Probability with gambling?

Question

You are offered an opportunity to play a game with payoffs of $ 50, $ 5, and $ 1.

You have to pay $ 3 to play the game. The rules states that the probabilities for the pay-offs are as shown in the table below.

(a) Complete the table, recalling that this is a probability model.

Dollar Results Win 50 Win 5 Win 1 Lose 3

Probability 0.005 0.1 0.55 ?

(b) Calculate your expected value in this game.

(c) How much do you expect to win or lose after 1000 plays?

Use a + to indicate winnings and - to indicating losses.

Answer 1

I gave borg a thumbs up, he is right on.

This sounds like a game an Indian Casino would offer! LOL

Good luck all, and have a happy 4th of July!

Answer 2

i disagree with borg since he deducted the initial wager from the amount won, which alters the definition of the amount won.  His math is spot on but since the amount won coudl be questioned the numbers may be innaccurate.  I will provide the alternate answers based on a more casino like interpretation of the payouts.

A.  the probibility of a loss fills in all remaining events which will occur at a frequency of [1-(0.005+0.1+0.55)]=0.345

B.  On average per bet you will gain/lose is the sum of all payouts times their frequency.

+0.005X50=0.25

+5X0.1=0.5

+1X0.55=0.55

-3X0.345=-1.035

sum=$0.265

At this point we have now realised that the ev since on avreage we will get back our 3 dollar bet plus 0.265. the total return for each bet is now 3.265 so to get the EV you woudl divide 3.265 by the amoutn bet of 3  and you get 3.265/3=1.088  

*****in percent your EV is +8.8%****

C.  To calulate expected loss/gain you just multiply the EV time the total amount wagered, in this case 1000bets times 3 dollars times +8.8% for the amoutn ****gained or lossed*** not the average total amount on hand after wagering.

It would be 1000x3x0.088= +264 dollars

Answer 3

a. x = 1 - (.005 + .1 + .55) = 0.345

b. EV = (47 * .005 ) + (2 * .1) + (-2 * .55) + (-3 * .345) = $-1.7 per attempt.

c. -1.7 * 1000 = $-1,700

Answer 4

That looks right other than mentioning the fact that only an idiot would play this game :)

A.J.

http://kingcobrapoker.com