Consider the following game. You and a friend are given theopportunity to play a winner...

Consider the following game. You and a friend are given the opportunity to play a winner take all game worth $20 dollars. The rules are such that twenty $1 bills are placed on a table. Players take turns picking up one, two, or three of these $1 bills. (For example, you could take three of them and then your friend could take one, then you go again and could take two of them, etc.). The person who picks up the last dollar bill gets all the money. Do you want to go first or second in this game and why?

Expert Solution

I want to go second.
reason: When my friend and I play rationally, each of us would like to maximize our winning. If I go second, I may pick 1, 2 or 3 after my friend has picked his choice. The game will be repeated for 4 rounds. Let us assume the note will be picked in the order --- 3, 2 , 1. In four rounds, 17 notes will be picked. 18th pick will be 1 note which my friend will pick. Now there are 2 notes which I will pick. Therefore, I will get all the notes.

So, if I want to all the money, I should go second.

This game is illustrated below:

Rahul Sunny answered 2 years ago

In this game, there is only one deck of cards. You play with a friend and...

In this game, there is only one deck of cards. You play with a friend and the deck of cards belongs to him/her. Numbered cards are worth their face value, jacks are worth 11, queen 12, kings 13 and aces 14. You have a suspicion that in this deck of cards, your friend has replaced some high cards in the deck with low cards. You take 10 cards and quickly calculate the average value: 4.5. You do the math: In...

A friend offered to play a game with you where you select 1 marble out of...

A friend offered to play a game with you where you select 1 marble out of 100: 40 red 30 blue 20 yellow and 10 green. If you pick a red marble you lose $1, if you pick a blue you win $2, if you pick a yellow you lose $5 if you pick a green you win $10. Each time you pick a marble it will go back into the bag. Round to 2 decimals and show work. a)...

Consider the Stage Game below, and consider the repeated game where players play twice (T =...

Consider the Stage Game below, and consider the repeated game where players play twice (T = 2). Payoﬀs for each agent are simply period one plus period two payoﬀs. L C R T 6,6 0,7 1,2 M 7,0 1,1 2,0 B 2,1 0,1 3,3 (a) Do any strategies dominate any other? (b) What are the two NE of the Stage Game? What is the diﬀerence between the two? (c) Call the TL strategy proﬁle (1 plays T, 2 plays L)...

A friend proposes a unique game of chance to you. He swears the game is straightforward...

A friend proposes a unique game of chance to you. He swears the game is straightforward but you're not sure. He proposes, you flip a coin and then roll a dice and your payout is the amount showing on the dice. However if you flip heads, you roll a 6 sided dice, and if you flip tails, you roll a 10 sided dice. What is the expected payout from this game?

The probability of winning on an arcade game is 0.678. If you play the arcade game...

The probability of winning on an arcade game is 0.678. If you play the arcade game 24 times, what is the probability of winning no more than 12 times? (Round your answer to 3 decimal places, if necessary.)

Let’s suppose that you are going to play the lottery game Powerball. To play, you pick...

Let’s suppose that you are going to play the lottery game Powerball. To play, you pick five different numbers from 1 through 69 plus one Powerball number from 1 through 26. Which is a more likely combination of winning numbers: 1, 2, 3, 4, 5, 6 or 7, 21, 25, 32, 40, 56? Explain your answer. For a $500,000,000 jackpot, which of the two combinations would likely be more lucrative for you if it were to win? In other words,...

Suppose you are playing a game with a friend in which you bet ? dollars on...

Suppose you are playing a game with a friend in which you bet ? dollars on the flip of a fair coin: if the coin lands tails you lose your ? dollar bet, but if it lands heads, you get 2? dollars back (i.e., you get your ? dollars back plus you win ? dollars). Let ? = "the amount you gain or lose." (a) What is the expected return ?(?) on this game? (Give your answer in terms of...

Consider the following game: You start with $1. The game is over when you run out...

Consider the following game: You start with $1. The game is over when you run out of money. You flip a coin-----Heads means that you win $1 and Tails means that you lose $1 What is the probability that the game will end after: a. 1 flip of the coin? b. 2 flips of the coin? c. 3 flips of the coin? d. 4 flips of the coin? You can set up a tree diagram. You can show your explained...

Your friend won a lottery! However, the winner was not knowledgeable in finance but was aware...

Your friend won a lottery! However, the winner was not knowledgeable in finance but was aware that you are a student of finance at USQ. He did not want to share his secret with anyone in the neighbourhood except you of course. He was given a choice between accepting a lump sum of $200,000,000 or an immediate payment of $20,000,000 now and a further $20,000,000 every year for the next 10 years (making 11 payments of $20,000,000) at a time...

You pay $1 to play a game. The game consists of rolling a pair of dice....

You pay $1 to play a game. The game consists of rolling a pair of dice. If you observe a sum of 7 or 11 you receive $4. If not, you receive nothing. Compute the expected value and standard deviation for this game?

Question