# 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.

613 questions
Filter by
Sorted by
Tagged with
29 views

1 vote
41 views

### Probability Question: Not sure why approach incorrect

This appears to be a common type of question: A & B are alternately picking balls from a bag without replacement. The bag has $k$ black balls and 1 red ball. The winner is the one who picks the ...
109 views

### How to bet on individual games in best of seven series so that no matter how my team wins I make same profit? (Assume games are coin flips)

Suppose I have a 100 dollar starting bankroll. I want to bet this on my team to win a best of 7 series, however assume I am restricted to only being able to bet individual games one at a time as they ...
• 95
110 views

### Gambler's ruin with asymmetric probabilities

A gambler with a capital of $1$ dollar goes to a casino, where they participate in a series of games. In each game, regardless of the others, they can win $1$ dollar with probability $p$ or lose $1$ ...
• 1,128
45 views

### Number of trials required to break even with a certain probability

I made a problem myself while reading an old econometrics book, but having a hard time solving it. A single trial of a game is as follows.  1. You pay L dollars to start the game.  2. Toss a coin ...
• 415
1 vote
39 views

### Distribution of players in Gambler’s Ruin

In a fair game, with 0.5 chance of winning or losing a large number of players begin at 0, (Zero wins, zero losses) each with ten coins. Players leave the game when they have lost everything or have ...
• 236
75 views

• 2,307
146 views

### Determining bet sizes given odds [duplicate]

Crossposted on Quant SE Recently, I was asked the following question in an interview with a prop trading firm. You are given the opportunity to make money by betting a total of 100 bucks on the ...
• 429
80 views

### Probability of winning in a 3 slots game with 9 types per slot [closed]

The game is as follows: you have three slots: [1][2][3] with the same 9 fair types for each slot. When all the slots are the same its a win, doesn't matter the type....
• 23
75 views

### Basic probability independence in roulette

I am teaching my students how roulette works and we were talking about the probability of betting on the first column of numbers $\{1,4,7,10, 13, 16, 19, 22, 25, 28, 31, 34\}$ and the probability of ...
60 views

### Calculating payout amounts for a game with scoring

Say I have a hypothetical computer gambling game that is very basic and just involves the player trying to score points before dying - with a score of 5 points being the maximum (beating the game). ...
33 views

### Estimating implied probability based on prediction betting odds

I am attempting to estimate prediction betting market efficiency for a project, and I am hoping for assistance with a couple of questions. The prediction market makers add a commission to the betting ...
• 181
1 vote
194 views

### A stock today price 100, tomorrow it becomes 50 or 200. There is also a casino you could bet win/loss with rate 1:1. Strategy

A stock today price 100, tomorrow it becomes 50 or 200. There is also a casino you could bet win/loss with rate 1:1. What is your strategy to make money? I denote the probability of stock rises the ...
163 views

### Optimal Betting Strategy in Coin Toss

Goal: Participate in a coin-tossing game with the aim to maximize your earnings. A fundamental part of the game is formulating a strategy that optimizes your earnings based on the observation of the ...
52 views

### Probability of going broke before reaching target with positive expected value.

In an interview today, I was given a hypothetical situation in which I can bet on the outcome of a biased coin (0.6H, 0.4T). I can bet £1 at a time; if I win i get my stake back and an extra £1, ...
• 111
1 vote
259 views

### Why is the Gambler's Fallacy a fallacy? [Solved]

The empirical probability distribution of the coin tossing bet is binomial distribution. For a fixed length of sequential events, it shows that the more balance the number of Heads strikes between the ...
• 47
1 vote
322 views

### Minimum probability of winning a bet

I have the below scenario. Suppose you are playing a game where you and your opponent have put $\$10$in the pot each. Your opponent bets another$\$10$. What is the minimum probability of you ...
• 264
231 views

### Counterfeit money, guaranteeing a profit

Bob and I found two 50 dollar bills out of nowhere. We know they're either both legitimate or both counterfeit. If they're legitimate, they're worth 50 dollars each, otherwise 0. I get one 50 dollar ...
• 337
83 views

### Maximizing Geometric Growth Rate (Kelly Formula) By Betting On Multiple, Non-Mutually Exclusive Events

Stack Exchange has many posts regarding bet sizing on multiple, mutually exclusive/independent events/gambles. I'm curious if anyone is familiar with using Kelly to bet on 1+ gambles that are not ...
• 181
288 views

### Boss Loot Drop Rate Probability

Scenario A: In a game, every time you beat a boss, you have a chance of receiving a drop. The base drop rate at zero wins is $1.5$%. This drop rate increases by $0.5$% after each win. So, your chance ...
136 views

### Football betting. How can I calculate the stake values for 2 teams to give the same profit whichever team wins taking into account both stakes? [closed]

I am trying to implement this formula using a spreadsheet (currently Libre Calc) but any mathematical advice will be gratefully accepted. Let's say, as an example, there are two teams with the ...
• 109
54 views

### Given the win odds of a horse race are known plus other info such as top 3 place odds, calculate the 2nd/3rd/4th place odds for each horse.

I have a problem where I am trying to calculate the place odds given win odds and other info such as top 3 place odds. I have used Harville's method successfully to calc place odds given we know the ...
• 1
244 views

### simplify the sum of this binomial coefficients -- generalized gambler ruin problem

While solving recursion $p_i = p_{i-B} (1-\alpha) + p_{i+1} \alpha$, related to a special gambler ruin problem, we came across the following summation. Let $0$ and $K$ be the extremes of the gambler ...
• 853
1 vote
60 views

### Average cost of an item from container with different chances [closed]

i need to find average cost for every item in container. It costs 50 currency to open one. I have following chances for items: lvl-1: 58% ...
• 13
1 vote
91 views

### Find the Mistake In My Calculation For the Odds of Hitting The Fire Bet In Craps.

Background Information: Inside the game of craps, one of the most notorious bets, the fire bet, is known for being exceptionally complicated and hard to win. In order to hit the fire bet, every ...
• 37
1 vote
57 views

### Closed Solution for Expected value of Martingale Strategy for 10 bets with 70% odds

I was answering a question on Reddit and could only answer by simulation via code rather than figure out the math. https://www.reddit.com/r/gambling/comments/15jualm/gambling_math_question/ If you are ...
• 111
113 views

• 71
951 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
275 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