Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

3
votes
1answer
151 views

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 ...
2
votes
1answer
74 views

If I draw 4 cards from a standard deck of 52, what is the probability the cards add to 20?

Assume the cards have the following values: K, Q, J, = 10 Ace-10 = 1-10 The long way to do this would be to calculate ways the cards can add up to 20 and divide by $50C4$ and do this for every ...
2
votes
1answer
54 views

Even-Money Gambling Expectation

You are playing a gambling game with a probability of $p$ of winning between (0.5, 1). You start with $Y_0$ money. Each round, you bet a fraction $k$ of that money. If you win, you get all your money ...
5
votes
0answers
400 views

How did Mohan Srivastava crack Ontario scratchcards?

Wired ran a 2011 article about how a statistician, Mohan Srivastava, cracked Ontario scratchcards such as this one. First, he thought about the program that produced the numbers on the cards. 'Of ...
4
votes
0answers
59 views

Expected number of coin tosses with a coin that changes over time

Imagine that I have a coin that changes monotonically over time. -- casino example -- (This is not necessary to understand mathematical problem, but just can help to imagine a real life situation, ...
4
votes
0answers
394 views

Applying Kelly Criterion to profit/loss bet

In a financial derivative trading situation, there are two outcomes to a bet (win/lose), but I don't necessarily lose my entire stake if I lose the bet, because I can buy my way out of the bet, taking ...
3
votes
0answers
1k views

Coin flip: Double or Nothing

I have an amount of chips to bet on a fair coin flipping and landing on heads. For each time in a row that it does land on heads, the amount of chips in the bet is doubled by the house, and I am able ...
2
votes
0answers
34 views

Potential strategy in a random game

Suppose there are two betting games $G_1$ and $G_2$, the outcomes of which are entirely independent of player input. The expected return for a single iteration of $G_1$ is $r_1$ and for $G_2$ is $r_2$...
2
votes
0answers
41 views

Expected profit from true and payoff odds

The true odds against event $E$ are $r$ to $1$ and the payoff odds are $t$ to $1$. You bet an amount $B$: You win $tB$ if the event occurs. You lose $B$ if the event does not occur. How do you ...
2
votes
0answers
116 views

Is there a generalization of the Kelly criterion where we add a fixed income/cost?

In the ordinary Kelly criterion the game is that you get to place a bet $B$ and your new wealth would be: $$W^+ = \begin{cases} W + cB & \text{ with the probability of }p\\ W - B & \text{ ...
2
votes
0answers
343 views

Proof that the Kelly Criterion is optimal?

Let's say you are betting on the outcome of some random variable. You can invest any amount $X$, and each outcome multiples that amount $X$ by a certain amount $ \ge 0$. You must choose $X$ less than ...
2
votes
0answers
60 views

Creating a bad outcome as a bookie?

I found this question from Ian Hacking's book on induction and probability. I understand that a Dutch Book is a gambling term wherein every outcome results in the bookie (us) winning. Although, the ...
2
votes
0answers
136 views

Sufficient number of riffle shuffles for randomizing a deck of n cards.

It has been proven previously that for a deck of $52$ cards, $7$ randomized riffle shuffles are enough to randomize the deck to the point that any further riffle shuffles will not meaningfully get the ...
2
votes
0answers
784 views

How to statistically beat this dice game?

There is a dice game on this site where you can bet a video game's currency in games. I was wondering if any of the more statistically minded could come up with a way of beating the system? The game's ...
2
votes
0answers
102 views

Is there a better way for calculating the odds for the horserace card game?

horserace card game in progress Game: The 4 aces ("horses") are laid face-up at one end of the table. 6 cards face-up are laid ("race track") in a straight line perpendicular to the aces. The race ...
2
votes
0answers
122 views

Optimal solution for the Iowa Gambling Task?

The Iowa Gambling Task is used to demonstrate our intuition with statistics and probability. Essentially the subject sits in front of four decks. Each round, the participant can draw from any deck of ...
1
vote
0answers
30 views

Gambler's ruin vs point difference

Two people want to investigate who is best at playing Scrabble. They decide to settle this by playing a series of games. Assume that there is always a winner for each game, and that winning or losing ...
1
vote
0answers
27 views

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 ...
1
vote
0answers
59 views

How to maximize geometric means of investments?

Say you have a gamble. With 50-50 chance you lost your money. With another chance your money triples. So on average you make 1.5 times money you "invested". So if you have $1$ to invest you can ...
1
vote
0answers
1k views

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 *...
1
vote
0answers
69 views

In 3 way-outcome betting, what is the corresponding 1 back + 1 lay bet of 2 back bet

In Soccer-Game we have three outputs, win / draw / loose, with corresponding quotes q1 / q0 / q2. Now suppose we would like to bet x to win and y to draw. We have two back quotes. In Exchanges, ...
1
vote
0answers
132 views

Creating betting strategy for variable payout game

Lets say I have a game where you choose a bet and then you and a computer choose a random multiplier. If you guessed lower or equal to the computer, you win your bet times the multiplier you guessed. ...
1
vote
0answers
312 views

How do i calculate the increase and decrease of betting odds depending on demand?

I am trying to find out a formula that helps me calculate the variance i need to add or subtract from an odd to match the demand. For exmple: Let's say we have two teams, team A and team B. Both ...
1
vote
0answers
55 views

Variance of the gain, given a set of wagers on $n$ Bernoulli trials

Let's assume we want to wager on a given set of n Bernoulli trials with probabilities $p_i$ with $i \in \{1, 2, ..., n\}$ and a corresponding payoff odds $b_i$, i.e., betting a certain percentage $f_i ...
1
vote
0answers
75 views

Given entropy, re-estimate odds

An RNG is reported to have an entropy of $2.521$ bits for 6 results. This is biased from a uniform random system which would have $2.585$ bits at maximum entropy. You want to create a betting game ...
1
vote
0answers
154 views

Has this generalization of gambler's ruin been studied?

I looked around to see if I could find a duplicate of this question and I found this Probability of Gambler's Ruin with Unequal Gain/Loss which is very close but lacking in the main ...
1
vote
0answers
60 views

Number of tries required to have a 50% or better of winning

I'm trying to set up "spin the fruit machine" for our summer fair. There will be $T$ tumblers, each with $N$ options. So the total number of possibilities is $T^N$. Ideally, I want the chances of ...
0
votes
0answers
14 views

How to calculate spread on gambling odds?

I'm trying to calculate the spread on a bet. People are telling me it's either 10% (absolute) or 17% (relative). I'm failing to see how to get either number. Bet is below: Context: Which stock ...
0
votes
0answers
24 views

How to use Wald's equation to determine expectation in gambling model?

$\begin{array}{l}{\text { In each game played one is equally likely to either win or lose 1. Let } S \text { be your }} \\ {\text { cumulative winnings if you use the strategy that quits playing if ...
0
votes
0answers
22 views

Calculate the probability of poker winning hand type (combination)

There are a lot of libraries that calculate the winning probability of texas holdem poker player and the probability of each player having some combinations(pair, straight...). Does anyone know where ...
0
votes
0answers
32 views

Winning a game probability

Suppose you are tied $1-1$ with Bob. To win the game, you have win greater than or equal to $5$ rounds and win at least $2$ more rounds than your opponent. The probability of winning a round is $40\%$ ...
0
votes
0answers
14 views

Random Walk on a number line and further cases

i) A monkey is sitting on 0 on the real line in period 0. In every period t ∈ {0, 1, 2, . . .} it moves 1 to the right with probability p and 1 to the left with probability 1−p, where p ∈ 1 2 , 1 . ...
0
votes
0answers
18 views

Expected value: random prizes until occurrence of termination 'prize'

I have 10 boxes of which 9 have a coin and 1 is empty. I can choose boxes and keep the prizes until the empty one appears. What's the expected value? First I thought: $E$ must the the mean between ...
0
votes
0answers
50 views

Probability question. Roulette dozens bet occurring consecutively.

Hello Mathematics Guru's, Can I first caveat this question by saying, I'm wholly aware the house always has a mathematical edge if you play long enough in Roulette, but i am interested to know the ...
0
votes
0answers
33 views

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, ...
0
votes
0answers
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{...
0
votes
0answers
37 views

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 ...
0
votes
0answers
61 views

Probability that one trial is a successful trial for events related to an Urn Problem

Consider an urn $C$ which contains three (distinguishable) kinds of elements, say $\alpha>0$ elements of kind $A$, $\beta>0$ elements of kind $B$, and $\gamma>0$ elements of kind $G$. We ...
0
votes
0answers
38 views

Calculating Kelly Criterion of a tiered payout

There is a bet, which can payout different amounts based on the result. possible results, in units, would be: +30 +10 +6 +4 +2 +1 0 -1 How do you calculate the Kelly Criterion for this? I know the ...
0
votes
0answers
615 views

Calculate expected goals from given odds

I'm trying to work out a formula to calculate the expected number of goals in a soccer match, using only odds data provided by a bookmaker: ...
0
votes
0answers
21 views

Percentage of time one projected value will be higher than another given means and standard deviations

I'm hoping someone might know the correct mathematical way to approach this. The best way I can frame it is in terms of sports betting. Let's say I project the New York Yankees to score 5 runs today, ...
0
votes
0answers
29 views

An event has a 90.1 percent chance of happening. What is the probability of of triggering this event 70 times consecutively

I have come up with a progressive betting strategy on a cryptocurrency gambling website for a random number generator game (between 0.01 and 99.99,) Basically if it rolls 9.9 or under, I win 10 times ...
0
votes
0answers
56 views

Optimal wager strategy for high win chance / high odds game

In a rigged game of chance where statistically I am expected to win, is there a difference between betting the same amount of money each time (for example using Kelly criterion) vs using variable ...
0
votes
0answers
90 views

Gambler's Ruin Problem: Finding a probability given specific duration, starting balance, and ending balance

I am working on Grimmet's Probability and Random Processes and encounter a problem of this style. In a betting game, we start with a balance of \$k. For each turn, we bet \$1, and the winning ...
0
votes
0answers
136 views

Math odds versus gambling odds

As far as I remember the mathematical concept odds is defined as: the probability something is true divided by the probability that it is not. Or as Wikipedia puts it: the ratio of the ...
0
votes
0answers
31 views

Expected number of points

Using the work made by the authors of the paper below, I have used the same type of recursive formulas for badminton. Not really sure how I can share my work, but at least I want to share my findings:...
0
votes
0answers
235 views

risk of ruin in coin flip game against an infinite bank

Mark and Alice agree to play the following game: they will flip a fair coin, with the winner receiving even money, and will play this game over and over until one side is wiped out. Mark has a finite ...
0
votes
0answers
37 views

Need help verifying my program using statistics

I'm writing a video poker simulator and I am trying to verify it is working correctly by looking at the results. To understand the operation, it works as follows: Generate a random hand Apply a ...
0
votes
0answers
46 views

Why is maximising expected monetary value not plausible for large amounts of money?

My teacher asked us which of these gambles do you prefer: $g_1=£500,000$ $g_2=0.1£2,500,000 \oplus 0.89£500,000 \oplus 0.01£0$ The EMV for each gamble is £500,000 and £695,000 respectively, ...
0
votes
0answers
615 views

Effect of Gambler's Ruin Bet Size on Duration

Suppose we have a classic Gambler's Ruin problem as follows: Person A starts with $100$ dollars, and will keep betting $10$ dollars each round until he either reaches $180$ dollars or goes broke, ...