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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.

88
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10answers
7k views

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 ...
35
votes
11answers
9k views

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 ...
34
votes
4answers
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 ...
18
votes
3answers
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,...
13
votes
2answers
720 views

3 person bet based on the perceived likelihoods of an outcome

Suppose 3 friends want to bet \$100 on whether candidate John Doe will win the next election. They state their perceived likelihood that the event will occur: Alice believes John Doe will win with ...
10
votes
2answers
755 views

Does variance do any good to gambling game makers?

People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers? In another word, what is a pratical gambling game that involving some ...
9
votes
1answer
627 views

Can you make money on coin tosses when the odds are against you?

The strategy Given an initial investment $n$ dollars and a "bet buffer" $b$. Calculate the bet size $x=\left\lfloor\frac{n}{2^b-1}\right\rfloor$ dollars. Wager $x$ dollars on random variable $C$ ...
9
votes
3answers
726 views

100-Sided Dice “Blackjack” Game

I am attempting to determine two variables in this game: The optimum strategy: (What number the bettor should stay at) The expected value given perfect play: (The percent return on a bet when using ...
7
votes
1answer
731 views

Combinatorics: Guarantee getting 10 out of 13 right as efficiently as possible (Stryktipset)

First, a little background "Stryktipset" is a popular form of football (soccer) gambling in Sweden, but I'm sure similar games exist in many other countries. The concept is simple: out of a list of ...
7
votes
1answer
532 views

Arbitrage opportunity

Given odds $o_i$ for $i=1,2,\ldots,n$ and the possibility to bet the amount $b_i\in \mathbb{R}$ on each event such that if event $i$ occurs you receive $b_io_i$ and if it doesn't you recieve $-b_i$. I ...
7
votes
1answer
172 views

Gambling system theorem given by Doob

Let$\{X_n\}_{n=1}^{\infty}$ be a sequence of i.i.d. random variable. Let $\{\alpha_k\}_{k=1}^{\infty} $be a sequence of strictly increasing finite stopping times. Then $\{X_{\alpha_k+1}\}_{n=1}^{\...
7
votes
4answers
44k views

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 ...
6
votes
2answers
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 ...
6
votes
2answers
254 views

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?
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 ...
6
votes
1answer
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 ...
5
votes
3answers
2k views

The gambler makes 100 bets and wins 10. How much money does he have at the end?

A gambler who makes 100 bets of $1, each at payoff odds of 8 to 1. He wins 10 of these bets and loses 90. How many dollars has the gambler gained overall? I don't seem to understand what "odds of 8 ...
5
votes
2answers
171 views

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 ...
5
votes
3answers
106 views

Why are odds of a coin landing heads $50\%$ after $'n'$ consecutive heads

I'm trying to understand how the odds of flipping a fair coin $4$ times in a row and landing heads each time is $\frac{1}{2^4}=\frac{1}{16}=6.25\%$; But at the same time if I've just flipped the coin ...
5
votes
0answers
400 views

How did Mohan Srivastava crack Ontario scratchcards?

Wired ran a 2011 article about how a statistician, Mohan Srivastava, cracked Ontario scratchcards such as this one. First, he thought about the program that produced the numbers on the cards. 'Of ...
4
votes
2answers
287 views

Why don't billionaires (or multi-millionaires for that matter) use the Martingale betting system?

Here is the link to my simulation: (The data is based on using the Martingale betting system in European Roulette) https://docs.google.com/spreadsheets/d/1GH48faKeK5clonmYO6aySzchGeRhp7nx8Kc0cA0UFVA/...
4
votes
1answer
125 views

Where am I going wrong in interpreting this problem as a gambler's ruin problem?

I was trying to solve this problem (Strategic Practice Week 3, Homework problem 4 in Harvard's Stat 110 class), by framing it as a gambler's ruin problem: Calvin and Hobbes play a match consisting ...
4
votes
2answers
2k views

Kelly Criterion for simultaneous independent bets

I'm trying to obtain a more generic version of the Kelly criterion for when we have simultaneous independent events to bet on, I'm going to focus on the case where we just have 2 different events. ...
4
votes
1answer
267 views

What gambling/board game or real life thing can (surprisingly) be modelled as a linear programming problem?

So I've taken Linear Programming 101. I've read my textbook, took the test and all that, and - besides all the theory, the nice algebraic interpretations, etc - I've encountered a lot of textbook ...
4
votes
1answer
95 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 ...
4
votes
1answer
155 views

Deciding to place a bet on outcome of a dice roll based on the probability

I have encountered several question of the following format. I have no trouble answering the first half but second half I have no clue on how to proceed. a: If you roll 5 standard six-sided dice, ...
4
votes
1answer
1k views

Game Theory/Bayesian approach to a bluffing game

Two players play the following card game with a deck consisting of (A,2,3,4,5). A dollar is placed in the pot by some third party, and player 1 is dealt a card. If it is an A, he has a winning card, ...
4
votes
0answers
59 views

Expected number of coin tosses with a coin that changes over time

Imagine that I have a coin that changes monotonically over time. -- casino example -- (This is not necessary to understand mathematical problem, but just can help to imagine a real life situation, ...
4
votes
0answers
394 views

Applying Kelly Criterion to profit/loss bet

In a financial derivative trading situation, there are two outcomes to a bet (win/lose), but I don't necessarily lose my entire stake if I lose the bet, because I can buy my way out of the bet, taking ...
3
votes
3answers
308 views

Is this Gambler's fallacy?

You can see the original question/quiz here A teacher in a class of 30 students, says that he will make a random draw every day and the (un)lucky student who's name is drawn will be examined ...
3
votes
2answers
455 views

Mathematics of hedging bets

I bet £20 at odds of 3.0. I have the chance to hedge this bet by laying an amount £$L$ at odds of 3.2, but will have to pay 5% commission on the winnings. How should I choose $L$ to maximise my ...
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 ...
3
votes
1answer
223 views

Can one arbitrage this horse race?

Say we are given the odds of an upcoming horse race and we want to know how to bet in order to win no matter the outcome. Essentially, is there a way to bet on every horse and still turn a profit? ...
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 $\$...
3
votes
2answers
398 views

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)....
3
votes
1answer
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 ...
3
votes
1answer
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, ...
3
votes
1answer
109 views

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 ...
3
votes
2answers
306 views

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 ...
3
votes
2answers
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 ...
3
votes
1answer
3k views

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 ...
3
votes
1answer
47 views

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 ...
3
votes
3answers
48 views

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 ...
3
votes
1answer
133 views

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 ...
3
votes
1answer
588 views

Probability of never losing when playing the St Petersburg Paradox repeatedly?

The St Petersburg paradox is a hypothetical game. The pot starts at \$1. A fair coin is flipped and if it is heads, the pot doubles, if it's tails, the player takes the pot. The game has a certain ...
3
votes
1answer
663 views

Gambler's Ruin variant: each bet is for 1/k dollars, what happens to probability of winning as k approaches infinity?

I am trying to a solve a variant on the Gambler's Ruin problem, in which two gamblers $A$ and $B$ make a series of bets until one of the gamblers goes bankrupt. $A$ starts out with $i$ dollars, B with ...
3
votes
0answers
117 views

A fair coin game - is it ever ending? [closed]

I start with $\$1$. If I have $x$ money, I will risk $\frac{x}{2}$ in a fair coin game, so I will have $\frac{x}{2}$ money with $50\%$ chance (I lost), and $1.5x$ money with $50\%$ chance (I won). So ...
3
votes
0answers
1k views

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 ...
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
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 ...