue for $100, yellow is $50, purple is for cleaning after the party, and red is a discount coupon.
If the game host did not say the exact number of blue, yellow, purple, and red balls, you could rely on statistical sampling to infer the composition of the box.
If, however, the host reveals that inside the box are 20 blue balls, 20 yellow balls, 30 purple balls, and 30 red balls, then any questions you ask are probability problems to solve rather than statistical ones. In short, you don’t need statistical sampling because your knowledge of the composition of the box is adequate. You could use probability theory to determine how likely it would be to pick the grand prize of $100.
Now, a lottery game is finite. For example, Fantasy 5 requires you to pick five numbers from 1–39 balls. Those 39 balls consist of 20 odd and 19 even numbers. You know the composition of the game; therefore, any questions you ask are probability problems to solve.
Did you see the difference between statistics and probability?
In the lottery, we can ask questions such as the probability of the winning numbers consisting of two odd and three even numbers, all of which are low.
Understanding the S/F Ratio
In the California Lottery, a player should remember two crucial concepts: probability and odds.
Probability and odds are not mathematically equivalent. They are two different words with different equations.
Probability determines the likelihood of an event by dividing the number of times a favorable event will occur by all the possible outcomes.
The formula for probability is:
Given the finite structure of a lottery game, you have a way of knowing how many possible combinations there are. For example, in Fantasy 5, there are 575,757 possible combinations. SuperLotto Plus has 1,533,939 possible combinations.
Regardless of your lottery game, there is only one way to win a jackpot. If you play Fantasy 5, you have a 1 in 575,757 probability of winning. In SuperLotto Plus, you have a 1 in 41,416,353 winning probability.
However, playing a lottery game requires a strategy to succeed. For this reason, you must also consider the concept of odds.
Odds compare the number of ways an event will occur to the number of ways it will not. Therefore, the odds are the ratio of success to failure.
We express this ratio as:
With odds, you may consider combinatorial compositions and choose the one that will give you the best shot possible.
And when we talk about combinatorial compositions, we deal with how we combine numbers.
Let’s take a look at the difference between the two combinatorial compositions below:
For example, you are playing in the Fantasy 5 game of the California Lottery. You marked any number on the playslip and ended up with 8–10–20–24–38.
This combination could be better if we analyze it according to the success-to-failure ratio.
First, a random lotto game distributes the probability across the number field. So it’s very likely that a winning combination will be composed of odd and even numbers. You rarely get a winning combination with all even numbers, though sometimes it happens. Again it’s very rare.
Mathematically speaking, a five-even combination gives you one favorable shot to match the winning combination out of 50 attempts.
Of course, the underlying probability of lotteries is something that you cannot manipulate. Yet, you can give yourself a better shot using the ratio of success to failure. You can make the most of your time and money buying lotto tickets by choosing combinations with more favorable shots.
Using Combinatorial Analysis in California Lottery
When understanding how a lotto game works, you must know the difference between a number and a combination.
A number is one ball in the number field. A combination is the pick size you must complete to play a lotto game. You cannot win a lottery with just one number.
For example, to win a Fantasy 5, you must combine five numbers. For SuperLotto Plus, a combination comprises five numbers from 1 to 47. Therefore, when you unintentionally mark four numbers on the play slip, the machine will not accept it because it is not considered a combination.
All the balls in the drum have the same shape, size, texture, and weight. This ensures that no biases will affect the drawing. All balls have an equal opportunity of getting picked from the drum.
Individual numbers have no special meaning unless combined to form a playable combination. Each combination will give you one way of winning a lotto jackpot. To increase your probability of winning, you need to buy more tickets with different combinations.
However, you should not just choose any combination. Instead, it would be best if you played for a combination with the best shots of winning the jackpot.
How do you do this? First, you pay attention to the combination’s composition.
The numbers you select give the combination a certain composition. We describe this composition as combinatorial templates. Some templates have a better ratio of success to failure than others, so picking one that gives the best shot at winning is essential.
Players may take advantage of this inequality in ratio. For example, a smart player would always settle for a combinatorial group whose ratio is better than the others. This way, he would be wrong less but be close to winning the jackpot most times he plays.
A note on combinatorial analysis: The numbers on the balls are “symbols,” but they can be anything like “animals,” “fruits,” or pretty much anything. Using odd, even, low, and high numbers is not the strategy. Instead, we use those sets as a model for mathematical calculation. In combinatorial mathematics, you can group anything. If you know combinatorial mathematics, you know how to optimize and make better decisions based on a given circumstance.
Lotterycodex is based on this combinatorial principle with the application of probability theory. It’s all about separating the dominant groups from the occasional and rare ones.
The lottery is one example where combinatorial mathematics may serve a meaningful purpose.
Suppose you avidly use the number sum strategy in lotteries and choose 4–18–26–34–36 for your Fantasy 5 ticket. The number sum method states that a combination is good as long as the sum of the numbers is between 75 and 125. The basis is that over 70% of winning lottery combinations for such a game have sums within this range.
The sum of 4–18–26–34–36 is 118, so it falls within 75–125. However, this is one of the least favorable combinations in Fantasy 5 because it has a very low S/F ratio.
Again, a 5-even winning combination rarely happens because a random lotto game distributes probability across the number field.
Therefore, the ratio is a better tool to help pick better numbers.
Lotterycodex — Advanced Combinatorial Analysis
When there is confusion, there will be mistakes.
Take 1–2–3–4–5 as an example. It follows the 3-odd-2-even composition, which offers the best ratio.
However, 1–2–3–4–5 flunks on the low-high department because it has all five low numbers.
The example above reinforces the importance of implementing a better combinatorial analysis.
We should combine odd-even and low-high numbers to avoid contradicting conclusions in one combinatorial analysis. We call this the Lotterycodex method.
Let’s see how Lotterycodex works for the two California Lottery games we have tackled above.
We divide the number field into four sets: low-odd, low-even, high-odd, and high-even.
Achieving balance not only for odd-even but also for low-high groups is important in a combination. This is the objective of the Lotterycodex combinatorial design.
With the right application of probability and combinatorial mathematics, you will know exactly which template to use and avoid.
Here’s an incomplete list of the Lotterycodex templates for a 5/39 game and their corresponding expected occurrences according to probability calculation.
For Fantasy 5, there are 56 Lotterycodex templates. The dominant templates are templates #1, #2, and #3.
Let’s proceed to the SuperLotto Plus 5/47 game and its corresponding Lotterycodex analysis.
The above sets will produce 56 Lotterycodex templates. The image below shows an incomplete list of expected occurrences according to probability calculation.
Lotterycodex templates serve as a useful guide that directs you toward the best course of action for the game. See The Winning Lottery Formula Based on Combinatorics and Probability Theory.
The Law of Large Numbers in California Lottery
Tossing a coin about ten times, you could see that one side will show more than the other. Toss the coin a thousand times. You can observe that the number of times the head showed is almost the same as the tail.
In the lottery, only a few combinatorial groups will dominate the game as the number of draws increases.
You have to pay attention to these dominant combinatorial groups.
Let us see how this works in the California Lottery Fantasy 5.
Template #41
= 0.0036473721 x 2000
= Occurs about seven times in 2000 draws
In the entirety of 2000 draws, template #41 can happen approximately seven times. It is almost like waiting for an eternity. If there are 365 draws per year in Fantasy 5, it might take five years for you to get seven favorable shots.
Template #17
= 0.0208421261 x 2000
= Occurs about 42 times in 2000 draws.
Can you wait for 2000 draws to get 42 favorable shots?
Template #1
= 0.0703421756 x 2000
= Occurs about 141 times in 2000 draws
Template #1 has the highest expected occurrence. This is the template that will ultimately dominate the game as draws continue to take place.
Here are some calculations for SuperLotto Plus.
Template #47
= 0.0035496848 x 5000
= Occurs about 18 times in 5000 draws
There are 52 weeks a year and only two weekly draws for SuperLotto Plus. Thus, there will be only 104 SuperLotto Plus draws in a year. This means you get only 18 favorable shots in 48 years.
Let us see what awaits you with template #1.
Template #1
= 0.0681539488x 5000
= Occurs about 341 times in 5000 draws
As the calculation shows, you will choose template #1 to get the best shot possible.
If you need help getting these templates, use the Lotterycodex calculator.
Quick Pick and Superstitions in California Lottery
There are many superstitious beliefs influencing players when taking part in lottery games. This report shows some people even buy their California Lottery tickets from a store they believe is brimming with luck.
Some people also bring their lucky pennies with them when they buy tickets. But, of course, superstitions are part of some people’s culture that we must respect.
Still, keep these beliefs from prevailing over your logic and common sense. Then, after knowing the mathematical facts and concepts you have learned from this discussion, you will use them wisely.
A mathematical strategy ensures you spend your money wisely in a lottery or any other entertainment game.
However, many players are unthinkingly picking numbers. They suppose that if it is their luck to win, they will win regardless of the combination.
Yet, it is time you take control of your luck and your winning odds.
Lotterycodex combinatorial analysis can point you to exactly where to make the changes. This is better than just picking numbers randomly.
You must prioritize combinatorics and probability over superstitions as your strategy.
Avoid unthinkingly choosing numbers that might give you the least S/F ratio. One possibility to avoid is marking the quick pick on your play slip.
Hearing success stories from people who won with the quick-pick method is inspiring. However, this way of playing is like playing without a strategy. Instead, you allow the machine to pick your numbers at random.
Every time you buy a lotto ticket, consider the ratio. If you are not fond of mathematics, you can use a Lotterycodex calculator.
Coincidences and Unusual Combinations in California Lottery
Fantasy 5 has 575,757 possible combinations, while SuperLotto Plus has 1,533,939 without the bonus number. Analyzing each of these combinations will take a lot of effort and time.
As you know, just a few of these combinations will bring you close to the jackpot. Therefore, you must be very selective to avoid losing more.
Take a look at these unusual and non-random combinations below:
Non-random combinations exist in a lotto game. The classic example is 1–2–3–4–5. It contains consecutive numbers from 1 to 5. Therefore, it has the least favorable S/F ratio.
Players who use these non-random combinations may want to quickly remember which numbers to look at when they check whether they won. Whatever the reason, all lotto players must realize that these non-random patterns are not impossible to occur but improbable.
There are also other variations of this consecutive number pattern. For example, look at 3–6–9–12–15. This combination has a consecutive pattern, but one with an interval of 3 between the numbers. You could call it skip-counting.
Another variation of consecutive patterns is apparent in 1–2–3–11–12. It contains two sets of consecutive numbers from two number groups.
There are combinations whose patterns can be unnoticeable. For example, the 2–4–7–11–16 combination. The intervals between each number are 2, 3, 4, and 5.
Although not impossible, these non-random combinations are too improbable to occur, and the law of truly large numbers can explain this.
This law of truly large numbers states that coincidences, rare incidents, and strange events happen when there are significantly large amounts of opportunities. You need 100,000 draws in the lottery to see some unusual winning combinations.
Avoid these non-random combinations at all times.
Be Sensible When You Play the California Lottery
Playing California Lottery draw games should be for fun.
The state lottery says that you lose more often than you win. This is true because the lottery always has a negative expected value. So, out of the number of times you play, you would have more losses than winnings.
Therefore, you must have fun when you play. It could be fun from the excitement of playing for combinations that take you very close to winning the jackpot.
Then, there is the ultimate fun when you finally become the jackpot winner. Either way, playing with your best shot is the best course of action to take. Consider using Lotterycodex templates.
Playing could even be more fun when you play with other people. The California Lottery suggests that you play socially rather than alone. For example, you may start a lottery syndicate with relatives and friends.
A syndicate aims to pool members’ money to buy tickets. Then, if any of the tickets they bought wins, members share the prize.
However, spending the pooled money on worthwhile combinations is important, whether solo or a syndicate. The goal is to spend money wisely on combinations that can take you closer to the jackpot.
People can only predict the combination that will win next in a lottery game. After all, it is random, and its probability is unchangeable. Therefore, be aware if anyone says he can tell you the next winning numbers.
The key strategy is applying the concepts of combinatorics and probability theory. Yet, this does not mean you will know exactly which combinations will win next. There is no promise of an instant win.
If you have time, read this document to see that changing your standpoint as a player is also beneficial.
Other Games To Play In The California Lottery
There are other draw games from the California Lottery. These are Daily 3, Daily 4, Daily Derby, and Hot Spot.
The instant games called Scratchers are scratch cards you can buy from retailers.
Refrain from quickly throwing away tickets that did not win. They might still make you win in the 2nd Chance draws.
Whatever game you play, always play responsibly. Play only according to the budget you have set. Never chase your losses.
