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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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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%) ...
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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 ...
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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 ...
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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 ...
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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 ...
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65 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 ...
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39 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: ...
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27 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 ...
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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 ...
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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 , ...
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40 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 ...
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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 ...
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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 $\$...
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35 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 ...
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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 ...
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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 ...
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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 $40\%$ ...
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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 $...
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123 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 ...
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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 . ...
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44 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 ...
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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 ...
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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 ...
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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 ...
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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}^{...
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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 $r_2$...
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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 $\...
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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, ...
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340 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{...
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1answer
48 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 ...
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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 ...
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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 ...
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57 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 ...
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1answer
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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 ...
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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 ...
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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 ...
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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 ...
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Does expected value change as the number of bets increases?

I am reading about Expected Value in the context of roulette-game. I understand that it is the weighted sum of all the probabilities. Here is the scenario: ...
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108 views

How do I know if I have enough data to calculate probability?

It's been a while since I took a stats class so I'm pretty rusty on this. I have a hobby where I've been collecting data on an online gambling game called "Crash" (you can see an explanation of the ...
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Changes to Blackjack Basic strategy when winning with 5 cards pays double

OK, so take a game of blackjack, but if you win with 5 or more cards in your hand, you win double what you normally would. How would I go about adapting basic strategy to account for this? My ...
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1answer
38 views

Number of expected winners in a game involving three kinds of marbles

In a bag there are some red marbles, some blue marbles, and some green marbles. There is at least one marble of each color in the bag. Richard, Bob and George ignore the exact numbers of marbles of ...
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1answer
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Fair Value of Game Involving Last Strictly Increasing Sequence

Assume there is a game that costs $\$x$ dollars to play, and costs an additional $\$1$ to roll a die each turn. You are allowed to stop the game at any time, and the amount of money you win is equal ...
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57 views

Is there a sure way to win? (Bet on given odds)

You have 25 numbers on a wheel. 12 are number 1 : Doubles your bet. (x2) 6 are number 3 : Triples your bet. (x3) 4 are number 5 : Quintuples your bet. (x5) 2 are number 10 : Decuples your bet. (x10) ...
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134 views

A game involving binomial probabilities

Consider the following tables: Given a number of independent trials $n=2,3,4\ldots$ each of these tables represents the list of all the possible $\binom{k+n-1}{n}=\binom{n+2}{n}=6,10,15\ldots$ ways (...
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Design of a peculiar Wheel of Fortune

Consider the two wheels of fortune illustrated below. The first one (left) is constituted by $c$ sectors with the same arc length: $\alpha$ of which are red, $\beta$ of which are blue and $\gamma$ of ...
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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 ...
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Probability that one trial is a successful trial for events related to an Urn Problem

Consider an urn $C$ which contains three (distinguishable) kinds of elements, say $\alpha>0$ elements of kind $A$, $\beta>0$ elements of kind $B$, and $\gamma>0$ elements of kind $G$. We ...
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How does one apply “risk tolerance” to a random walk?

Suppose we play a game in which you gamble on the outcome of several successive events. You bet $b$ dollars each time and you (a) lose the bet if you're wrong or (b) gain $wb$ dollars if you are right....
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The Abel-and-Cain Urn Problem

An urn contains three distinguishable kinds of balls, say $A,B,C$. Abel bets to get, in $t$ trials with replacement, at least one ball of kind $A$ and at least one ball of kind $B$. Cain bets to ...
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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 ...