Expected Value of Gambling Game: Solve It Now!

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Discussion Overview

The discussion revolves around calculating the expected value of a gambling game involving rolling a die and drawing a card from a deck. Participants explore the probabilities associated with each part of the game and seek clarification on how to compute the expected value, including considerations of potential buy-ins.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem, noting the probabilities of rolling a 3 and drawing a heart from a deck of cards.
  • Another participant questions whether the expected value should account for a buy-in to the game, indicating a need for clarification on the game's structure.
  • A third participant expresses confusion about the expected value calculation, seeking further details on the expected output.
  • A later reply introduces a formula for expected value, suggesting that if there is no buy-in, the expected value can be simplified to the product of the payout and the probability of winning.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on whether a buy-in is involved or how it affects the expected value calculation. The discussion remains unresolved regarding the specifics of the expected value computation.

Contextual Notes

There are missing assumptions regarding the game's rules, such as whether a buy-in is required and how it impacts the expected value. The discussion also reflects uncertainty about the interpretation of the expected value in the context of the game.

Who May Find This Useful

This discussion may be useful for students or individuals interested in probability, expected value calculations, and gambling game analysis.

eatinbyzombies3
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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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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.
 
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?"
 
Are you given an answer that you are expected to be able to compute?
 
$$E[X]=\sum_{x} x \cdot P[X=x]$$
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:

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

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

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