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Questions tagged [lotteries]

Questions involving gaming games based on drawn numbers: Divisions, Systems and Dividends. Consider also using (combinatorics), (probability) or (betting) where appropriate.

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Why exactly “(1-p) math” gives wrong probability of next lottery draw if something special happened many times in a row (10 even => play odd)?

Let's take not odds/even example, but a more complicated one, but same logic can be applied to both. Given some lottery, say $5$ out of $36$ lottery ($5$ unique numbers out of pool of $36$ numbers ...
4
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1answer
38 views

Math probability that “5-out-of-36” lottery draw has at least one pair of numbers with difference = 1.

Given a $5$ out of $36$ lottery ($5$ unique numbers out of pool of $36$ numbers ranging $[1,2,…,36]$). How to calculate probability that a draw has at least one pair of consecutive numbers (like ...
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1answer
25 views

Probability of not guessing any number in lotto drawing 7/34

I'm trying to calculate the probability of not guessing any numbers in a 7/34 lotto drawing. My approach was to multiply the probabilities of guessing a single number 7 times in a row while removing 1 ...
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0answers
37 views

Mega millions: how likely is it to be this close?

Someone sent this around at the office, as a unique show of how unlucky one can be: First, spit-balling in my head, I replied "oh, that's not that unlikely, there must be hundreds or thousands of ...
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2answers
430 views

Calculate lottery's second prize using combination - lottery probability question.

Assume a lottery game of the following rules: Picking your numbers: Pick a total of 6 different numbers from the lot containing 42 numbers (1 to 42). Draw: Draw 7 balls, with no repetition(i.e: ...
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0answers
47 views

Probability of winning the lottery: how are those two interpretations different?

Winning this specific lottery consists of choosing 5 numbers from a list of 50 numbers $\{1,2,3,...,50\}$ and then choosing 2 numbers from a list of 9 $\{1,2,...,9\}$. You win if all your numbers are ...
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2answers
161 views

Boxed lottery tickets, rencontres numbers and number of degree-$n$ permutations of order exactly $d$

This is a question that I encountered at work that I am trying to get a deeper understanding of. We sell tickets in a lottery where you guess $4$ numbers out of range of $36$ (the range is irrelevant ...
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2answers
34 views

Lottery ticket sales and ‘coverage’

Take a small 6/40 lottery with 3,838,380 possible combinations. Prior to the draw, the operator sells only 3 million randomly drawn tickets (for simplicity’s sake, I’m completely ignoring the fact ...
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1answer
35 views

Probability of winning with multiple tickets in multiple draws

Unfortunately, after hours of searching I was unable to find an answer to the following scenario: Let's assume I play five unique combinations in a weekly 6/49 lottery, where the chance of matching ...
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1answer
578 views

UK Lottery Odds Calculation Error

I found the probability topic in stats and mechanics to be very interesting, and I attempted to try using it to calculate the odds of winning the UK National Lottery, but failed. My calculation was (1/...
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1answer
37 views

Are the two item selection turn lottery methods identical?

Owners of a land plot build a building together, in which there are many apartments. Every owner has the right to own a certain number of apartments. The sum of the rights of all owners is equal to ...
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1answer
28 views

Calculating permutations when an event can end the game

There are 50 balls. 40 Black and 10 White. You draw balls without replacement and win if you draw all 10 white balls before drawing 4 black balls in a row. How do I calculate the probability of ...
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2answers
56 views

Probability: independant lottery ticket

I have one chance over 1,000,000 to win a lottery. If I buy the same number of ticket with different combination on each, I have 100% chance of winning. What if my ticket number are randomly choosen ? ...
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3answers
76 views

How many powerball tickets will guarantee a 3/5 match?

Trying it figure this out, but looks like the obvious answer might not be right. According to the probabilities there is a 1 in 579.76 chance of matching 3 of 5 numbers in a Powerball ticket. So how ...
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3answers
32 views

What is best strategy in a slightly biased lottery with known differences of frequency of some balls?

I know for sure which numbers appear more often in a 5 out of 36 lottery (5 unique numbers out of pool of 36 numbers ranging [1,2,…,36]). I know that 4 balls appear more often than the average, 11 ...
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2answers
13 views

Lottery - better try to hit numbers-group that appears often, than hope for a “one-in-thousand-years” combination? [duplicate]

Please correct my reasoning: There is a 5 out of 36 lottery (5 unique numbers out of pool of 36 numbers ranging [1,2,…,36]). Strategy 1: just play any random combination. Like 12345, or better 11111....
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0answers
20 views

Play 100 tickets in one lottery draw or 100 plays/draws with 1 ticket - same chances to win?

5/49 lottery is when 5 different numbers are selected (without replacement) out of 49 possible numbers in range 1..49. Total number of possible combinations is C(49, 5). (1) If I make a stake once ...
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1answer
19 views

Better play 100 tickets in one lottery draw or 100 plays/draws with 1 ticket?

I heard many people say that it is better to play 100 tickets in one draw of 5/49 lottery, rather than 100 plays/draws with 1 ticket. Is there any scientific basis for this, or actually there is no ...
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1answer
116 views

What probability distribution is best to describe lotteries?

What kind of probability distribution is best suited to describe lotteries? Wikipedia provides extensive list of probability distributions (another list of them - see at bottom). But reading ...
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1answer
36 views

powerball draw question

This seems intuitive but would like a second opinion. Powerball with 69 numbers. Need to choose 5 correct (order does not matter). ...
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0answers
19 views

What is the probability of pattern “number appears-none-appears” to happen in a lottery?

In a lottery 5 out of 36 (5 numbers drawn from [1..36] without replacement) what is the probability of same number (say, 13 - but logic applies to any number) to appear in this pattern: start of game:...
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1answer
41 views

Probability for a lottery [closed]

What's probability to choose the 6 correct numbers in a lottery (made up of 42 numbers)? I do know how to do it with combinatorics $${42 \choose 6} = (42·41·40·39·38·37)\div ( 1·2·3·4·5·6) = ...
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1answer
45 views

Defining a probability of success in a lottery

Suppose that I have the following lottery: $p(x)W-(1-p(x))L$ Where $p$ is the probability of winning W and x is a variable that influences the probability of success. The expected utility for the ...
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2answers
54 views

Probability of getting 7 numbers smaller or equal to 59, from a draw of 20 numbers out of 80

What is the Probability of getting $7$ numbers smaller or equal to $59$, from a draw of $20$ numbers out of $80$? I can work out the probability of getting them in the 1st $7$ numbers $$59/80 * 58/...
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2answers
74 views

Maximum Likelihood Estimator of number of lottery tickets

A lottery has $N$ tickets numbered $1, 2, \dots, N$ with $N$ unknown. A random sampling of 5 winning tickets is numbered, say, $\{a, b, c, d, e\}\in[1, N]$. The question I am trying to solve gives $...
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3answers
147 views

Probability of binomial distribution with dependent events

Problem: I played lottery and I bought $5000$ numbers of $100.000$. In the raffle, there are $2000$ prizes (or $2000$ tests), in that $2000$ prizes, $5$ are high prizes. Question: What's my ...
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1answer
44 views

Probability of finding a random number in a random interval vs. random samples

Suppose there is a lottery where a random natural number between 1 and n = 1000 is drawn in secret. They sell two different tickets to customers: A ticket with k = 10 random numbers on it (not sorted,...
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1answer
91 views

Which route is better for a Neutral-risk person?

There are two routes, 1 and 2. It is known that route 1 takes 60 minutes and route 2 takes 41 minutes. If there is problems in the traffic: Route 1 will increase to 70 minutes; Route 2 will ...
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1answer
66 views

Euromillions - Does covering all the balls across a number of tickets increase chances of a (small or large) win?

So in the UK the Euromillions lottery tonight will be £167M. For those outside Europe, a Euromillions ticket consists of 5 numbers (from 1-50) and 2 lucky stars (from 1-12). Jackpot is won if the ...
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0answers
43 views

Long term lottery probability with multiple-number tip

There is a lottery where is drawn six numbers out of 49 with two draws per day. In this lottery is possible to select in one ticket more than six numbers - i.e. when you select 8 numbers then your ...
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2answers
92 views

Probability of two people winning a prize, according to the number of tickets each person has

Since I find it hard to abstractly describe what I want to understand, I came up with the following example. Suppose that 6 people hold each a given number of a very special type of lottery tickets. ...
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1answer
652 views

how do you calculate gold lotto

For my assignment I am trying to calculate the probabilities of Australian Saturday gold lotto (45 balls 6 winning 2 supplementary). I need help finding the division calculations to find the division ...
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1answer
132 views

Consecutive subset in lottery

What is the probability that in 7 drawn numbers in lottery (out of 39) there are 4 consecutives? I have been chasing my tail here. So, we have $39-3=36$ sequences of 4 consecutive numbers. If we ...
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1answer
69 views

lotto advice debunking [closed]

In lotto game 7/39, combination of 7 numbers are drawn at random. Should we trust 'lotto experts' and their lotto advice? For example, should we pick 4 of the higher and 3 out of the lower numbers (...
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3answers
84 views

Probability that the second and third card extracted are both aces?

I would like to know if the following reasoning is correct: the situation is the extraction without replacement of 3 cards out of 40, where there are 4 aces. I would say the cardinality of the sample ...
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2answers
112 views

Probability that at least two equal numbers are extracted

Consider an urn containing 90 balls numbered from 1 to 90, plus 3 balls attached with 3 distinct (known) numbers still from 1 to 90, say 1,2,3. I'm trying to find the probability that at least two ...
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1answer
318 views

What is the expected value of a lottery ticket if one could wait finitely many draws to try to get the highest prize?

Normally, lottery tickets are valid for only one drawing. If one wants to play the same numbers for multiple draws, the cost of the ticket is multiplied accordingly. What if one could hold on to it ...
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359 views

How did Mohan Srivastava crack Ontario scratchcards?

Wired ran a 2011 article about how a statistician, Mohan Srivastava, cracked Ontario scratchcards such as this one. First, he thought about the program that produced the numbers on the cards. 'Of ...
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3answers
519 views

Lottery probability, picking 10 numbers to get 6 winning numbers

What are your chances of winning in the following scenario? Consider a lottery game with 49 numbers and 6 are chosen as the winning numbers. You're allowed to select 10. What is the probability that ...
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2answers
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Predicting lottery numbers

I am working on a model and formula for predicting lotto numbers. Some success. Looking at recent ozlotto and sat lotto draws (pics). There were a total of 19 numbers drawn (2x sat (6 numbers)) and 1x ...
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1answer
132 views

In a country's State Lottery, five balls are drawn (without replacement) from a drum filled with balls numbered from 1 to 45.

When buying a ticket an entrant chooses five numbers between 1 and 45 inclusive. To win a prize in a lottery, at least three of the balls drawn must match numbers on one's ticket. To win the jackpot, ...
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1answer
912 views

Combinations and the EuroMillions lottery even when another Lucky Star is added.

Firstly, my level of mathematics understanding is only at O level, or GCSE level if you like. However, my education level is just under degree level, having a HND in Computer Science. Someone is ...
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1answer
264 views

On the EuroMillions lottery

To play the EuroMillions lottery, one selects five main numbers from $1$ to $50$ and two Lucky Stars numbered from $1$ to $11$. I would like to know what the number of possibilities is given the ...
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1answer
155 views

Determine if this lottery system is profitable

I have a problem where I'm supposed to determine if a lottery system is profitable. I solved the problem and found it to be profitable, but I am not 100% sure about all of my calculations. Below is ...
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1answer
238 views

Probability of winning the jackpot at a certain state's lottery [closed]

A certain state's lottery consists of choosing $6$ numbers at random without replacement from the set $\{1,2,3,\ldots,40\}$. What is the probability that someone wins the jackpot? I just want to ...
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2answers
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What is the probability that the number “3” gets picked up at EuroMillions?

EuroMillions is a game where you have to tick 5 numbers in a grid of 50 numbers (from 1 to 50) (there is also a stars system, but let's omit it). Then, the draw: 50 balls numbered from 1 to 50 in box, ...
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19answers
20k views

Should I put number combinations like 1111111 onto my lottery ticket?

Suppose the winning combination consists of $7$ digits, each digit randomly ranging from $0$ to $9$. So the probability of $1111111$, $3141592$ and $8174249$ are the same. But $1111111$ seems (to me) ...
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1answer
470 views

Estimating the number of tickets bought in a lottery

A national lottery has the format where $7$ numbers are chosen from $45$ without replacement. The first $6$ numbers chosen constitute the "winning numbers", while the last number chosen is the "...
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7answers
43k views

Is it better to play $\$1$ on $10$ lottery draws or $\$10$ on one lottery draw?

If I had 10 dollars to spend on a 1 dollar lottery draw, would I have more chance of winning if I spent all 10 dollars in one draw or bought 1 dollar tickets for 10 separate draws? Edit: in terms of ...