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Wizard
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Wizard
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March 10th, 2022 at 7:52:10 PM permalink
We haven't analyzed a Price is Right game for a while. Let's remedy that by analyze the Spelling Bee game!


Direct: https://www.youtube.com/watch?v=S7nXtS3GwYQ

Here are the rules.

  1. There is a board containing tiles 1 to 30. Behind each number there is a C, A, R, or Car, distributed randomly. The distribution is as follows: C = 11, A = 11, R = 6, Car = 2
  2. The player immediately gets to pick two numbers.
  3. The player has an opportunity to win up to 3 more numbers playing a pricing game, which you can see in the video.
  4. The player wins a car if he can spell "C-A-R" (in any order) with the numbers he is given/earned. This can be done either with at least one each of the three letters in C-A-R, or at least one number with "CAR."


There is also a cash offer to surrender the game, but let's not confuse the issue with that, yet.

The question for now is what is the probability of winning the car given 2, 3, 4, and 5 tiles?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
charliepatrick
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March 11th, 2022 at 3:08:30 AM permalink
^ The above video shows up as unavailable, but one can find lots of videos by googling such as this one. https://www.youtube.com/watch?v=q3km2vSjFqo
Deucekies
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March 11th, 2022 at 4:19:08 AM permalink
I'll take the easy one. The probability of winning with two tiles is (2/30)+(2/30)=(4/30) or 13.3%.
Casinos are not your friends, they want your money. But so does Disneyland. And there is no chance in hell that you will go to Disneyland and come back with more money than you went with. - AxelWolf and Mickeycrimm
Joeman
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March 11th, 2022 at 5:54:41 AM permalink
1 - [(28/30) * (27/29)] = 13.1%
"Dealer has 'rock'... Pay 'paper!'"
Wizard
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March 11th, 2022 at 6:04:46 AM permalink
Quote: Joeman

1 - [(28/30) * (27/29)] = 13.1%

link to original post



I agree.

How about 3, 4 and 5 tiles?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Joeman
Joeman
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March 11th, 2022 at 6:36:40 AM permalink
I get 37.2%


With 3 tiles, you can win by either of 2 routes:
i - Pick 'CAR' at any time:
1 - [(28/30) * (27/29) * (26/28)] = 19.3%

ii - Pick one each of 'C', 'A', & 'R,' in any order. Since picking 'C' or 'A' are equally likely, the only variable is in which point you pick the 'R'. So...:
a. - Prob of spelling 'C-A-R' picking the 'R' first:
(6/30)*(22/29)*(11/28) = 5.96%

b. - Prob of spelling 'C-A-R' picking the 'R' second:
(22/30)*(6/29)*(11/28) = 5.96%

c. - Prob of spelling 'C-A-R' picking the 'R' third:
(22/30)*(11/29)*(6/28) = 5.96%

Summing up all probabilities, I get 37.2%

Note that since all 3 probabilities in "ii" are the same, I am probably missing a simpler solution.


That's it for me for now. I'll have to leave the 4 and 5 tile solutions to somebody else.

ETA: A little off topic, but FYI, there is a free streaming service called PlutoTV that has a channel that plays old Bob Barker TPiR episodes 24/7.
"Dealer has 'rock'... Pay 'paper!'"
Wizard
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March 11th, 2022 at 8:09:23 AM permalink
Quote: Joeman

I get 37.2%


ETA: A little off topic, but FYI, there is a free streaming service called PlutoTV that has a channel that plays old Bob Barker TPiR episodes 24/7.
link to original post



I agree on the 37.2%.

I may check that out. I miss the classic three Barkers Beauties.



To answer the question you're all wondering -- I'm a Holly man.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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March 11th, 2022 at 9:36:18 AM permalink
Quote: Joeman

That's it for me for now. I'll have to leave the 4 and 5 tile solutions to somebody else.



For 4, there are C(30,4) = 27,405 combinations of tiles
Combinations with both CAR cards: C(28,2) = 378
Combinations with one CAR card: 2 x C(28,3) = 6552
Combinations of C,C,A,R: 55 x 11 x 6 = 3630
Combinations of C,A,A,R: 11 x 55 x 6 = 3630
Combinations of C,A,R,R: 11 x 11 x 15 = 1815
Total winning combinations = 16,005
Probability of winning = 1067 / 1827, or about 58.402%

For 5, there are C(30,5) = 142,506 combinations of tiles
Combinations with both CAR cards: C(28,3) = 3276
Combinations with one CAR card: 2 x C(28,4) = 40,950
Combinations of C,C,C,A,R: 165 x 11 x 6 = 10,890
Combinations of C,C,A,A,R: 55 x 55 x 6 = 18,150
Combinations of C,A,A,A,R: 11 x 165 x 6 = 10,890
Combinations of C,C,A,R,R: 55 x 11 x 15 = 9075
Combinations of C,A,A,R,R: 11 x 55 x 15 = 9075
Combinations of C,A,R,R,R: 11 x 11 x 20 = 2420
Total winning combinations = 104,726
Probability of winning = 52,363 / 71,253, or about 73.49%

TinMan
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March 11th, 2022 at 9:37:50 AM permalink
I know the surrender aspect is for later but this story occurred to me:

I recall watching this game on a TPIR episode when I was 10 or so. Contestant had revealed 4/5 cards and they were all the same letter (lets say C). Bob offers him whatever the surrender value was. Guy declines and goes for it, hoping to get 1 of the CAR cards. No other way to spell car. At the time I thought it was foolish but may not have been a bad decision, depending on the value of the car to him relative to the surrender value and number of unknown cards remaining.

Edit/conclusion: of course he got the CAR card. Otherwise doubt Id remember this.
If anyone gives you 10,000 to 1 on anything, you take it. If John Mellencamp ever wins an Oscar, I am going to be a very rich dude.
Wizard
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March 11th, 2022 at 10:40:32 AM permalink
Quote: ThatDonGuy



For 4, there are C(30,4) = 27,405 combinations of tiles
Combinations with both CAR cards: C(28,2) = 378
Combinations with one CAR card: 2 x C(28,3) = 6552
Combinations of C,C,A,R: 55 x 11 x 6 = 3630
Combinations of C,A,A,R: 11 x 55 x 6 = 3630
Combinations of C,A,R,R: 11 x 11 x 15 = 1815
Total winning combinations = 16,005
Probability of winning = 1067 / 1827, or about 58.402%

For 5, there are C(30,5) = 142,506 combinations of tiles
Combinations with both CAR cards: C(28,3) = 3276
Combinations with one CAR card: 2 x C(28,4) = 40,950
Combinations of C,C,C,A,R: 165 x 11 x 6 = 10,890
Combinations of C,C,A,A,R: 55 x 55 x 6 = 18,150
Combinations of C,A,A,A,R: 11 x 165 x 6 = 10,890
Combinations of C,C,A,R,R: 55 x 11 x 15 = 9075
Combinations of C,A,A,R,R: 11 x 55 x 15 = 9075
Combinations of C,A,R,R,R: 11 x 11 x 20 = 2420
Total winning combinations = 104,726
Probability of winning = 52,363 / 71,253, or about 73.49%


link to original post



I agree.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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March 11th, 2022 at 10:49:09 AM permalink
Quote: TinMan

I know the surrender aspect is for later but this story occurred to me:

I recall watching this game on a TPIR episode when I was 10 or so. Contestant had revealed 4/5 cards and they were all the same letter (lets say C). Bob offers him whatever the surrender value was. Guy declines and goes for it, hoping to get 1 of the CAR cards. No other way to spell car. At the time I thought it was foolish but may not have been a bad decision, depending on the value of the car to him relative to the surrender value and number of unknown cards remaining.

Edit/conclusion: of course he got the CAR card. Otherwise doubt Id remember this.
link to original post



We can get to it now.

Regarding your story, I remember once on the Punchboard game, somebody got the second highest prize and had one punch to go. He foolishly went for it -- and got the top prize.

I find from the start, with two tiles only, the indifference point on the car value is $15,263.16.

In your case, the player obviously had a probability of 1/26 of winning of winning the car, for an indifference point of $26,000. I don't know your age, but I would imagine low-end cars were not going for as much back then.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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March 11th, 2022 at 10:58:22 AM permalink
Quote: Wizard

I may check that out. I miss the classic three Barkers Beauties.

To answer the question you're all wondering -- I'm a Holly man.
link to original post


Technically, neither Diane nor Holly are "classic"; the "classic" two are Janice, and Anitra Ford.

How familiar are you with the stories of how well the three of them got along with Bob?


There has only been one tie in a showcase in the 50-year history of the show, and even that was in the old weekly syndicated (if you are familiar with Match Game PM, think of it as "TPIR PM") version back when it was hosted by Dennis James.

Both Bob and Drew always include "If you are the winner" when they explain how someone can win both showcases. In the history of the show (although in the first year or two, they did not have the rule where you could win both showcases - including the first episode where somebody got a showcase exactly right), only one contestant was within the range needed to win both, but the other contestant was closer - and that was by one dollar.


There was a period of a few years when the show would not only not offer foreign cars, but would not offer GM cars either. The foreign cars were banned because the producers wanted to feature "American-made" cars, and GM was banned because Bob pretty much demanded it after GM would not sign something that said that it did not use animals for testing of any sort. Most are familiar with the sudden disappearance of furs from the show (and, in fact, Bob made it quite clear that no episodes with furs can air in repeats - and, somehow, his estate can still mandate this), but it's not quite as well-known that, at some point, the ban went to pretty much anything with meat inside of it. "Pepperoni Hot Pockets" were suddenly replaced by "Cheese & Broccoli Hot Pockets" on Grocery Game, for example.

avianrandy
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March 14th, 2022 at 3:02:12 PM permalink
I may check it out also. Holly seemed much more down to earth I guess I would say.Also,on spelling bee if you go the exact price on one of the items you automatically got the 3 extra tiles.i was watching a clip this morning of give or keep game. The totals were adding up wrong and itwas giving Bob a headache.finally the producers admitted they put some of the wrong prices on the items. The contestant won but it was very confusing. That clip was on YouTube.
avianrandy
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March 27th, 2022 at 2:28:35 AM permalink
Just seen a lady on TPIR win a dodge Omni playing 3 strikes without pulling a single strike! Price had 4 numbers. Bob wanted to say something on her last pull but didn't want to hex her.Thenumbers were 4,6,7,9. Very lucky and she had I think 8 draws. I had never seen a contestant win with no strike before. Was glad to see her win.
avianrandy
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March 27th, 2022 at 3:24:07 AM permalink
Car was a 1984 dodge Omni
ThatDonGuy
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March 27th, 2022 at 9:54:40 AM permalink
Quote: avianrandy

Just seen a lady on TPIR win a dodge Omni playing 3 strikes without pulling a single strike! Price had 4 numbers. Bob wanted to say something on her last pull but didn't want to hex her.Thenumbers were 4,6,7,9. Very lucky and she had I think 8 draws. I had never seen a contestant win with no strike before. Was glad to see her win.
link to original post


It is thought that, originally, it was easier somehow to tell the numbers from the strikes apart by feel. There is another school of thought that some players would "peek" just before the chip was pulled out of the bag, and if they saw the red of a strike, they would let go of it before pulling it out, but this is much less likely, although there was a brief period when the strikes were colored white as well as the numbered chips.

Eventually, the producers realized how hard it was to win the game, especially with 5-digit cars, which is why it is only played for really expensive cars.
avianrandy
avianrandy
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March 27th, 2022 at 10:37:27 AM permalink
It is a tough game to win. I remember a couple years ago they played it for a Ferrari. With 6 numbers.at one point,the contestant pulled out an8 and said it was the first number of the car.i distinctly remember drew Carey chuckling this was going to take a while. I don't think they have played it for a 6 figure vehicle since. I guess the producers do t want to run in to days of our lives
ThatDonGuy
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March 27th, 2022 at 12:18:49 PM permalink
Quote: avianrandy

It is a tough game to win. I remember a couple years ago they played it for a Ferrari. With 6 numbers.at one point,the contestant pulled out an8 and said it was the first number of the car.i distinctly remember drew Carey chuckling this was going to take a while. I don't think they have played it for a 6 figure vehicle since. I guess the producers do t want to run in to days of our lives
link to original post


I may have mentioned this before in this forum, but even if they tell you the price of the car in advance, you would still have only a 3/8 (with 5 digits - 1/3 with 6) chance of winning the car.
Oh, and pardon me for being pedantic (as usual), but Days of Our Lives is "on another network" - you're thinking of The Young & the Restless.
avianrandy
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March 27th, 2022 at 12:25:00 PM permalink
Ok lol. I don't watch soap operas. Love my game shows though.days,young and restless,as world turns, general hospital allsame to me

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