Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [gambling]

For questions about the mathematics behind gambling, such as the expected value of a game or the efficiency of a gambling strategy.

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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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Would you ever stop rolling the die?

You have a six-sided die. You keep a cumulative total of your dice rolls. (E.g. if you roll a 3, then a 5, then a 2, your cumulative total is 10.) If your cumulative total is ever equal to a perfect square, then you lose, and you go home with…
Newb
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±1-random walk from 5 until 20 or broke

You play a game where a fair coin is flipped. You win 1 if it shows heads and lose 1 if it shows tails. You start with 5 and decide to play until you either have 20 or go broke. What is the probability that you will go broke?
koon93
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When to stop rolling a die in a game where 6 loses everything

You play a game using a standard six-sided die. You start with 0 points. Before every roll, you decide whether you want to continue the game or end it and keep your points. After each roll, if you rolled 6, then you lose everything and the game…
Kulawy Krul
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Kelly criterion with more than two outcomes

I want to calculate the Kelly bet for an event with more than two possible outcomes. Suppose the following game: A jar contains $10$ jelly beans. There are $7$ black jelly beans, $2$ blue jelly beans, and $1$ red jelly bean. The player wagers $x$…
Vilhelm Gray
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Gambler's fallacy and the Law of large numbers

Can someone explain me, how the Law of large numbers and the Gambler's Fallacy do not contradict. The Gambler's Fallacy says, that there is no memory in randomness and any sequence of events has the same probability as any other sequence. However,…
clamp
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Asymmetric ruin probability

I have $50$ dollars and I’m gambling on a series of coin flips. For each head I win $2$ dollars and for each tail I lose $1$ dollar. What’s the probability that I will run out of money? Hint: Suppose we have $x$ dollars, then the probability of ruin…
henry21
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3 person bet based on the perceived likelihoods of an outcome

Suppose 3 friends want to bet \$100 on whether candidate John Doe will win the next election. They state their perceived likelihood that the event will occur: Alice believes John Doe will win with probability $35\%$ Bob believes John Doe will win…
Rafael Magalhães
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100-sided die probability

The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the expected value of the game? There is no limit on number…
demyx999
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Does variance do any good to gambling game makers?

People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers? In another word, what is a pratical gambling game that involving some distributions that is relating to variance other than…
Victor
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A winning wager that loses over time

This problem was posted in Scientific American (vol. 321.5, Nov 2019, p. 73), and it was troubling. The game: We flip a fair coin. If we flip heads we gain 20% of our bet If we flip tails we lose 17% of our bet. Starting bankroll:…
Tom Boshoff
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A plan to defeat a betting game where the odds of winning are 50/50. Help me understand why it's flawed.

My friend has this plan where he implies that it's impossible to lose, as long as the odds of winning are 50/50 on each bet. His idea is that basically you keep doubling your bet until you win and then start over again. So for example, you bet 1…
JaTochNietDan
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Can you make money on coin tosses when the odds are against you?

The strategy Given an initial investment $n$ dollars and a "bet buffer" $b$. Calculate the bet size $x=\left\lfloor\frac{n}{2^b-1}\right\rfloor$ dollars. Wager $x$ dollars on random variable $C$ that $C=1$ with $P\left\{C=0\right\}=p>.5$ and…
geofflittle
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Kelly Criterion for simultaneous independent bets

I'm trying to obtain a more generic version of the Kelly criterion for when we have simultaneous independent events to bet on, I'm going to focus on the case where we just have 2 different events. In the case where we have just one event the…
jpceia
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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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