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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The probability to visit a state for the first time after n steps in a markov chain [closed]
I have the following Markov Chain:
delta states, numbered from 1 to delta. the transitions ...
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0
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What are the ods of winning a 2.0 sportsbet odd 14 times in a row? [closed]
Odds of winning a 2.0 sportsbet odd 14 times in a row?
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Probability of winning a multiple-round game, where a player needs to get to $n$ points before losing all their initial point.
I'm trying to do the following problem in Sheldon Ross' A First Course In Probability (page 86-87).
EXAMPLE $4k$.
Suppose that initially there are $r$ players, with player $i$ having $n_i$ units, $...
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Determining bet sizes given odds [duplicate]
Crossposted on Quant SE
Recently, I was asked the following question in an interview with a prop trading firm.
You are given the opportunity to make money by betting a total of 100 bucks on the ...
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1
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Probability of winning in a 3 slots game with 9 types per slot [closed]
The game is as follows: you have three slots: [1][2][3] with the same 9 fair types for each slot.
When all the slots are the same its a win, doesn't matter the type....
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1
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57
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Basic probability independence in roulette
I am teaching my students how roulette works and we were talking about the probability of betting on the first column of numbers $\{1,4,7,10, 13, 16, 19, 22, 25, 28, 31, 34\}$ and the probability of ...
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Calculating payout amounts for a game with scoring
Say I have a hypothetical computer gambling game that is very basic and just involves the player trying to score points before dying - with a score of 5 points being the maximum (beating the game). ...
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28
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Casino Optimization Problem
A certain game starts with a starting capital C and runs for a number N of rounds. In each round i (with 1 ≤ i ≤ N) the player has the option of not betting anything or betting all of his capital, so ...
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Estimating implied probability based on prediction betting odds
I am attempting to estimate prediction betting market efficiency for a project, and I am hoping for assistance with a couple of questions.
The prediction market makers add a commission to the betting ...
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A stock today price 100, tomorrow it becomes 50 or 200. There is also a casino you could bet win/loss with rate 1:1. Strategy
A stock today price 100, tomorrow it becomes 50 or 200. There is also a casino you could bet win/loss with rate 1:1. What is your strategy to make money?
I denote the probability of stock rises the ...
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Optimal Betting Strategy in Coin Toss
Goal:
Participate in a coin-tossing game with the aim to maximize your earnings. A fundamental part of the game is formulating a strategy that optimizes your earnings based on the observation of the ...
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Probability of going broke before reaching target with positive expected value.
In an interview today, I was given a hypothetical situation in which I can bet on the outcome of a biased coin (0.6H, 0.4T). I can bet £1 at a time; if I win i get my stake back and an extra £1, ...
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Why is the Gambler's Fallacy a fallacy? [Solved]
The empirical probability distribution of the coin tossing bet is binomial distribution. For a fixed length of sequential events, it shows that the more balance the number of Heads strikes between the ...
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2
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Minimum probability of winning a bet
I have the below scenario.
Suppose you are playing a game where you and your opponent have put
$\$10$ in the pot each. Your opponent bets another $\$10$. What is the
minimum probability of you ...
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2
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Counterfeit money, guaranteeing a profit
Bob and I found two 50 dollar bills out of nowhere. We know they're either both legitimate or both counterfeit. If they're legitimate, they're worth 50 dollars each, otherwise 0. I get one 50 dollar ...
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Maximizing Geometric Growth Rate (Kelly Formula) By Betting On Multiple, Non-Mutually Exclusive Events
Stack Exchange has many posts regarding bet sizing on multiple, mutually exclusive/independent events/gambles.
I'm curious if anyone is familiar with using Kelly to bet on 1+ gambles that are not ...
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Boss Loot Drop Rate Probability
Scenario A:
In a game, every time you beat a boss, you have a chance of receiving a drop. The base drop rate at zero wins is $1.5$%. This drop rate increases by $0.5$% after each win. So, your chance ...
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Football betting. How can I calculate the stake values for 2 teams to give the same profit whichever team wins taking into account both stakes? [closed]
I am trying to implement this formula using a spreadsheet (currently Libre Calc) but any mathematical advice will be gratefully accepted.
Let's say, as an example, there are two teams with the ...
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Given the win odds of a horse race are known plus other info such as top 3 place odds, calculate the 2nd/3rd/4th place odds for each horse.
I have a problem where I am trying to calculate the place odds given win odds and other info such as top 3 place odds.
I have used Harville's method successfully to calc place odds given we know the ...
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simplify the sum of this binomial coefficients -- generalized gambler ruin problem
While solving recursion $p_i = p_{i-B} (1-\alpha) + p_{i+1} \alpha$, related to a special gambler ruin problem, we came across the following summation. Let $0$ and $K$ be the extremes of the gambler ...
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Average cost of an item from container with different chances [closed]
i need to find average cost for every item in container.
It costs 50 currency to open one.
I have following chances for items:
lvl-1: 58%
...
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2
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Find the Mistake In My Calculation For the Odds of Hitting The Fire Bet In Craps.
Background Information: Inside the game of craps, one of the most notorious bets, the fire bet, is known for being exceptionally complicated and hard to win. In order to hit the fire bet, every ...
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Closed Solution for Expected value of Martingale Strategy for 10 bets with 70% odds
I was answering a question on Reddit and could only answer by simulation via code rather than figure out the math.
https://www.reddit.com/r/gambling/comments/15jualm/gambling_math_question/
If you are ...
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Hedging bets on two independent events?
Let us say that there are two independent events $A$ and $B$. Event $A$ occurs with probability $0.3$ and event $B$ occurs with probability $0.4$. You can bet on these events with odds of $3:1$ and $7:...
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Closed-Form Solution to Generalized Gambler's Ruin
Consider the following more generalized version of the gambler's ruin problem:
A gambler starts with $n$ dollars. On each successive game, the gambler either wins $g$ dollars with probability $p$ or ...
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2
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Price of Option in Betting Game
We both put 20 USD into a box. Then, we each generate a number in the interval (0,1) with uniform distribution. The person with the higher number wins and takes 40 USD, whilst the loser is left with 0 ...
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Limited rerolls, want last roll to be as high as possible. When do you settle?
Suppose you are playing a singleplayer game with a 20-sided die. You roll the die, then look at the number, and decide whether to roll again or stop. Your score is the value of your last roll, and you ...
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2
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Two-player game about betting on the sum of two dice [closed]
There are two players and each one has a fair die with sides 1-6. The
two players each roll their dice, and each player can only see the
number rolled on their own die. They each come up with a bid ...
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Using the Kelly criterion, what is the maximum amount you should wager when the odds are unknown?
Thinking from a general, layman's perspective, when one cannot properly assess the risks of a particular situation, but still wants to apply probability to maximize chance of gains, how can one use ...
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Inequality of probabilities regarding gambling problem
A gambler went to a casino where one can stake any amount against a chance of probability $p$ of winning a prize equal to his stake, where $0 < p < \frac12$. Also, the gambler has to pay an ...
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When will I win the lottery?
I am from an imaginary country where we have a lottery every week. The winner gets 1 millon dollars. The agency, every week, issues 1.1 million tickets, 1 dollar each. The winner gets 1 million, ...
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Optimal strategy that maximizes fortune
A player can bet a quantity $u_k\geq0$, at each instant $k$ if $u_k \leq x_k$, where $x_k$ is his current fortune at instant $k$.
He wins the money he bets with probability $\frac{1}{2}<p <1$ or ...
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Gambler's ruin - Why is the probability of never reaching the barriers 0?
I have found online this pdf which treats the gambler's ruin problem. However, in the first page the writer implicitly assumes that the gambler must reach one of the barriers (state $0$ or $N$) in ...
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Blackjack problem, prediction problem, and an issue with usable ace
I have an issue with the way a usable ace should be interpreted in the the Blackjack problem and I appreciate your input.
Game overview:
The game is played between a player and a dealer.
The ...
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European Russian Roulette Casino Probability Help
I employed a simple betting strategy while playing European Russian roulette, which features a single zero on the wheel. My approach involved exclusively betting on black, and in the event of a loss, ...
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Kelly criterion for $3$ outcomes — win, fractional loss, or full loss
As the title suggests, I want to calculate the Kelly criterion for a bet with 3 possible outcomes: win, fractional (partial) loss, or full loss.
Here is the proof of the Kelly criterion for a bet with ...
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1
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A card player with $\$32$ wins $4$ of $7$ games, where he and his opponent bet $50\%$ of his money each time. How much money does he have in the end?
Found the following problem related to "tricky" problems from elementary mathematics:
Mr. White and Mr. Green were playing cards. Mr. White made the suggestion: “Let’s play for money. For ...
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A Gambling Game (Continued)
I previously asked the following question: A Gambling Game
For a brief summary, $ n>1 $ gamblers in a gambling game each are assigned a random integer in a specified interval $[1,y]$. Let $S$ be ...
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Calculating the Chances of Doubling the Original Money (Multiple Chances of Winning with Different Multipliers)
Previously, I've asked a question related to this.
But now I need to know what if there are multiple chances of winning with different scaling multiples.
The goal is still to double the original money....
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Odd or probability question in gaming theory.
I have two games with different probabilities of winning. Let's say Game A has 80% of return to player percentage while Game B has 100% (which means a player will win no matter what). And there is a ...
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Calculating the Chances of Doubling the Original Money (Betting Odds)
Here are the bets I am making:
Starting balance: $100
Starting bet: $0.05
Win chance: 4%
Win amount 24.75x
On loss, increase each bet by 4.5%
On win, reset bet amount
So with a 0.05 bet, winning $1....
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When to stop exploring and start exploiting in multi-armed bandit problem
I'm reading Algorithms to Live By: The Computer Science of Human Decisions and it came to a conclusion that in the problem described below, the optimal strategy is to stop exploring after 38 ...
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Probability of at least $m$ different numbers in $n$ spins on roulette board
Given an American roulette wheel with $38$ possible outcomes ($0$-$36$ or $00$), what are the odds of landing on at least $m$ different numbers in $n$ spins?
Attempt:
P(at least m different in n ...
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1
answer
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How to correctly size bets when the probability of an event occurring is unknown?
I have studied the Kelly criterion in relation to bet-sizing based on positive expected value (EV) events. However, I can't figure out a way to adapt it to solve the following problem:
Let's say we ...
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2
answers
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3 cards betting game
Bob and John are playing a betting game of multiple rounds. Each round, they both draw a single card from a deck consisting of only three cards: 1 Queen, 1 King, and 1 Ace. Whoever reveals to have the ...
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Why are higher risk-reward ratios better than lower ones in gambling?
Assume a game where you can place bets of $1\$$. The game is played as long as you either win $4\$$ or lose your $1\$$. There're two ways to place your bets:
Option 1: With a high risk-reward ratio of ...
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Calculating expected value for a betting event given: Decimal Odds, Stake, Potential Profit, & Implied Probability?
I am trying to get the expected value of a bet on a UFC money line fight (betting which fighter will win)
decimal odds at: $1.6$
Stake: $$30$
Potential Profit ($PP$): $(1.6 * 30) - 30$
Implied ...
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3
answers
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How does the expected value change in a lottery when one stops playing after winning?
Using as an example for lotteries in general, the expected value of roulette is negative, which means in the limit of playing for eternity, one is expected to lose a certain amount of money for each ...
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Odds of winning the Malaysian lottery [part 2]
Part 1
Jackpot Bonus number: remaining of number inside the 8 matching number.
Updated:
Per ticket is 8 numbers and no need to specify which is bonus number
Grand Prize: 8 matching number from 36 ...
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2
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On jackpots in the Malaysian lottery
Below is the Jackpot in my home country. Based on my calculation, the probability of Jackpot 2 is higher than Jackpot 1 although Jackpot 1 has higher prize, which does not make sense to me.
Is my ...
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