# 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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### Random Walk with a reflecting barrier

I've got stuck in the below question as I do not know how to handle the reflecting barrier. We have a random walk with N+1 states from 0 to N. State N is an absorbing state and state 0 is a reflecting ...
1 vote
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### How to calculate the average number of turns until going bust for a simplified blackjack style game?

If for each turn, you draw a random number from a uniform distribution with a range between 1 and 20 inclusive and you add this number to your total sum, what is the average number of turns it would ...
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### Probability of Successive Lotto Games

My wife and I were both terrible at probability at school. So, we pretty much gave up straight away on this one. I wanted to know how the odds in a game of chance change (if at all) as more games are ...
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### What is market width in sport betting?

Examles: If the odds are -141/+123 ,then the market width is 141-123 = 18 cents If the odds are -110/-114 ,then the market width is 10+14 = 24 cents Why is that? How can Market width be used as an ...
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### Gambler’s Ruin Problem: how to calculate different probabilities?

I need to resolve a gambler's ruin problem so I have been looking into problem number 5 in the following pdf, which is similar to mine and it is resolved: https://www.webpages.uidaho.edu/~fuchang/...
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### betting in fair game over infinite horizon, is it possible to win?

If a gambler were to play in a fair game, lets say he wins/loses 1 dollar with equal probability in each step. Let $X_i$ denote the amount of money he has after $i$ steps. And he plays until he either ...
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### Computing the profit given the probability of winning in a sport bet

Suppose that you can correctly predict the outcome of a tennis match (i.e. the winner) with probability $x > 0.5$. If you gamble on $N$ matches on some betting website, where odds are assigned by ...
1 vote
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### Maximize the return of gambling with unknown distribution given samples

Given that I played a game with unknown probabilities and odds (actually they are some trades in reality) and I recorded the results into a spreadsheet. How can I calculate the best allocation in each ...
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### Does the casino have an edge on a commission free 50/50 luck game?

I have an interesting discussion with someone on Youtube: Assume a commission free roulette (without the number 0) so you have a true 50/50 chance on black or red. Also assume that all players will ...
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Here's a question from my probability textbook: $A$ and $B$ play at draughts and bet $\$1$even on every game, the odds are$\mu : 1$in favor of the player who has the first move. If it be agreed ... 1 vote 2 answers 121 views ### Is the way to win at roulette to bet on green? I apologize for the juvenile, and probably incorrect, math you are about to see. I have no intention of gambling. This post is made solely from curiosity. Anyways, I am underage, and thought of the ... 1 vote 0 answers 24 views ### Gambler fallacy and probability of tossing coins Q. Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes: If the three coins are simultaneously tossed again, compute the compute the probability of : (... 4 votes 1 answer 89 views ### Converting odds to probabilities Gambling odds on sports betting are designated with a number in the set$(-\infty , -100) \cup [+100 , +\infty)$. If one places a wager of$w$dollars at$p \in (-\infty , -100) \cup [+100 , +\infty)$... 2 votes 2 answers 285 views ### Expected Geometric Growth Rate (Kelly's Criterion) The Wikipedia article for Kelly Criterion establishes its main formula using the expected geometric growth rate$r = (1 + fb)^p * (1 - fa)^q$, where$f$is the fraction of an account (that starts with ... 4 votes 1 answer 109 views ### Allocating money to different bets on loaded coins [closed] I hope this question was not asked before. It is a very interesting problem I came across and for which I have not yet found a solution. If you know where to find it, please feel free to redirect me. ... 0 votes 0 answers 49 views ### Markov chain problem binomial distribution question (Gambler's ruin) I have 16 euros in my pocket. I play heads or tails with$p=q=1/2$. I always bet on heads. If the coin turns heads i win 0 euros and if the coin flips tails i lose 1 euro. What is the probability of ... -1 votes 2 answers 206 views ### payoff of a coin flip is$2^N$We have a fair coin. The game ends when we get a head. the payoff is$2^N$where N is the number of flips until we get the head. What is the expected value of the game? or, how much would you pay to ... 0 votes 0 answers 29 views ### How can I simulate a game of blackjack for different 'return to players' I'm trying to simulate one game of blackjack, I'm doing it using code, but I think it's still a maths related question more than a programming one. My current working is this, for a return to player ... 1 vote 0 answers 42 views ### Markov chain with interpolation I would like to solve this gambler problem using interpolation or any other technique that allows you to solve it with only pen and paper (without knowing the known gambler's problem formulas). Of ... 0 votes 1 answer 130 views ### The probability of losing half by Kelly's criterion According to "Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos And Wall Street", the probability of losing half initial money at some point using ... 0 votes 1 answer 60 views ### Kelly Criterion with Taylor Approximation for Multiple Events I am trying to understand how to approximate the kelly criterion when I have multiple winning events. The Taylor approximation says that$\log(1+fr) = fr + \frac{(fr)^2}{2}$If I have 3 winning events,... 0 votes 1 answer 89 views ### Betting Game on World Series you and a friend are betting on individual games of the World series. For each game, if your team wins, you win a certain (positive) amount of money, and if your team loses, you lose that amount. You ... 1 vote 0 answers 55 views ### Gambler's ruin with different strategies At a certain casino game if you bet \$x you will loose your \$x with probability .505 (so your fortune will decrease by x) and win \$2x with probability .495 (so your fortune will increase by x). You ...
Consider a deck with 26 black and 26 red cards. You draw one card at a time and you can choose either guess on whether it is red beforehand or simply observe the result. If the card is red you get $1\$...
Inspired by this question, I have been investigating the following problem: Suppose we start with $1$ unit of currency and place a series of wagers where with each wager we gain a unit of currency ...