# 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.

258 questions
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### 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 ...
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### 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 ...
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### 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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### 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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### 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 ...
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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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### 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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### 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 ...
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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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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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 *...
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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 ...