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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.
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Perhaps the main reason for the confusion is the fact that they are synonymous.
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. I always refer to odds and probability as two distinct words.
So, let’s talk about the difference and why they are so essential to all lottery players like you.
The definition of probability
Probability is the measurement of the 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.
As the word probability sounds a bit too technical, some writers prefer to use a simpler word. For instance, we 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, the usage of decimals or fraction won’t be much of an issue. But 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
On 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 are 25 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 the ratio of success to failure.
From the perspective of the lottery, odds refer to the ratio of winning to losing.
The Visual Difference
Let’s say we have four marbles.
For illustrative purposes, we will focus on the red marble.
First, let’s calculate the probability:
P(red marble) = 1 / 4 or 25%
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 refer to the ratio of success to failure.
So in this particular example, the odds refer to the ratio of red marble occurring successfully to the number of times red marble will fail to occur.
Odds in favor of red marble = 1:3
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 lotto playing strategy.
Odds and Probability in the Lottery
All combinations in the lottery have an equal probability of getting drawn because there’s only one way to win the jackpot.
So does that mean 5-10-15-20-25-30 is equally likely?
Well, yes. That’s because theoretically:
P(5-10-15-20-25-30) = One way to win the jackpot / All possible combinations
Types Of Lottery Tickets
The same calculations apply to 1-2-3-4-5-6, or 2-4-6-8-10-12. The same formula applies to all combinations.
But ask yourself, are you willing to play the 1-2-3-4-5-6 combination and spend $2 on it?
You’ll probably answer no. That’s because your gut feeling indicates that such a combination is unlikely to occur in a lottery draw.
Your feeling is much stronger than your logical thinking. Because if you stand up firmly and say 1-2-3-4-5-6 possesses the same probability as any other combinations, then why do you worry?
You see, a strategy based on “gut feeling” doesn’t add up. You’ve got to explain things from a mathematical perspective.
Lite bet9ja. In this article, I would like to propose a way to explain that “gut feeling” in terms of number composition.
Combinations are not created equally.
You have to understand that a combination is a composition of numbers.
And composition matters.
The best way to explain number composition is through “combinatorial patterns.”
Let’s ask this question.
What is the probability of a 6-even-0-odd pattern occurring in a lotto 649 draw?
P(6-even-0-odd) = 0.0096251266464032
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 probability of the two patterns:
How do we understand the difference between the two combinations?
It’s simple. The key is to understand the difference between odds and probability.
There are 4,655,200 ways you can combine 3-odd-3-even combinations.
So if you play 3-odd-3-even combination, 33 in every 100 draws will put you in 1 to 4.6 million advantage rather than 1 to 14 million.
Therefore your ratio of success to failure is thus:
In comparison, 6-even combinations will give you the odds of 1 to 134,595, but be aware that this advantage will happen only once in 100 draws.
That means if you play 2-4-6-8-10-12, then expect that your chance to win the jackpot only comes around every 104 draws.
And if you play the 3-odd-3-even combination, you have the opportunity to match the winning combination every 3 draws.
Surely, this approach will not “increase your chance” of winning the jackpot. It’s all about “how not to be mathematically wrong.”
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That’s why Lotterycodex exists to help you know how not to be wrong with the power of mathematics. We’re talking about a certain mathematical advantage.
As a lotto player, I don’t think you are willing to spend money on a combination that will only go down the drain for the majority of the draws.
So while all combinations exhibit the same probability, Lotterycodex suggests that all lotto players take advantage of combinatorial patterns and get the best shot possible.
Numbers don’t lie.
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And that’s how probability theory can help improve your skill for picking better combinations.
The Lottery Strategy
Understanding the difference between odds and probability is very crucial to the lottery players.
In lotterycodex, I use probability to forecast the likely outcome of the lottery. And I do that from the context of number patterns given the law of large numbers.
So to set things straight, we cannot predict 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.
Without probability, a mathematical strategy is not possible.
I invite you to check out the free lottery guide where I list down all the bad, the worst and the best number combinations in the lottery according to combinatorics and probability theory.