Lotterycodex Mathematics Meets The Lottery

Odds, Probability, and the Lottery

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Odds and probability are two different terms.  They are not mathematically equivalent.  Knowing the difference between the two is crucial for you as a lottery player.

Perhaps the main reason for the confusion is the fact that they are synonymous. Because when you say an event has a high probability, then the odds are high as well.

In addition to that, people are used to encountering such terms being used interchangeably in conversations, internet sites, and published materials.  Ronald Wasserstein of the American Statistical Association had a good catch of that occasion in one article in The New York Times.

But let’s set one thing straight.  In Statistical science, odds and probability are two different mathematical terms.  And in all of our discussions about the lottery, I always refer to odds and probability as two distinct words.

So, let’s talk about the difference between the two and why they are so essential to all lottery players like you.

The definition of probability

Probability is the measurement of a likelihood of an event’s occurrence.  The value is expressed between 0 and 1, where 0 indicates impossibility and 1 means certainty.

So when the value is between 0 and 1, we usually expressed this in decimal terms.  And sometimes as fraction too.

As the word probability sounds a bit too technical, some writers prefer to use a simpler word.  For instance, many prefer to use the more comfortable term “percentage” to represent “chances” as an alternative to probability.

So when an event A has a 25% chances of occurring, we express the probability as follows:

P(event A) = 25% = 1/4 = 0.25

How you express probability may depend on your audience.  So if you talk to a group of highly technical people, then usage of decimals or fraction won’t be much of an issue.  But if you talk to a group of laymen, I believe, a percentage is a much friendlier approach.

The definition of odds?

Odds refers to the ratio.  There are two flavors of which we express odds:

  • Odds against = The number of ways an event does not occur against the number of ways an event does occur.
  • Odds in favor =  The number of ways an event occur against the number of ways an event does not occur

In this page, we will make use of the latter approach.

So let’s say an event A will occur 25 times out of 100 total events.

Therefore the odds in favor of A is 25 is to 75.

Odds in favor of A = 25 / 75 = 1/3 or 1:3

  • 25 refers to the numbers by which event A will occur.
  • 75 refers to the numbers by which event A will not occur.

As you can see, from a layman’s point of view, odds are a ratio between success and failure.

From the perspective of the lottery, odds refers to the ratio of winning and losing.

The difference (Illustrated)

Let’s say we have four marbles.

4 marbles = 1 red and 3 blue marbles

For illustrative purposes, we will focus on the red marble.

First, let’s calculate the probability:

P(red marble) = 1 / 4 or 25%

One red marble over 4 marbles

So when you put all those marbles in a bag, and you are told to pick one with your eyes closed, the probability that you will get the red one is 25%.

Now, let’s calculate the odds:

As I have explained above, odds refers to the ratio of success to failure.

So in this particular example, the odds refers to the ratio of red marble occurring successfully to the number of times red marble will fail to occur.

one fourth divided three fourth equals one third

Therefore:

Odds in favor of red marble = 1:3

One red marbles over 3 blue marbles

So let’s recap:

Probability of red marble = 1/4 or 25%

Odds in favor of red marble = 1/3 or 1:3

Did you see the difference?

Now, the discrepancy may be too tiny.  But when the number of events gets bigger such as in the lottery, knowing the difference takes a significant role in your playing strategy.

Odds and Probability in the Lottery

Allow me to explain odds and probability from the context of “number patterns.”

Let’s ask this question.

What is the probability of 6-odd-0-even pattern occurring in a lotto 649 draw?

P(6-odd-0-even) = 0.012664640324215

What is the probability of 3-odd-3-even number patterns occurring?

P(3-odds-3-evens) = 0.33289911709365

Here’s the data table showing the difference between odds and probability:

a data table showing the difference between odds and probability

So there. You see that probability and odds are not the same.

But here’s one thing.  Did you notice that both number patterns have the same odds in favor of winning the grand prize?

Why?  Because there is “only one way” to win a grand prize and there are 13.9 million ways to lose.

Odds in favor of winning the grand prize equals the ratio of only one way to win to 13.9 million ways to lose

So, no matter what patterns we use, the odds in favor of winning the grand prize doesn’t change.

It doesn’t matter if you use all odd numbers.

It doesn’t matter if I use a balanced mix of odd-even numbers.

We both have the same odds in favor of winning the grand prize.

But, one thing is sure.

Your probability of winning is different from that of mine.

And that’s how probability theory can help improve our chances of winning.

The Lottery Strategy

Understanding the difference between odds and probability is very crucial to the lottery players.

It’s like the difference between “accuracy” and “precision.”

In scientific works, the words accuracy and precision are not interchangeable.

In lotterycodex, I use probability theory to forecast the likely outcome of the lottery. And I do that from the context of “number patterns.”

So to set things straight, I am not predicting the “exact” combination.  No one can do that.

Some people take it from a different context.  And that’s how the confusion starts.

All in all, thanks to probability theory.  Thanks to the great mathematicians who invented all these mathematical tools for us to enjoy.  See my post How to Use Math to Win the Lottery.

Probability theory in the lottery - in a lotto 649 game, players are advised to play the 3-odds-3-even patterns because of its high probability of occurring in a draw.

No probability.  No strategy.

Now that you know the difference between the two, it’s about time to learn how to win the lottery with the use of probability theory.

Or, I invite you to check out the lottery analysis section where I list down all the bad, the worst and the best number combinations in the lottery according to probability theory.

More on odds and probability

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Lotterycodex Mathematics Meets The Lottery

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Edvin Hiltner

I get a good grasp of mathematical theory through persistent learning. I get my inspirations from the works of Gerolamo Cardano and Renato Gianella in the fields of Combinatorics and Probability theory.

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