Expected Value of Gambling Game: Solve It Now!

In summary, the game involves rolling a die and pulling a card from a deck. If the die lands on a 3, you move on to the next step. If the card is a heart, you win $100. The expected value of the game is determined by the probability of getting a 3 and a heart, which can be calculated using the formula E[X] = 100 * P[X=3 and a heart].
  • #1
eatinbyzombies3
3
0
Here is the question: You are playing a gambling game (silly, yea I know). The first part of the game is to throw a die. If it comes up a 3, you move on. Otherwise, you lose. The second part of the game entails pulling a card out of a standard deck. If it is a heart, you win $100. Otherwise, you lose. What is the expected value of the game?

Here is what I know: you have a 1 out of 6 chance of rolling a 3 and a 13 out of 52 (i hope) chance of pulling a heart.

I don't know how to get the answer that is needed. Can anyone help me?
 
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  • #2
Re: help, I am confused

Are you supposed to find the expected profit? If so, what is the buy-in to the game?

edit: I have edited the topic title to reflect the nature of the problem.
 
  • #3
MarkFL,
I don't know. that is the question word for word that I have on my paper from my Professor. That is what is confusing, it just says "What is the expected value of the game?"
 
  • #4
Are you given an answer that you are expected to be able to compute?
 
  • #5
\(\displaystyle E[X]=\sum_{x} x \cdot P[X=x]\)
That seems complicated but it's not so bad. Assuming there is no buy-in to play the game and that the only payout occurs when you get a 3 and a heart, the above equation simplifies to:

\(\displaystyle E[X]=100 \cdot P[X= \text{3 and a heart}]\)

Now you just need to figure out that probability of getting a 3 and a heart and you'll be done. :)
 

Related to Expected Value of Gambling Game: Solve It Now!

What is "Expected Value" in a gambling game?

"Expected Value" in a gambling game refers to the amount of money a player can expect to win or lose on average over a large number of bets. It is calculated by multiplying the probability of winning or losing by the amount won or lost in each outcome, and then summing these values together.

Why is "Expected Value" important in gambling?

"Expected Value" is important in gambling because it helps players make informed decisions about whether or not to participate in a particular game. A positive expected value indicates that a game is likely to bring in profits over the long term, while a negative expected value means that the player is likely to lose money in the long run.

How is "Expected Value" calculated in a gambling game?

"Expected Value" is calculated by multiplying the probability of each outcome by the amount won or lost in each outcome, and then summing these values together. For example, if a player has a 50% chance of winning $10 and a 50% chance of losing $5, the expected value would be (0.5 x $10) + (0.5 x -$5) = $2.50.

Can "Expected Value" be used to predict the outcome of a single bet?

No, "Expected Value" cannot be used to predict the outcome of a single bet. It is an average value that is only useful when considering a large number of bets. In the short term, individual outcomes may deviate from the expected value, but over time, the expected value will hold true.

How can "Expected Value" help players make better gambling decisions?

By understanding "Expected Value," players can make more informed decisions about which gambling games to participate in. Games with a positive expected value are more likely to bring in profits in the long run, while games with a negative expected value should be avoided. However, it is important to remember that expected value is not a guarantee and outcomes may vary in the short term.

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