Price is Right

[beatlefreak84]

Hello everyone,

This past week, I had my math students, who are currently learning probability, write a short paper on some probability issues.  Essentially, I just wanted to see where their thinking was on some key issues; I didn't care whether they gave right or wrong answers.

However, one of the questions asked them to look at the rules of the car games (on gscentral.net), and, assuming they didn't know anything about the prices of items, which game would they most like to play for the new car, and which game would they least like to play for the new car, and why?

But, because a good number of them weren't that familiar with TPIR, I got a few off-the-wall responses.  Thus, I thought I'd ask this group the same question and see what you all say:  If you didn't know anything about prices, which game would you like to play for your new car, and which would you NOT like to play for your new car?

Just for the record, my answers:

Most like:  Pass the Buck (just for showing up, you have a 1/6 shot of winning the car!)
Least like:  Switcheroo (even though you have a 1/5 shot of winning the car, unless you get all 5 prizes right the first time around, which has a 1/120 shot, you can easily second-guess yourself out of a car!)

Anthony

[xavier45]

Let 'em Roll would be a good one. Just roll 5 cars and you win. You don't need to know anything about prices for cars. And even if you don't win the car, you still win some cash.

[Matt Ottinger]

[quote name=\'beatlefreak84\' post=\'181312\' date=\'Mar 14 2008, 12:37 PM\']Least like:  Switcheroo (even though you have a 1/5 shot of winning the car, unless you get all 5 prizes right the first time around, which has a 1/120 shot, you can easily second-guess yourself out of a car!)[/quote]
If you're a math teacher, and you're talking about random distribution of numbers ("assuming they didn't know anything about the prices"), surely you realize that Switcheroo has a 1/5 chance of winning the car no matter what you do.  True, you might switch from a correct first choice to an incorrect second choice, in which case you live with the regret, but you might just as easily switch to the right one.  No matter what, on the reveal it's a one-in-five shot.  Purely mathematically, that's one of the best games to play.  I now wonder where YOUR thinking is on some key issues!

Taking your assignment literally, I think the worst game from a probability level would be Ten Chances.  Without having a really good idea about the first and last digit, placing five random numbers into the correct order would seem to have the longest odds of any game.  And to take it a step further, if you truly don't have a clue about prices, you may not even get past the first two smaller items to even have a chance at the car!

Meanwhile, the probabilities in Cover Up fascinate me.  Has any math type tried to tackle that one?

[Clay Zambo]

How 'bout Double Prices?

[BrandonFG]

-Let Em Roll
-Pass the Buck
-Spelling Bee
-Card Game...long as I draw the $2000 card. :-P

Temptation switched to cash instead of the prizes, no? I don't need another car, so I'd be perfectly all right with a couple thousand dollars extra in my pocket. However, if I happened to win the car, I have no problem selling it. ;-)

Would hate to have One Away, Any Number, or Cover Up...basically any game that actually requires you to be familiar with the price of a car. I don't watch the show enough to figure out how much a feature adds to the price...

[Joe Mello]

[quote name=\'fostergray82\' post=\'181325\' date=\'Mar 14 2008, 01:33 PM\']
-Card Game...long as I draw the $2000 card. :-P[/quote]
So if you draw the $5,000 card, you're screwed?

[quote name=\'fostergray82\' post=\'181325\' date=\'Mar 14 2008, 01:33 PM\']Temptation switched to cash instead of the prizes, no?[/quote]
Unless they're converting all the ARP's of the gifts to cash, no.  Cash is part of the package sometimes, and there was a $5,000 cash gift in the last aired playing, but there's still other prizes.

[Chuck Sutton]

I always thought Lucky 7 was murder even in the days when car prices were four numbers and the first was a gimme.

Now you have to guess 4 numbers 0-9 and only miss by six total, doing it by pure chance; the odds seem astonomical.

The Dice Game seems somwhat simplier if you don't the the price. Only 1-6 available and at least two rolls(three if the number isn't a 1 or 6) get the number without guessing.

[WhammyPower]

I'd rather have Bonus Game.  It's a 50% shot at winning a car (if you're lucky enough to play for one) if you base it on pure luck.

[beatlefreak84]

[quote name=\'Matt Ottinger\' post=\'181315\' date=\'Mar 14 2008, 11:53 AM\']
If you're a math teacher, and you're talking about random distribution of numbers ("assuming they didn't know anything about the prices"), surely you realize that Switcheroo has a 1/5 chance of winning the car no matter what you do.  True, you might switch from a correct first choice to an incorrect second choice, in which case you live with the regret, but you might just as easily switch to the right one.  No matter what, on the reveal it's a one-in-five shot.  Purely mathematically, that's one of the best games to play.  I now wonder where YOUR thinking is on some key issues!

Taking your assignment literally, I think the worst game from a probability level would be Ten Chances.  Without having a really good idea about the first and last digit, placing five random numbers into the correct order would seem to have the longest odds of any game.  And to take it a step further, if you truly don't have a clue about prices, you may not even get past the first two smaller items to even have a chance at the car!

Meanwhile, the probabilities in Cover Up fascinate me.  Has any math type tried to tackle that one?
[/quote]

First off, yes; I did acknowledge that the chances of winning a car in Switcheroo were 1/5 (reread my original post!); I said what would make the game undesirable for me would be that the only way I would be sure I'd win the car is if I priced all 5 correctly; the other best case would be if I got 0 right (then, I'd have a 1/4 chance since I'd know the digit I have is wrong).  But, anything in the middle, and I'd have no clue how to proceed.  The chance that I would switch myself out of a car is not something I'd like to deal with.  But, yes; from pure mathematics, it's a very good game to play.  It's just that "gray area" in the middle where you don't know for sure that scares me about the game.

You know, a lot of my students said 10 Chances for both directions; the ones that said it would be a really good game to play were those who knew the "ends in 0" rule, as, worst case, you'd give yourself 2 shots at the car.  One of my students also (correctly) argued that, if you knew what the first digit of the car was as well, 6 chances for the car guarantees a win.  But, without the "ends in 0" rule, you're absolutely right, as that's pretty terrible odds...

I don't know if anybody's tackled Cover Up, but we're on spring break now, so I may take a look at it...

Anthony

[MikeK]

[quote name=\'WhammyPower\' post=\'181351\' date=\'Mar 14 2008, 02:53 PM\']I'd rather have Bonus Game.  It's a 50% shot at winning a car (if you're lucky enough to play for one) if you base it on pure luck.[/quote]
Do you mean Double Prices?  And how often is it played for a car, outside of the $1M Spectaculars?

I'll take Pick a Number, and I have to fill in the first digit.

[clemon79]

[quote name=\'MikeK\' post=\'181356\' date=\'Mar 14 2008, 11:59 AM\']
Do you mean Double Prices?  And how often is it played for a car, outside of the $1M Spectaculars?
[/quote]
No, he means Bonus Game. If you wild-ass guess, you should win 2 of the 4 screens, which means you have a 50/50 chance of getting the screen with the Bonus in it.

What about Let 'em Roll? Wild-assed guesses should get you one extra roll for a total of 2, so you have a 50/50 chance of getting a car on each die, and two chances to roll each one. In strict terms of probability, assuming a perfect spread of possible outcomes, those feel like pretty good odds.

[Jeremy Nelson]

Cover Up is actually a 1/720 chance on the first guess, if we take this probablilty exercise literally. However, since the first digit is usually a gimme, and given that most car prices don't have a repeating number, the odds are much better than 1/720. From then on, it varies based on which numbers you get right.

You have pretty good odds on 5 Price Tags as well. Even if you have a brain dead contestant, they have a 1 in 2 shot of getting a guess at the car with the small prizes. Not only that, but then they get up to four tries. From then on, the odds are the number of small prizes right to 5.

[Chuck Sutton]

[quote name=\'clemon79\' post=\'181357\' date=\'Mar 14 2008, 03:03 PM\']
[quote name=\'MikeK\' post=\'181356\' date=\'Mar 14 2008, 11:59 AM\']
Do you mean Double Prices?  And how often is it played for a car, outside of the $1M Spectaculars?
[/quote]
No, he means Bonus Game. If you wild-ass guess, you should win 2 of the 4 screens, which means you have a 50/50 chance of getting the screen with the Bonus in it.

[/quote]
  Yes the Bonus Game(or of couse the Shell Game)  in the end is 50/50 even with wild ass guesses.   If you want a longer explaination to get to the same answer; my formula for wild ass guesses at Plinko that got me in to so much trouble in the other thread works perfectly here.

There are 16 combinations of t/f guesses.   1 combination of wild ass guesses gets you a win.  4 combos get you a 3/4 chance 6 a 1/2 chance 4 a 1/4 and 1 combo no chance

That adds up to 8/16.

[MikeK]

[quote name=\'clemon79\' post=\'181357\' date=\'Mar 14 2008, 03:03 PM\']
[quote name=\'MikeK\' post=\'181356\' date=\'Mar 14 2008, 11:59 AM\']
Do you mean Double Prices?  And how often is it played for a car, outside of the $1M Spectaculars?
[/quote]
No, he means Bonus Game. If you wild-ass guess, you should win 2 of the 4 screens, which means you have a 50/50 chance of getting the screen with the Bonus in it.[/quote]
The key word in your argument is "should".  You won't necessarily get a 2 in 4 chance all the time.  I read WP's comment as a guaranteed 50/50 shot every time.  Hence, Double Prices.

[BrandonFG]

[quote name=\'Joe Mello\' post=\'181346\' date=\'Mar 14 2008, 02:41 PM\']
[quote name=\'fostergray82\' post=\'181325\' date=\'Mar 14 2008, 01:33 PM\']
-Card Game...long as I draw the $2000 card. :-P[/quote]
So if you draw the $5,000 card, you're screwed?
[/quote]
Can't tell if this is in jest...did they up the high range card?