Can Gambling and Probability Puzzles Enhance Cognitive Skills?

• His_Dudeness3
In summary, the probability distribution for a single game of roulette is as follows: the player has a 33.3% chance of coming out ahead, with a gain of $1 on each successful game. His_Dudeness3 Hey everyone, I was given this fun little probability question from my tutor after I finished early in one of my classes about three weeks back, and I just can't seem to crack it! Something about gambling and probability makes my brain go haywire (or maybe its some other, deeper problem ). Anyway,here it is, and have fun! A roulette wheel is numbered from 0 to 36. 0 is Green. Half of numbers are Red and half are Black. The game has an entrance fee$1. The player then stakes
$10 and must choose the parity (Odd or Even) and the color (Red or Black). If he gets right parity or color$12 is returned, that is a gain is $1. If he get right both parity and color$20 is returned, , that is a gain is $9. If he does guesses neither correct color nor parity, and the number is not 0, then the entrance fee$1
is returned. If 0 comes up, the player gets nothing.

(a) If X is the gain on a single game, complete the table of the probability distribution
of random variable X:

(b) Find E(X) and standard deviation of X

(c) If player plays twice, what is the probability that he comes out ahead (i.e.
positive net gain).

(d) If player plays this game fifty times, find the mean and standard deviation of
his overall net gain.

(e) Use your answer to part (d) and a suitable approximation to calculate the
probability of coming out ahead after playing fifty games.

(f) Given a roulette wheel where the half of odd numbers are Red and half are
Black, and similarly for even numbers, check that color and parity appear
independently.

Doesn't look that interesting to me.
a)b) Analysing the question (pretty simple)
c)$$Pr(X_1+X_2>0)$$ use conditional probability to solve that (Law of Total probability)
d) Use linearity of expectation and the indipendence for the variance.
e)Depends on d) but my hunch is that you can work out how many s.d. the mean is away from zero and use that.
f)no idea what that is asking for

Focus said:
Doesn't look that interesting to me.
a)b) Analysing the question (pretty simple)
c)$$Pr(X_1+X_2>0)$$ use conditional probability to solve that (Law of Total probability)
d) Use linearity of expectation and the indipendence for the variance.
e)Depends on d) but my hunch is that you can work out how many s.d. the mean is away from zero and use that.
f)no idea what that is asking for

For some reason, I can't figure out if the distribution I get for part (a) is correct (as pretty much the rest of your answers would be wrong if you don't get the right distribution):

x -11 -10 1 9
Pr(X) (1/37) (32/37) (2/37) (1/37)

Can anyone clarify if this is correct?

this is not interesting at all, nor is this even close to the payout scheme of roulette

1. What is the difference between probability and gambling?

Probability is a measure of the likelihood that an event will occur, while gambling is the act of risking money or something of value on an uncertain outcome. While probability can be used to calculate the chances of a certain outcome in gambling, there are other factors such as luck and skill that also play a role.

2. How do casinos use probability in their games?

Casinos use probability to ensure that they have a mathematical advantage in every game they offer. This means that over time, they will make more money than they pay out to players. For example, in roulette, the probability of winning on a single number bet is 1 in 38, giving the casino a 5.26% edge.

3. Can probability be used to beat the odds in gambling?

While probability can give players an idea of their chances of winning, it cannot guarantee a specific outcome. In the long run, the odds will always favor the house in casino games. However, certain strategies and techniques can be used in games like poker to improve the chances of winning.

4. How does the concept of expected value relate to probability and gambling?

Expected value is a concept in probability that represents the average outcome of a series of trials. In gambling, it can be used to calculate the potential winnings or losses of a particular bet. For example, if a bet has a 50% chance of winning $10 and a 50% chance of losing$5, the expected value would be ($10 x 0.5) + (-$5 x 0.5) = \$2.50.

5. Is it possible to predict the outcome of a gambling game using probability?

No, it is not possible to predict the outcome of a single gambling game using probability. Probability only gives an idea of the likelihood of certain outcomes based on past events and mathematical calculations. The outcome of each game is ultimately determined by chance and cannot be predicted with certainty.

• General Math
Replies
11
Views
2K
• General Math
Replies
1
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
53
Views
6K
• General Math
Replies
9
Views
3K
• Calculus and Beyond Homework Help
Replies
1
Views
2K
• General Math
Replies
5
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
5
Views
3K
• Set Theory, Logic, Probability, Statistics
Replies
5
Views
4K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
3K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
9K