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.

609 questions
Filter by
Sorted by
Tagged with
1 vote
24 views

Optimal Strategy for Card Betting Game

I'm mulling over the following question: You are playing a game with two other people where each player initially contributes 10 dollars to the pot, creating a total pot of 30. During each turn, two ...
27 views

transferring money between two players with game

Suppose there is a 2 player betting game. The total EV of the game, between the two players is say, $H$, where $H\leq 1$. player 1 and player 2 together choose their probability of winning. the ...
• 11
118 views

How to Model Stake's : "Mines Gambling Game"

Mines is a gambling game on stake that I came across after watching a streamer play it. There are 25 tiles, and the player has the option to choose between 1-24 mines to be randomly placed under the ...
• 135
27 views

Clarification regarding betting game and linearity of expectation

Here is the problem I'm dealing with: You have 3 blue and 3 red cards. These cards are mixed and placed face-down in a deck, ready to be turned over one-by-one. Before each card is turned, you are ...
28 views

Approach Clarification for Optimal Strategy Question

Here is the problem I am trying to solve: You're playing a game with a deck of 52 cards. At each stage of the game, the top card of the deck is dealt face-up. You can stop dealing at any time. If the ...
1 vote
60 views

• 1,038
123 views

Quickly putting something to the power of 100 without a calculator (Shortcuts)

For some probability questions, I was wondering if anyone knew of any tricks on how to do do the following; let's say we have a fraction of 49/50 and we want to put this to the power of 100 quickly ...
32 views

Optimal set-up of rewards for betting on an elemination game

There is an elemination game with 10 unkown players. There are 8 rounds. At the end of each of the first 7 rounds, 1 player is eliminated. In the last round, the winner will be decided between the ...
• 428
21 views

Expected number of turns until Loss, modified Gamblers Ruin

Consider a modified gamblers ruin Markov Chain on the set of natural numbers {0,1,2,3...}. We start in state 1, and at each turn, for state i, we have a probability p to go to state i+1, and a ...
• 53
69 views

Find the Optimal Strategy to an Involved Betting Game

Say there are $2$ players. Each is given one card, and the person with the higher number wins. The first player goes and can either bet 1 dollar or fold (giving the pot to the second player). If the ...
• 625
177 views

Analysis: Would constructing lottery combinations by drawing one number at a time give combinations different probabilities of being drawn?

I’m not sure that all lottery combinations have the same probability of being drawn. Numbers are drawn one at a time to construct the $6$ numbered combination we see in a straight pick $6$ lottery (...
• 129
71 views

Help me find the formula for this problem please (probably easy!) [closed]

This is kind of a gambling question but is solely about the numbers. You may have heard of the Martingale strategy, which to put in simple terms if you have unlimited money and you are allowed to bet ...
43 views

Avoid unecessary subsets from a set when aiming prizes of lower order

Crossposted at MathOverflow I have a Lottery app and I'm implementing a feature to optimize the number of bets that are necessary to cover a subset of numbers since they can repeat on several bets. ...
• 109
81 views

Kelly betting: What's the correct terminal value of this betting game?

Let's assume a betting game where each bet has a win probability of $W$. In case of a win, we gain $B$, in case of a loss, we loose $A$ of our invested capital $kC$, where $k$ is the fraction of our ...
• 224
1 vote
75 views

• 329
57 views

Closed-Form Solution to Generalized Gambler's Ruin

Consider the following more generalized version of the gambler's ruin problem: A gambler starts with $n$ dollars. On each successive game, the gambler either wins $g$ dollars with probability $p$ or ...
• 71
950 views

Price of Option in Betting Game

We both put 20 USD into a box. Then, we each generate a number in the interval (0,1) with uniform distribution. The person with the higher number wins and takes 40 USD, whilst the loser is left with 0 ...
• 453
42 views

Limited rerolls, want last roll to be as high as possible. When do you settle?

Suppose you are playing a singleplayer game with a 20-sided die. You roll the die, then look at the number, and decide whether to roll again or stop. Your score is the value of your last roll, and you ...
• 201
1 vote
273 views

Two-player game about betting on the sum of two dice [closed]

There are two players and each one has a fair die with sides 1-6. The two players each roll their dice, and each player can only see the number rolled on their own die. They each come up with a bid ...
• 155
1 vote
141 views

Using the Kelly criterion, what is the maximum amount you should wager when the odds are unknown?

Thinking from a general, layman's perspective, when one cannot properly assess the risks of a particular situation, but still wants to apply probability to maximize chance of gains, how can one use ...
• 121
74 views

Inequality of probabilities regarding gambling problem

A gambler went to a casino where one can stake any amount against a chance of probability $p$ of winning a prize equal to his stake, where $0 < p < \frac12$. Also, the gambler has to pay an ...
• 115
104 views

When will I win the lottery?

I am from an imaginary country where we have a lottery every week. The winner gets 1 millon dollars. The agency, every week, issues 1.1 million tickets, 1 dollar each. The winner gets 1 million, ...
61 views

Optimal strategy that maximizes fortune

A player can bet a quantity $u_k\geq0$, at each instant $k$ if $u_k \leq x_k$, where $x_k$ is his current fortune at instant $k$. He wins the money he bets with probability $\frac{1}{2}<p <1$ or ...
• 15
I have found online this pdf which treats the gambler's ruin problem. However, in the first page the writer implicitly assumes that the gambler must reach one of the barriers (state $0$ or $N$) in ...