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-   -   Price Is Right Wheel - What are the odds of this? (http://boards.straightdope.com/sdmb/showthread.php?t=837020)

Mahaloth 09-23-2017 08:57 AM

Price Is Right Wheel - What are the odds of this?
 
Watch the video first if you like fun happenings.

So:

The first guy spun a $1.

The lady spun a $1

The final guy also got a $1.

Then, the first guy got $1 again!

Then, the lady got $1 again.

The end.

What are the odds for this kind of luck on the wheel? I swear, that last guy almost had $1 on his final spin!

terentii 09-23-2017 10:16 AM

How many spaces on the wheel and how many of them are $1?

(Sorry, I just can't watch that clip all the way through. :( )

Leaffan 09-23-2017 10:18 AM

I don't know about the odds, but that was fun to watch!

Chronos 09-23-2017 10:27 AM

Whenever you ask "What are the odds of this?", you have to specify exactly what "this" is. Getting five $1s on those particular five spins? I think the wheel has 20 spaces on it, so that'd be 1/20^5, or 1 in 3.2 million. But when you ask "What are the odds that five spins in a row would all come up $1, at any time in the show's history?", then the odds aren't nearly so long, perhaps somewhere in the vicinity of one in several hundred (I'm not exactly sure how long the show has run, or how many spins they make per day). And if you extend "this" even further, to include similarly-remarkable events on other game shows, it becomes much more likely yet.

USCDiver 09-23-2017 10:27 AM

Quote:

Originally Posted by terentii (Post 20494206)
How many spaces on the wheel and how many of them are $1?

(Sorry, I just can't watch that clip all the way through. :( )

There are 20 slots (one each for values of $.05-$1 in $.05 increments). Only one $1 space. But it isn’t truly random, since the player spins the wheel as hard or soft as they want (provided the wheel makes at least one full turn) and combinations of two numbers which add to $1 count too.

Mahaloth 09-23-2017 10:58 AM

Quote:

Originally Posted by terentii (Post 20494206)
(Sorry, I just can't watch that clip all the way through. :( )

Why? I haven't seen that show in years and it was pretty neat. Drew Carey was hilarious at the end. He couldn't believe it.

pkbites 09-23-2017 11:03 AM

That was fun to watch! :):cool:


I love TPIR but don't get to watch it often because of my schedule.

Was that a recent episode? If so, did Drew gain some of his weight back or was his suit jacket just wearing on him oddly?

Cayuga 09-23-2017 11:48 AM

I think it happened this past week, the first week of the new season. And yes, Drew looked a little more … padded.

There are 20 slots marked $.05 – $1.
$1 wins automatically.
2 spins totaling $1 also win.

So in one spin, a player has a 5% chance of winning.
Assuming he doesn't get $1, he has a 5% chance of winning on his second spin.

A-a-a-a-and that's as far as I can go. I know the total odds of one person winning once isn't 0.5 x 0.5 = 0.25 = 2.5% (because if you win the first time, you don't spin the second time (I think that matters, right?)), but I don't know what it is.

Do we need to look at two spins as one event with 20 x 20 = 400 possible outcomes? Or 380, since you don't spin twice if you get $1 the first time. There are 11 favorable outcomes ($1, $.05/$.95, $.10/$.90 … $.45/$.55, $.50/$.50). So the odds are 11/380, which is roughly a 2.9% chance of winning. As for that happening five times in a row, I don't know.

I realize I could be way off base on this — high school math was a long time ago. I'd really be interested in having someone explain.

(And to keep Chronos happy, let's say "on those five attempts," not "at any point in the run of the show.")

(Is "on any given five consecutive attempts" the same as "on those five attempts"?)

Kamino Neko 09-23-2017 12:04 PM

The five $1.00 spins aren't the most amazing thing - it's that it happened in an episode where the prize for hitting the dollar was higher than usual.

Mahaloth 09-23-2017 12:31 PM

Quote:

Originally Posted by pkbites (Post 20494318)
Was that a recent episode? If so, did Drew gain some of his weight back or was his suit jacket just wearing on him oddly?

It's recent and it looks like it was the first of the season. Yes, he has gained weight. It's understandable. It's hard to keep it off, I'm sure.

Gatopescado 09-23-2017 01:06 PM

I think that was this Friday show (9/22). I watch this crap every day.

They gave away a shit-ton of cash! I recall at least 2 cars and a boat.

Every person won their pricing game. I think it was $30k on the wheel bonus cash. It was as Drew called it, "A perfect game".

Guest-starring: Id! 09-23-2017 05:04 PM

I thought the odds of dippy dingbat Ryan's overall success at this show was quite impressive.

And yeah Plinko might not quite measure up to the Big Wheel.....

Chronos 09-23-2017 06:07 PM

You do know that they select contestants based on how excited and energetic they seem, right? So it's not really a surprise to see a guy going crazy on stage like that.

Guest-starring: Id! 09-23-2017 06:39 PM

Quote:

Originally Posted by Chronos (Post 20494975)
You do know that they select contestants based on how excited and energetic they seem, right? So it's not really a surprise to see a guy going crazy on stage like that.


I wasn't aware of this.

If contestants normally get this unglued, I might start watching it.

Chronos 09-23-2017 10:20 PM

Well, that guy was more unglued than usual. But yeah, they're all pretty excited.

pkbites 09-24-2017 01:29 AM

Quote:

Originally Posted by Eddie The Horrible (Post 20494891)
I thought the odds of dippy dingbat Ryan's overall success at this show was quite impressive.

Holy dog snot! That was freaking awesome! :):eek::cool:

BTW, I have that cordless flosser. It works great! And I paid $37.99 so TPIR was pretty much on the money to how much it was.

Monocracy 09-24-2017 07:25 AM

The odds that all three contestants roll a dollar on their first spin(s) is 1 in 1079. This assumes that the first contestant will spin the wheel twice if (s)he doesn't hit a dollar on the first spin, which isn't realistic, because (s)he would stop if they spun a pretty high number.

Chance of NOT rolling a dollar on first spin: .95
Chance of NOT rolling a dollar on second spin: .95
Chance of NOT rolling a dollar on either spin: .95 x .95 = .9025
Chance of contestant rolling a dollar: 1 - .9025 = .0975

Chance of all three contestants rolling a dollar: .0975^3 = .000927
.000927 is 1 in 1079


Chance of NOT rolling a dollar on bonus spin: .95
Chance of all 3 contestants NOT rollling a dollar on their bonus spin: .95^3 = .857
Chance of at least one contestant rolling a dollar on bonus spin: 1 - .857 = .143

Chance of all three contestants rolling a dollar AND at least one contestant rolling a dollar on bonus spin: .000927 x .143 = .000132
.000132 is 1 in 7565


Chance of rolling a dollar on bonus spin: .05
Chance of all three contestants rolling a dollar on bonus spin: .05^3 = .000125

Chance of all three contestants rolling a dollar AND rolling a dollar on bonus spin: .000927 x .000125 = .000000116
.000000116 is 1 in 8.6 million


I don't know how to calculate 2 contestants rolling dollars on their bonus spins, but it's somewhere between 1 in 7265 and 1 in 8.6 million.

Note: Numbers have been rounded in text, but not in calculations.

Also remember, this event actually happened so the real odds of it happening are 100%. There are millions of "What are the odds?" events that can happen on a game like The Price Is Right, so if the game gets played as many times as it has, some unlikely events will occur. The real challenge is predicting a long odds event BEFORE it happens.

pulykamell 09-24-2017 08:50 AM

Quote:

Originally Posted by Monocracy (Post 20495649)
Also remember, this event actually happened so the real odds of it happening are 100%.

I'm not sure I would use the word "odds" in that case. To me, the word only really make sense referring to the probability prior to an observation.

Quote:

There are millions of "What are the odds?" events that can happen on a game like The Price Is Right, so if the game gets played as many times as it has, some unlikely events will occur.
Now that could be the next layer of the question. Given how many wheel spins there have bin in the show's history, what was the probability that 5 dollar-totaling spins in a row would have occurred at some point during the show's run.

pulykamell 09-24-2017 09:00 AM

Quote:

Originally Posted by Monocracy (Post 20495649)
I don't know how to calculate 2 contestants rolling dollars on their bonus spins, but it's somewhere between 1 in 7265 and 1 in 8.6 million.

Well, if you're counting "in a row" as part of it, I'm getting a number of 1 in 430-450K (using your intial numbers), depending on whether you want to throw out the case where the last guy also gets a dollar on his spin.

Kamino Neko 09-24-2017 09:27 AM

Quote:

Originally Posted by pulykamell (Post 20495753)
Now that could be the next layer of the question. Given how many wheel spins there have bin in the show's history, what was the probability that 5 dollar-totaling spins in a row would have occurred at some point during the show's run.

There have been ~10,000 episodes, with 2 Big Wheel segments each, since the current format began in 1972.

So, that's around 20k chances for all three initial spins to hit the dollar. This has happened a dozen or so times. Which fits with my quick back of the envelope calculation as to how often that would happen.

Since 5-dollar-space rounds are necessarily a relatively rare subset of the 3-dollar-space starters, and we're excluding ones where the first or second contestant is the one who misses the second dollar, we're a rather long way from the point where the number of trials multiplied by the probability of it happening approaches 1.

Cayuga 09-24-2017 01:21 PM

Quote:

Originally Posted by Monocracy (Post 20495649)
Also remember, this event actually happened so the real odds of it happening are 100%.

That's not how it works.

Yes, the odds that it happened are 100%, but that's a pointless statement. The odds that it would happen are unaffected by whether it did or not.

The odds of a die coming up 2 are 1 in 6. I just rolled a die here on my kitchen table, and it came up 2. Even so, the odds of a die coming up 2 are still 1 in 6.


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