# 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.

84 questions
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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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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 $r_2$...
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### 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 ...
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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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### 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 ...
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### 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 ...
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: ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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:...
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### 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 ...
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### 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 ...
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, ...
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, ...