Lottery Probabilities: Is Playing Yesterday's Winning Set a Wise Choice?

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Discussion Overview

The discussion centers on the probabilities associated with playing the same winning lottery numbers from a previous draw. Participants explore the implications of independence in lottery draws and the perceived likelihood of repeating winning combinations in a game where numbers are selected from a defined range.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates the probability of winning by selecting the same numbers as yesterday, stating it is equal to the probability of any other combination due to the independence of draws.
  • Another participant emphasizes that while the odds of repeating the same winning numbers are low, the choice of numbers remains independent, suggesting that any specific combination has the same likelihood of winning.
  • A further contribution highlights that the odds of seeing the same combination twice in a row are very small, but questions the odds of seeing different combinations on consecutive days, suggesting they are equally low.
  • Some participants discuss the mathematical foundation of randomness in lottery draws, noting that each outcome is equally likely, but express uncertainty about the formal definition of randomness.
  • Clarifications are made regarding the number of possible outcomes and the specific probability of repeats, with one participant stating that there is only one way for a specific winning combination to repeat.
  • A link to an external article is provided, which discusses a case of repeated lottery numbers, adding context to the discussion.
  • One post diverges from the main topic, providing historical context about lotteries and their regulation, which does not directly address the probability question.

Areas of Agreement / Disagreement

Participants generally agree on the independence of lottery draws and the equal probability of any combination winning. However, there is disagreement regarding the implications of this independence and the perceived likelihood of repeating winning numbers versus selecting different combinations.

Contextual Notes

Some participants express uncertainty about the definitions and mathematical principles involved in randomness and probability, indicating that the discussion may rely on varying interpretations of these concepts.

dsputnik
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Hi,

I've had a question bugging me for a while and I've finally decided to seek an answer.

Suppose you have a lottery game where one selects 6 numbers from 1 through 53. If you select the 6 winning numbers you win, regardless of the order. So our probability of winning is 53 C 6 = 53!/6!(53-6)!, or 1/22,957,480.

Now suppose that some set T was the winning combination yesterday and you are considering playing the same set today. Intuitively, it would be difficult to imagine the same winning numbers appearing twice in a row (historically it hasn't happened in any lottery game with similar probabilities), yet, being that they are independent trials, the probability is equal.

Is one equally as likely to win the lottery by playing yesterdays winning numbers than by choosing some other combination? It would seem to me that the probability of seeing the same combination win twice in a row is much less than to have different winning combinations.

Please enlighten me.

D Sputnik
 
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Is one equally as likely to win the lottery by playing yesterdays winning numbers than by choosing some other combination?
Yes
It would seem to me that the probability of seeing the same combination win twice in a row is much less than to have different winning combinations.
True, because the probability of getting the same combination twice in a row is the square of getting the combination once. However once a combination comes up, the next drawing is independent, so getting that combination again is as likely as any other combination.
 
The odds are obviously far greater that today's numbers will not be the same as yesterday's numbers rather than getting the same numbers again. However, that's not your choice. You have to specify which of the different sets of numbers to pick, and there happen to be a LOT of those.

Suppose yesterday's numbers were 1,2,3,4,5,6. The odds of seeing 1,2,3,4,5,6 twice in a row is very small (1/22,957,480 squared to be precise), but what are the odds of seeing 1,2,3,4,5,6 one day, and then the next day seeing 2,12,22,32,42,52? Just as low.
 
Just to formalize what Mathman and Shredder said (to review my prob. knowledge,

given that both answers were complete.)

If the 5 numbers are selected at random, then, as you said, there are

22,957,480 tickets, only one of which is the winning one. By def. of

randomness ( I think the actual definition of randomness in the discrete

case is that each outcome in the process is equally likely, but I am not

100% on that.) . Then each of the 22957480 outcomes today can be paired up

with 22957480 tomorrow, for a total of (22957480)^2 possible outcomes in two

days. And out of those (22957480)^2 outcomes ( of the form (5-ple#1,5-ple#2))

, only one will be a repeat.

But, as Shreder said, the event : getting different combinations in 2 days

has high probability.
 
No. There are 22957480 possibilities of repeats out of (22957480)^2 outcomes.
 
"No. There are 22957480 possibilities of repeats out of (22957480)^2 outcomes. "

I meant for a specific value, e.g., for the winning combination, there is only

one way in which the same winning numbers --or any other _fixed_ numbers--

can come out twice consecutively.

And the probability of a repeat is --assuming random selection -- 1 in 22957480.
 
Hello
A lottery is a form of gambling which involves the drawing of lots for a prize.Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments. At the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in many countries, including the U.S.A. and most of Europe. This remained so until after World War II. In the 1960s casinos and lotteries began to appear throughout the world as a means to raise revenue in addition to taxes.



http://lotterytexts.com/
 
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