The Price Is Right!

[zuluking]

I'm watching The Price Is Right this morning (I have no life), while playing online and this happens......

Showcase Showdown wheel spin. 1st person spins a 95, 2nd person spins and 50 and then a 45. 3rd person spins a $1.00. What are the odds?

[fluff]

I saw one episode where both contestant hit 100 twice and finally on the third turn the tie was broken when one contestant hit 100 and the other one didn't.

I'm not sure how many numbers are on that wheel although I think it's 20?

[Homer]

Do you want the probability of all three players getting 95 cents or more, or of the first two getting 95 cents and the last getting 1 dollar?

The probability of all three getting 95 cents or more is:

(2/20 + 18/20*2/20)^3 = .006859 = .6859% = 144.8:1

However, I made a flawed assumption that players will always spin twice unless they get 95 cents or a dollar. If you know the amount that the first player is willing to stay at, then you can solve the problem properly. Additionally, I'm assuming that if the first player gets 1.00 and the second player gets .95, it doesn't count (you want everyone to stay until the end, right?). Anyhoo, if the first player will stay at 70 cents and spin again at 65 cents or less, the answer would be:

P(1) = (2/20 + 13/20*2/20) = .165

P(2) = 1/2(1/20 + 19/20*1/20) + 1/2(2/20 + 18/20*2/20) = .14375

* Of the times the 1st player gets .95 or 1.00, 1/2 the time it will be .95 and 1/2 the time it will be 1.00.

P(3) = 3/4(1/20 + 19/20*1/20) + 1/4(2/20 + 18/20*2/20) = .120625

* Of the times both the 1st and 2nd player get .95 or 1.00, 3/4 of the time at least one will have 1.00 and 1/4 of the time both will have .95.

P(all 3 get .95 or 1.00 and survive until end of round) = P(1)*P(2)*P(3) = .002861 = .2861% = 348.5:1

It's highly possible I screwed up the math somewhere along the way.

-- Homer

[brassnuts]

The wheel is not completely random. People are aiming for the 100 slot.

[Homer]

Some, yes, but not many. The best is when there's a strong guy who whips the thing around like 30 times. The wheel looks like it's about to snap off.

[zuluking]

Jesus Homer! /images/graemlins/grin.gif

[M.B.E.]

For anyone interested in the mathematics of "The Price is Right":

http://tinyurl.com/22f5s

http://tinyurl.com/2dd8g

[M.B.E.]

One of the links in my previous post wanted you to pay $29 for access to the article. Here are two links where you can obtain a pdf version free (unclear whether this is the final version, however):

http://www.mgmt.purdue.edu/faculty/cason/papers/Wheel.pdf

http://fac.comtech.depaul.edu/rtenorio/Wheel.pdf

[Homer]

Anyhoo, if the first player will stay at 70 cents and spin again at 65 cents or less, the answer would be:

Me intuition good.

[Nottom]

OK enough abou tspinning the Price is Right wheel, when is someone going to figure the EV of spinning the wheel on Wheel of Fortune vs. Solving the puzzle when there are still a few letters to be uncovered?