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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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Is it fair to play the game for $1000 [closed]

In a game where a fair coin is tossed 100 times, the player wins \$60,000 if more than 60 heads appear. The cost to play the game is \$1,000. Is it fair to play the game based on the expected value?
Valiant Tyro's user avatar
0 votes
0 answers
33 views

Betting Odds Optimization Problem [closed]

A friend recently introduced me to polymarket, which allows people to bet on real life events such as the presidential election. Whilst not a bettor myself, I noted that the odds market is sub-...
Conscientious Bettor's user avatar
0 votes
0 answers
52 views

Conditional Probability and Betting Stakes Problem

I recently came across a conditional probability problem that's used in a betting scenario( problem attached below). And my question is how does one know which stake to use for a given bet in order to ...
Man Dem's user avatar
2 votes
0 answers
37 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 ...
Mario Diw's user avatar
5 votes
1 answer
199 views
+50

Long term probability of going bankrupt?

Suppose there is a coin flipping game where you start with 5 dollars. At each turn, there is a $p$ probability of winning 1 dollar and a $1-p$ probability of losing 1 dollar. The game ends at 0 ...
konofoso's user avatar
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0 votes
0 answers
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 ...
splake's user avatar
  • 11
0 votes
1 answer
168 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 ...
PotusOtis's user avatar
  • 135
0 votes
1 answer
29 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 ...
Abhay Agarwal's user avatar
0 votes
1 answer
30 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 ...
Abhay Agarwal's user avatar
1 vote
1 answer
60 views

Mistake in Conditional Probability/Betting question approach

Problem You and your friend draw a number from [0, 100] uniformly at random. You are given the option to redraw your number once you've drawn the first time. Whoever has the higher number wins 20$. ...
Abhay Agarwal's user avatar
1 vote
2 answers
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 ...
Abhay Agarwal's user avatar
2 votes
0 answers
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 ...
ghiufhe's user avatar
  • 95
2 votes
1 answer
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 $1$ ...
thefool's user avatar
  • 1,128
2 votes
1 answer
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 ...
xiver77's user avatar
  • 415
1 vote
1 answer
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 ...
Rich's user avatar
  • 236
0 votes
2 answers
75 views

Probability: Starting with $\$200$, chance of winning $\$100$ by placing on black in Roulette?

Suppose we want to win $\$100$ playing Roulette by putting our chips on black, starting with $\$200$. That is: ending up with $\$300$. If we place all our chips on black, then the chance of winning $\$...
Jason Born's user avatar
  • 1,038
0 votes
1 answer
125 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 ...
Julien Maas's user avatar
0 votes
0 answers
34 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 ...
user146125's user avatar
0 votes
0 answers
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 ...
AlexS123's user avatar
0 votes
0 answers
70 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 ...
Eric Aldrin's user avatar
-3 votes
1 answer
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 (...
steveK's user avatar
  • 137
-3 votes
1 answer
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 ...
Big T Larrity's user avatar
0 votes
1 answer
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. ...
guipivoto's user avatar
  • 109
2 votes
1 answer
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 ...
WolfgangP's user avatar
  • 224
1 vote
0 answers
78 views

Probability of winning a multiple-round game, where a player needs to get to $n$ points before losing all their initial point.

I'm trying to do the following problem in Sheldon Ross' A First Course In Probability (page 86-87). EXAMPLE $4k$. Suppose that initially there are $r$ players, with player $i$ having $n_i$ units, $...
ensbana's user avatar
  • 2,307
2 votes
0 answers
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 ...
quantrader23's user avatar
0 votes
1 answer
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....
cheeser's user avatar
  • 23
0 votes
1 answer
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 ...
CCHS Math's user avatar
0 votes
0 answers
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). ...
George's user avatar
  • 1
0 votes
0 answers
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 ...
findingmyway's user avatar
1 vote
0 answers
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 ...
SteppenSheep's user avatar
2 votes
0 answers
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 ...
Raphaël Krief's user avatar
0 votes
0 answers
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, ...
Sylith's user avatar
  • 111
1 vote
5 answers
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 ...
User's user avatar
  • 47
1 vote
1 answer
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 ...
Bell's user avatar
  • 264
3 votes
2 answers
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 ...
Computers's user avatar
  • 337
2 votes
0 answers
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 ...
findingmyway's user avatar
-1 votes
1 answer
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 ...
Vincent's user avatar
-1 votes
1 answer
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 ...
kerry's user avatar
  • 109
0 votes
0 answers
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 ...
pos's user avatar
  • 1
0 votes
0 answers
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 ...
Daniel S.'s user avatar
  • 853
1 vote
1 answer
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% ...
eagle.s's user avatar
  • 13
1 vote
2 answers
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 ...
Kyotiq's user avatar
  • 37
1 vote
0 answers
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 ...
Evan's user avatar
  • 111
0 votes
0 answers
113 views

Hedging bets on two independent events?

Let us say that there are two independent events $A$ and $B$. Event $A$ occurs with probability $0.3$ and event $B$ occurs with probability $0.4$. You can bet on these events with odds of $3:1$ and $7:...
Danjx's user avatar
  • 329
0 votes
1 answer
60 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 ...
C18's user avatar
  • 71
8 votes
2 answers
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 ...
Anon's user avatar
  • 453
0 votes
0 answers
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 ...
Xiutecuhtli's user avatar
1 vote
2 answers
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 ...
vietajumping's user avatar
1 vote
0 answers
142 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 ...
math's user avatar
  • 121

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