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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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) far less likely to be the lucky number than…
arax
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"Math Lotto" Tickets - finding the minimum winning set

"Math lotto" is played as follows: a player marks six squares on a 6x6 square. Then six "losing squares" are drawn. A player wins if none of the losing squares are marked on his lottery ticket. 1)Prove that one can complete nine lottery tickets…
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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 lottery definition, you pick 6 numbers from a pool…
user2400
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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 course, it would be really nice if the computer…
user425888
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Probability of not guessing any number in lotto drawing

A game consists of picking 6 different numbers from a set of 36. Each player completes one or more tickets, each with 6 different numbers. After the draw is made, the winner(s) are any players who do not have these 6 numbers on their ticket. Show…
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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 to this problem) in an order. Four numbers are…
Q the Platypus
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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 (1/59*1/58*1/57*1/56*1/55*1/54). The reason was…
Droi Rea
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Odds of winning lottery with multiple unique tickets

If I buy one lottery ticket with odds of $14M$ to one if I buy another ticket with different numbers does this slash the odds to $7M$ to one? if so it follows that if I double my tickets again to $4$ Tickets it will half again to $3.5M$ to one? So…
Pad Regan
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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 $22, 23$ -a pair of numbers whose difference $23-22…
caasdads
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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: ball drawn is not put back in the lot) from the lot…
Paul Karam
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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. Person A holds 2 tickets, person B holds 3…
AndraSol
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Lottery 6/49 guess at least one number

What is the probability to guess at least 1 number in Lottery 6 of 49? I tried to use binomial coefficient $\binom{6}{1}\binom{43}{5}$ divide $\binom{49}{6}$ but this gives me probability of one match number. How to tackle the problem? Thank you in…
linok
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Fleecing the Raffle

There is an ICPC 2016 contest question about cheating in a raffle. It gives n names in the raffle box and p prizes, and you give back the optimal probability of winning a prize in the raffle by possibly cheating. The rules of cheating are that you…
sshine
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Pigeon Hole Principle - Minimum customers needed such that at least one is a winner

I was reading about pigeon-hole principle from this paper. If n items are put into m pigeonholes with n > m ( m,n ∈ N ∗ ), then at least one pigeonhole must contain more than one item. One of the applications of the principle is stated as: Pitter…
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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 "additional number". Participants purchase tickets…
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