Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit 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.

0
votes
1answer
59 views

How to calculate the optimal amount to bet?

Suppose each player is randomly and secretly assigned a number between $1$ and $6$ and then a communal dice is rolled four times. After each roll, you can place a bet or fold. After the fourth bet is ...
2
votes
1answer
47 views

How to arbitrage these bookmakers?

Suppose the following (decimal) odds are offered for an upcoming sports event: bookmaker $B_1$ offers $4.2$ if team $X$ wins, $2.0$ if $Y$ wins, and $3.4$ for a draw. bookmaker $B_2$ offers $4.7$ if ...
0
votes
1answer
1k views

Probability - Expected value of winning a raffle with 2 prizes

My work is having a raffle and I'd like to know if my expected value goes up if I purchase more than 1 ticket? Here are the rules: A ticket costs $5. Two tickets will be randomly drawn. The winner of ...
0
votes
1answer
36 views

Have two decks of cards ever been shuffled in the same order?

Assuming that all the shuffles are truly random shuffles, and that approximately 1 trillion shuffles have been shuffled in the history of the world. What are the odds that a shuffle has come up with ...
0
votes
0answers
24 views

How to use Wald's equation to determine expectation in gambling model?

$\begin{array}{l}{\text { In each game played one is equally likely to either win or lose 1. Let } S \text { be your }} \\ {\text { cumulative winnings if you use the strategy that quits playing if ...
0
votes
1answer
17 views

How Would You Calculate Your Edge With These Variables?

Say we are playing a casino game where we have there potential outcomes, and 3 probabilities associated for each one, all which sum to 1. They are: Win $1.00 (80%) Lose $4.00 (17%) Lose $1.00 (3%) ...
1
vote
0answers
30 views

Gambler's ruin vs point difference

Two people want to investigate who is best at playing Scrabble. They decide to settle this by playing a series of games. Assume that there is always a winner for each game, and that winning or losing ...
0
votes
0answers
22 views

Calculate the probability of poker winning hand type (combination)

There are a lot of libraries that calculate the winning probability of texas holdem poker player and the probability of each player having some combinations(pair, straight...). Does anyone know where ...
0
votes
1answer
33 views

Does the time when you buy a sweepstake ticket change your odds of winning?

Context: At work there is a Grand National (horse racing) Sweepstake Competition. Rules of the Sweepstake: there are 40 tickets, each ticket is assigned to a horse (not assigned yet), you can buy ...
2
votes
2answers
51 views

Inconsistency when applying the Kelly Criterion

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 ...
1
vote
1answer
66 views

How to construct a wheeling system for soccer betting?

A single bet consists of predicting the result of $n$ games, where each game has $3$ different possible outcomes: win, draw, loss. Given a set of guesses for each game, I want to calculate the ...
0
votes
1answer
40 views

How much money would it cost to “buy out” every possible number in the 6-digit Lottery?

So, the constraints are as follows: First 5 numbers are digits 1 ; 69 The 6th number is a number 1 - 26 Order does not matter Numbers do not repeat Tickets cost $2 each My reasoning is as follows: ...
0
votes
2answers
30 views

probability of x losers in n trials

I am new here and I am not sure if this is the correct place to ask this question. It seems like a simple probability question but I am stuck on it. It is a problem I am trying to solve. Lets say I ...
0
votes
1answer
29 views

Sucker Bet - Coin Flipping Stochastic Process

Having a lot of trouble working out this exercise. I have tried constructing the 8x8 matrix with all possible combinations of three flips of the coin {HHH, HHT, HTH, ... , TTT} and then calculating an ...
2
votes
1answer
718 views

Puzzle on rolling dice game

A gambler goes to bet. The dealer has 3 dice, which are fair, meaning that the chance that each face shows up is exactly 1/6. The dealer says: "You can choose your bet on a number, any number from 1 ...
0
votes
1answer
21 views

Pairs of matching symbols slot machine

Hello everybody I'm happy to be here :) Me and my friends start to develop a slot game 5x3. Im very new in this field of gambling mathematics and I learn step by step. After a long discussion , ...
1
vote
1answer
42 views

Problem similar to Gambler's Ruin

I am working on a problem that is similar to the gambler's ruin problem. We start with a bet of $\$1$. With probability $p$ the game is won and we win the amount of the bet, i.e., if we ...
4
votes
1answer
93 views

Kelly Criterion for a finite number of bets

I am not a mathematician but I have read extensively about the Kelly Criterion and understood it well (I think at least). Kelly criterion allows you find out the fraction f* of your bankroll that you ...
3
votes
1answer
590 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 ...
3
votes
2answers
64 views

When gambling, do I get my money's worth? (Or: Does the amount I lose per bet determine the number of bets until I lose all my money?)

This question came up when I asked on Puzzling.SE, How long will my money last at roulette? The basic question is: if I take $\$20$ to a roulette table which has a house edge of $1/37$, and I bet $\$...
1
vote
1answer
38 views

Multiple winning coin tosses in a Row, some losses, but what is total Percentage?

I would appreciate your help in the following scenario. I flip a coin and the following events happened: 3 Wins, 1 loss 3 Wins, 2 losses 5 Wins, 2 losses 1 Win, 1 loss 4 Wins, 2 losses 1 Win, 1 ...
0
votes
1answer
61 views

How to calculate probabilities for the next colour to be out in Wheel of Fortune Casino Game.

Recently i've been very interested in how to parse data from html into my c program. I'm now considering to calculating the probabilities for the next colour to be out in the Wheel of Fortune. But ...
6
votes
4answers
275 views

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 ...
0
votes
1answer
62 views

When to quit a coin toss doubling game?

The game is as follows: I put in a dollar and if I get heads, I double my money. I can then continue playing and double my $2. Basically, I'm always allowed to continue playing and double the previous ...
0
votes
1answer
36 views

Variance equations that yield inconsistent results

Consider a game of chance were a player places a bet, and coin is flipped if the coin lands on heads the player wins $2b$ where $b$ is the bet value. If the coin lands on tails the player looses the ...
0
votes
1answer
42 views

Bet to place for profit

Suppose there are $3$ runners $R1, R2$ and $R3$. The betting odds paid on each runner are $r1:1$, $r2:1$ and $r3:1$. This means that if, for example, you bet $\$2$ for runner 1 winning, you will make $...
0
votes
0answers
32 views

Winning a game probability

Suppose you are tied $1-1$ with Bob. To win the game, you have win greater than or equal to $5$ rounds and win at least $2$ more rounds than your opponent. The probability of winning a round is $40\%$ ...
0
votes
1answer
128 views

Calculate slot machine game multiplier

I'm developing a slot machine game with 5 slots, each slot has 6 options (pear, lemon, ..., etc.). Each spin, 5 random values get generated, one for each slot, making the slots spin to the option ...
0
votes
0answers
14 views

Random Walk on a number line and further cases

i) A monkey is sitting on 0 on the real line in period 0. In every period t ∈ {0, 1, 2, . . .} it moves 1 to the right with probability p and 1 to the left with probability 1−p, where p ∈ 1 2 , 1 . ...
1
vote
1answer
46 views

Odds of Bankruptcy Flipping a Weighted Coin Infinity Times

A random tangent I have been thinking about, please be gentle I am not a mathematician: Imagine a coin toss where Heads means we win a coin and Tails means we lose a coin. We start with 1 coin and ...
0
votes
0answers
18 views

Expected value: random prizes until occurrence of termination 'prize'

I have 10 boxes of which 9 have a coin and 1 is empty. I can choose boxes and keep the prizes until the empty one appears. What's the expected value? First I thought: $E$ must the the mean between ...
0
votes
0answers
50 views

Probability question. Roulette dozens bet occurring consecutively.

Hello Mathematics Guru's, Can I first caveat this question by saying, I'm wholly aware the house always has a mathematical edge if you play long enough in Roulette, but i am interested to know the ...
0
votes
1answer
28 views

Is there a formula to get the total wins from odds combination?

Here is the problem: given a set of bets, how can I calculate the maximum possible wins of all combinations without looping through them? I know how to get the number of combinations ($\frac{n!}{r!(n ...
2
votes
1answer
54 views

bounded gambling systems (Theorem 4.2.8 in Durrett: Probability Theory and Examples)

Theorem 4.2.8 in Durrett: Probability Theory and Examples states Let $X_n, n \geq 0$ be a supermartingale. If $H_n \geq 0$, is predictable and each $H_n$ is bounded then $(H \cdot X)_n := \sum_{m=1}^{...
0
votes
1answer
1k views

Gambling to pay off debt?

Someone told me something interesting today. They said they were going to take their bonus check from work, to the casino because they have "better odds" of paying off more debt then if they would ...
2
votes
0answers
34 views

Potential strategy in a random game

Suppose there are two betting games $G_1$ and $G_2$, the outcomes of which are entirely independent of player input. The expected return for a single iteration of $G_1$ is $r_1$ and for $G_2$ is $r_2$...
0
votes
1answer
51 views

The intuition of fair odds (information theory)

I'm reading about gambling in Elements of Information theory. As stated in the book, given that the gambler bets $o_i$-for-$1$ on horse $i$, Fair odds (w.r.t some distribution): the odds is fair if $\...
0
votes
0answers
33 views

Probability that a bottomless gambler visits a certain state.

In section 4.6 of his book on probability models, Ross analyzes the gambler ruin problem (a gambler who starts with some units of money, stops when he either reaches N or goes broke). In particular, ...
0
votes
1answer
2k views

Trying to beat 50/50 odds.

I were reading about negative progression systems for betting on 50/50 games and why they are doomed to fail (Martingale,Labouchere and D'Alembert system). If you get on a long losing streak, you will ...
3
votes
1answer
151 views

How much advantage would a Blackjack player gain by being able to see the underside of cards?

In the novel Spaceland by Rudy Rucker, the protagonist Joe Cube is grafted with an eyestalk that sticks vout into the fourth dimension. This lets him see under and inside three-dimensional objects ...
2
votes
1answer
155 views

Optimal way to decide Blackjack play with a soft score

I am designing a Blackjack AI such that it would try to play optimally each hand against the dealer. When I'm having a hard score the algorithm is easy: as long as my risk of busting is lower than ...
0
votes
0answers
377 views

Can anyone confirm expectations for the game of blackjack?

I computed the probabilities and expectations for blackjack in Mathematica and here is what I came up with: If player is given only the option to stand the expected win per unit bet is $$ -\frac{...
1
vote
1answer
57 views

Casino/House bankroll for Blackjack

Given a maximum bet size of "x" in blackjack, how many maximum bets should the house keep in its bankroll/account to prevent it ever realistically losing all its money against players playing ...
3
votes
1answer
47 views

How to maximize returns in this scenario

You have a machine. You can put money into it. You have $s$ initial budget. $p$ percent of the time the machine will double your investment. $(100-p)$ percent of the time it will just swallow your ...
0
votes
0answers
37 views

What is the probability of throwing 4 and then winning in craps?

Owen plays the following game (craps) involving two fair six-sided die. -If Owen's first throw is a 7, or 11 he wins immediately - If Owen's first throw is a 2,3, of 12 he loses immediately -Any ...
1
vote
0answers
1k views

Mathematical Optimisation of Martingale Strategy.

Here is a short background of how the strategy works.Your next bet should always be enough to make up for all your previous losses and earn some little profit.E.g if your losses were 10 dollars stake *...
1
vote
1answer
81 views

What is the gambler expected return in this game?

Question :A gambler is invited to play a simple game in which two coins are tossed. He will receive nothing if both coins show tails, or \$12,if one shows heads and one shows tails, or else $60 if ...
1
vote
0answers
27 views

Expression of the fortune of a gambling problem

I was working on a gambling problem where the gambler with an initial fortune $F_0$ stakes a proportion of $\theta$ of his current fortune (Billingsley Ex. 7.5). The wager $W_n=\theta F_{n-1}$ and ...
1
vote
1answer
56 views

Odds of wilds on slot machine

I am working on calculating the odds that any particular combination of icons will appear in a 5-reel slot machine. I have the formulas for most types of combinations figured out. However, I'm stumped ...
-1
votes
1answer
57 views

Gambler´s ruin problem

A gambler starts with an initial fortune of 9. He wins 1 with p=1/3 and losses 1 with q=2/3. The game ends when the gambler looses all of his money or when we reaches 15. What is the probability ...