# 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.

259 questions
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### Would you ever stop rolling the die? [duplicate]

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 ...
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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 ...
9k views

### ±1-random walk from 5 until 20 or broke [closed]

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 ...
7k views

### 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,...
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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. [duplicate]

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 ...
71 views

### Prove the limit property of a 'random' walk/gambling problem

Suppose a person plays a sequence of independent games. At the $n$th game, he plays with equally with $n$ other people, gaining $n$ units of money with probability $\frac{1}{n+1}$, losing $1$ unit of ...
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### Is this casino promotion exploitable?

The promotion is like this: Starting credit: 500 dollars Maximum bet: 500 dollars Win up to 10000 dollars and get 10000 dollars free. House edge 52.5%. Is this exploitable?
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### Casino turns 50% of your losses into “free play”, are odds in your favor?

As a limited-time promotion, if you gamble during your first week at this casino, and you suffer a net loss of money, the casino will give you half of your losses (up to a certain amount) as "free ...
479 views

### If I bet half of my money each round in a fair gamble, what's the probability…

that I can make 10 times of what I initially have? Here's the formal description. In a fair gamble, I lose or double my wager each with probability 1/2. No matter how much money I have, I always ...
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### What is the probability of rolling at least two 6's with 3 Dice and 2 Rolls?

Question: What is the probability of rolling at least two 6's, when rolling 3 dice with two rolls? (with your first roll you keep dice only if they are 6's and roll the remainder for your second roll)....
596 views

### Arbitrage betting strategy to guarantee profit

Given the following bets you can make: (1) A bet of $1$ wins $2$ if event A occurs (2) a bet of $1$ wins $2$ if event B occurs (3) a bet of $1$ wins $4$ if event C occurs. In each case, you ...
246 views

### Why Is It Rational to Bet on the Most Probable Event?!

Suppose that someone is going to bet in a game. A dice is rolled, and there are only these two options for betting: Option 1. Give 1 dollar and bet on 6. Option 2. Give 1 dollar and bet on 1, 2, 3, ...
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### Odds of Coming Out Ahead in Roulette

I have an interesting roulette problem that I initially thought was easy but now I'm second guessing my self. The problem is as follows: A friend of yours thinks that he has devised a purely ...
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### What fraction of the fund should one bet?

Say we have a gambler who makes money through sports betting. My aim is to develop a model to help our gambler maximise his winnings and minimize losses. In my model, rather than betting a fixed ...
256 views

### can this cashback casino promotion be exploited?

Cashback Casino Promotion: Deposit amount: $1000 Maximum bet:$500 Turnover: $2500 House edge: 2.5% If you lose all your money, receive$100 FAQ: *Turnover is the total amount of bets the ...
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### Need help with proof for arbitrage betting

Recently I came across this article about sports betting arbitrage. The article gives formulas for calculating arbitrage profit and individual bet amounts for a two-outcome event. But it doesn't prove ...
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### Determining the statistical significance of the performance of a gambler

Imagine someone claims they win significantly more than they lose when betting on roulette. Presuming that it were possible to have a winning system how could you calculate the statistical ...
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### Best strategy for machine that changes win chance weekly

Imagine you have a machine that you pay 1\$, push a button, and it will randomly give you 2$ (you win) or keep your money (you lose) Now, the probability for you to win changes every week at the same ...
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### A game of psychology and/or math.

Consider the following game. You and your opponent is given a uniform random number in the interval $(0,1)$. Player 1 looks at his number and can either bet or fold. If he folds, he loses nothing ...
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### Coin flip: Double or Nothing

I have an amount of chips to bet on a fair coin flipping and landing on heads. For each time in a row that it does land on heads, the amount of chips in the bet is doubled by the house, and I am able ...
Context So I'm doing some research regarding the Kelly Criterion. By considering a coin tossing game in which you have even money odds where there is a probability $p > 1/2$ of winning, a ...