Consider the following three games. Which one would you be most likely to play?
ID: 3132259 • Letter: C
Question
Consider the following three games. Which one would you be most likely to play? Which one would you be least likely to play? Explain your answer mathematically.
Game I: You toss a fair coin once. If a head appears you receive $3, but if a tail appears you have to pay $1.
Game II: You buy a single ticket for a raffle that has a total of 500 tickets. Two tickets are chosen from the 500. The holder of the first ticket selected receives $300, and the holder of the second ticket selected receives $150. (You don't pay for the ticket)
Game III: You toss a fair coin once. If a head appears you receive $1,000,002, but if a tail appears you have to pay $1,000,000
Explanation / Answer
Game-1
Expected Gain=0.5*3-0.5*1=$1,Here I am paying 1$ if i lose and i get 3$ if I win.
Game-2
Expected Gain=(1/500)*300+(1/499)*150=0.9$ but here its for free,I am not supposed to pay even if I lose.
Game-3
Expected Gain=0.5*1000002-0.5*1000000=1$,But here there is a 50% chance of huge lottery and a 50% chance of going bankrupt.
Though the expected gain is the same in Game 1 and Game 3,There is a chance of a loss,whereas Game 2 doesnt have a chance of loosing.I need not pay anything.I just have a upside profit(if it occurs).
I as a person,would not play Game3,as there is a huge downside loss,and would happily play Game 1 as it has a chance of an upside profit.Game 2 isnt played because the chance of winning is 2 in 500.