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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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378 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{...
9
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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 $C$ ...
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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 ...
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1answer
700 views

Game Theory Optimal Solution to 2 Player Betting Game

Both players start with $\$n$ Each player antes $\$1$ and rolls a private 100-sided die so that they are the only one that sees the result. After the rolls a round of betting occurs (same method as ...
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1answer
85 views

Prove a thm on stopped processes given fundamental principle 'you can't beat the system'?

How does the principle below imply the thm below? From Williams' Probability w/ Martingales: Principle: Thm: What I tried: $$E[X_{T \wedge n} - X_0 | \mathscr{F_m}] =/ \le X_{T \wedge m} - X_0 \ \...
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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 ...
9
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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 ...
18
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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,...
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2answers
643 views

Profitable strategy in coin tossing?

There is a coin with a probability $p$ of heads, and $1-p$ of tails. Tosses are independent of each other. When you bet an amount of money $x$, you receive $2x$ if it lands heads, and you lose what ...
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2answers
72 views

Is the outcome of a roulette spin independent of prior outcomes? Why?

Red and black on roulette table (without green "0"). The outcome is independent of prior outcomes, right? It does not matter how many times in a row black (or red) comes up prior, the outcome is still ...
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4answers
1k views

Arbitrage sports betting [closed]

Player A vs Player B. Bookie 1 offers 1.36 odds on player A winning. Bookie 2 offers 5.5 on player B winning. We have $1000 in total to bet. How would you place your bets such that ...
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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 ...
7
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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 ...
6
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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?
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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
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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 ...
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vote
1answer
202 views

Should you ever stop rolling, THE SEQUEL

Inspired by this question, I want to know if there is a version of the scenario that actually fits Newb's intuition about the problem. Scenario template You roll a 6-sided die and add up the ...
10
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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 ...
2
votes
1answer
304 views

Betting a constant fraction on a biased coin

I'm looking at a betting game where I have \$100 and want to double my money by repeatedly betting on a biased coin; it shows heads with probability $p<\frac{1}{2}$ in which case I win even money. ...
2
votes
1answer
96 views

How many ways does the gambler break even?

I got this math problem online: A gambler starts with $\$10$ and plays a game for $20$ rounds. At each round, his wealth either increases by $\$1$ or decreases by $\$1$, but the moment his wealth ...
1
vote
1answer
149 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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1answer
126 views

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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1answer
342 views

Gambler's ruin model

In the gambler's ruin model, $X_n$ is a gambling player's fortune after the $n^{th}$ game, when making 1 dollar bets at each game. Also, for fixed $0<p<1$, we can find random variables $\{Z_i\}$...
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1answer
219 views

Gambling Game martingale

State the optional sampling theorem for martingales and bounded stopping times. You start with a capital of £100 and bet repeatedly on the toss of a coin. On each toss you may bet any whole number of ...