LMAD: Three of a Kind
February 6th, 2010 at 7:31:26 AM
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There is a game that is played on the new edition of Let's Make A Deal with Wayne Brady, called Three of a Kind.
Rules:
A married couple is called up to play, and is shown a board with six playing cards, face-down, numbered 1-6. There are 3 aces, and 3 queens on the board. They are asked to pick 3 cards, which are moved to the top of the board, and kept face-down for the moment. If they have chosen 3 of the same card, they win a car.
The host turns over two of the cards the couple picked, which are always the same. (ie. the host shows the couple they picked two queens, or two aces). At that point, they are offered a sure-thing if they bail out, usually a trip or prize package of about $3,000 - $4,000.
The host then turns over two cards the couple did NOT pick, which will be a pair opposite what the couple picked. (ie. the host shows 2 aces if the couple has 2 queens). They are offered the sure-thing again, with an additional $500 in the mix.
If they decide to go for the car, their final card is revealed. 3 of a kind wins the car, a non-match means they win nothing.
Analysis:
What are the odds of winning the car?
What are the odds that the couple picked two of a kind, and they left an opposite two of a kind unpicked?
IF the host were to offer a switch after all reveals, when there is one picked card face-down and one unpicked card face-down, should the couple take the switch? What would be their odds of winning by taking the switch? * The switch is NOT an option ever offered on the show.
Going strictly by prize value, and assuming the car was worth between $14,000 - $16,000, what is the move that gives the highest return: Go for the car, or take the bail-out + $500?
Notes:
I've already determined the answers to the preceding questions, but wanted to pose them to the forum for fun, and to ignite discussion. I have a few other comments I'd like to make, but I want to see your take on it all first.
Rules:
A married couple is called up to play, and is shown a board with six playing cards, face-down, numbered 1-6. There are 3 aces, and 3 queens on the board. They are asked to pick 3 cards, which are moved to the top of the board, and kept face-down for the moment. If they have chosen 3 of the same card, they win a car.
The host turns over two of the cards the couple picked, which are always the same. (ie. the host shows the couple they picked two queens, or two aces). At that point, they are offered a sure-thing if they bail out, usually a trip or prize package of about $3,000 - $4,000.
The host then turns over two cards the couple did NOT pick, which will be a pair opposite what the couple picked. (ie. the host shows 2 aces if the couple has 2 queens). They are offered the sure-thing again, with an additional $500 in the mix.
If they decide to go for the car, their final card is revealed. 3 of a kind wins the car, a non-match means they win nothing.
Analysis:
What are the odds of winning the car?
What are the odds that the couple picked two of a kind, and they left an opposite two of a kind unpicked?
IF the host were to offer a switch after all reveals, when there is one picked card face-down and one unpicked card face-down, should the couple take the switch? What would be their odds of winning by taking the switch? * The switch is NOT an option ever offered on the show.
Going strictly by prize value, and assuming the car was worth between $14,000 - $16,000, what is the move that gives the highest return: Go for the car, or take the bail-out + $500?
Notes:
I've already determined the answers to the preceding questions, but wanted to pose them to the forum for fun, and to ignite discussion. I have a few other comments I'd like to make, but I want to see your take on it all first.
-Dween!
February 6th, 2010 at 8:09:44 AM
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I'll take a shot --- trying to dredge up what I learned years ago and add some of the examples from WOO, the math site, and this forum.
combin(6,3) = 20 possible combinations they could pick
Two of these are three of a kind, so the odds of winning the car are 1 in 10.
All combinations will include two of kind. (I bet people get really excited when they see a pair!)
Take the switch. The reveal of the other pair would mean that the winning card is now one of only two cards available. 9 times out of 10 they did not pick it right the first time. I'm not sure, but I think the odds of winning by switching would be 9 in 10.
With the values provided, take the bail out + 500. The EV of the car is only 10% of its value.
Now -- where did I go wrong?
combin(6,3) = 20 possible combinations they could pick
Two of these are three of a kind, so the odds of winning the car are 1 in 10.
All combinations will include two of kind. (I bet people get really excited when they see a pair!)
Take the switch. The reveal of the other pair would mean that the winning card is now one of only two cards available. 9 times out of 10 they did not pick it right the first time. I'm not sure, but I think the odds of winning by switching would be 9 in 10.
With the values provided, take the bail out + 500. The EV of the car is only 10% of its value.
Now -- where did I go wrong?
February 6th, 2010 at 10:01:52 AM
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Actually, Seattledice, I think everything you've said is spot on. In fact...
Both the audience and the couple get very excited when the first two cards are shown to be a pair... and they cheer when two un-picked cards are NOT theirs.
I imagine this is a great budget-cutting game for the show. It gives the illusion that people are close to winning. I've only seen this game played twice, and neither time has the sure-thing prize been taken. Granted, the show is currently taped in Vegas, and people say, "We're here to gamble, I came with nothing, etc," so going for the car seems to be the thing to do.
Quote: seattlediceAll combinations will include two of kind. (I bet people get really excited when they see a pair!)
Both the audience and the couple get very excited when the first two cards are shown to be a pair... and they cheer when two un-picked cards are NOT theirs.
I imagine this is a great budget-cutting game for the show. It gives the illusion that people are close to winning. I've only seen this game played twice, and neither time has the sure-thing prize been taken. Granted, the show is currently taped in Vegas, and people say, "We're here to gamble, I came with nothing, etc," so going for the car seems to be the thing to do.
-Dween!
