For questions about the mathematics behind gambling, such as the expected value of a game or the efficiency of a gambling strategy.
Questions tagged [gambling]
633 questions
97
votes
19 answers
Should I put number combinations like 1111111 onto my lottery ticket?
Suppose the winning combination consists of $7$ digits, each digit randomly ranging from $0$ to $9$. So the probability of $1111111$, $3141592$ and $8174249$ are the same. But $1111111$ seems (to me) far less likely to be the lucky number than…
arax
- 2,815
90
votes
10 answers
Would you ever stop rolling the die?
You have a six-sided die. You keep a cumulative total of your dice rolls. (E.g. if you roll a 3, then a 5, then a 2, your cumulative total is 10.) If your cumulative total is ever equal to a perfect square, then you lose, and you go home with…
Newb
- 17,987
- 14
- 70
- 116
39
votes
4 answers
±1-random walk from 5 until 20 or broke
You play a game where a fair coin is flipped. You win 1 if it shows heads and lose 1 if it shows tails. You start with 5 and decide to play until you either have 20 or go broke. What is the probability that you will go broke?
koon93
- 653
35
votes
11 answers
When to stop rolling a die in a game where 6 loses everything
You play a game using a standard $6$-sided die. You start with $0$ points. Before every roll, you decide whether you want to continue the game or end it and keep your points. After each roll, if you rolled $6$, then you lose everything and the game…
Kulawy Krul
- 471
27
votes
3 answers
Kelly criterion with more than two outcomes
I want to calculate the Kelly bet for an event with more than two possible outcomes. Suppose the following game:
A jar contains $10$ jelly beans. There are $7$ black jelly beans, $2$ blue jelly beans, and $1$ red jelly bean. The player wagers $x$…
25
votes
1 answer
How likely are you to win this multi-stage lottery?
The first round begins with a $\frac1{10}$ chance of you winning. If you win, congratulations! Once you have won, the simulation is complete. If not, you enter a second round. This second round gives you a $\frac1{100}$ chance of winning. If you…
MonitorLizard
- 353
22
votes
4 answers
Gambler's fallacy and the Law of large numbers
Can someone explain me, how the Law of large numbers and the Gambler's Fallacy do not contradict.
The Gambler's Fallacy says, that there is no memory in randomness and any sequence of events has the same probability as any other sequence.
However,…
clamp
- 669
18
votes
3 answers
Expected value of repeatedly betting on a coin flip?
Edit - I just stumbled across this YouTube video that explained this phenomenon very well so thought I'd include it here for future readers
Consider the following game:
You start with $1000
Flip a fair coin
If it's heads gain 21%, if it's tails…
pyjamas
- 299
17
votes
4 answers
100-sided die probability
The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the expected value of the game? There is no limit on number…
demyx999
- 681
16
votes
4 answers
How many tickets should Paul buy?
An old friend of mine who is now studying mathematics in Germany sent me an exercise from the German Mathematics Olympiads, which was thought for 16-years-old students.
Since I used to participate in MO, my friend asked me to help him with this…
Dr. Mathva
- 9,003
16
votes
4 answers
Asymmetric ruin probability
I have $50$ dollars and I’m gambling on a series of coin flips. For each head I win $2$ dollars and for each tail I lose $1$ dollar. What’s the probability that I will run out of money?
Hint: Suppose we have $x$ dollars, then the probability of ruin…
henry21
- 305
- 1
- 4
- 5
13
votes
2 answers
3 person bet based on the perceived likelihoods of an outcome
Suppose 3 friends want to bet \$100 on whether candidate John Doe will win the next election. They state their perceived likelihood that the event will occur:
Alice believes John Doe will win with probability $35\%$
Bob believes John Doe will win…
Rafael Magalhães
- 133
11
votes
3 answers
Kelly Criterion for simultaneous independent bets
I'm trying to obtain a more generic version of the Kelly criterion for when we have simultaneous independent events to bet on,
I'm going to focus on the case where we just have 2 different events.
In the case where we have just one event the…
jpceia
- 121
10
votes
2 answers
Does variance do any good to gambling game makers?
People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers?
In another word, what is a pratical gambling game that involving some distributions that is relating to variance other than…
Victor
- 8,498
10
votes
2 answers
Optimal strategy in betting game
You and your friend are playing a game. You both start with a score of $0$. Also, you both start with $\$1$. At each step, you're allowed to bet a fraction of your $\$1$, and whoever bets more money wins that "round". However, whoever wins the round…
user790132