Price is Right -- Spelling Bee Game
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4 members have voted
March 10th, 2022 at 7:52:10 PM
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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.
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?
Direct: https://www.youtube.com/watch?v=S7nXtS3GwYQ
Here are the rules.
- 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
- The player immediately gets to pick two numbers.
- The player has an opportunity to win up to 3 more numbers playing a pricing game, which you can see in the video.
- 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?
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
March 11th, 2022 at 3:08:30 AM
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^ 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
March 11th, 2022 at 4:19:08 AM
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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
March 11th, 2022 at 5:54:41 AM
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1 - [(28/30) * (27/29)] = 13.1%
"Dealer has 'rock'... Pay 'paper!'"
March 11th, 2022 at 6:04:46 AM
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Quote: Joeman1 - [(28/30) * (27/29)] = 13.1%
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I agree.
How about 3, 4 and 5 tiles?
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
March 11th, 2022 at 6:36:40 AM
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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.
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!'"
March 11th, 2022 at 8:09:23 AM
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Quote: JoemanI 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.
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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.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
March 11th, 2022 at 9:36:18 AM
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Quote: JoemanThat'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%
March 11th, 2022 at 9:37:50 AM
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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 (let’s 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 I’d remember this.
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 (let’s 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 I’d 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.
March 11th, 2022 at 10:40:32 AM
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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%
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I agree.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
