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Wizard
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October 3rd, 2019 at 6:58:28 AM permalink
I've been wondering about the optimal strategy for the Race Game in the Price is Right, assuming you had no knowledge of the values of the prizes. For those not familiar with the game, it is explained and shown in this video.


Direct: https://www.youtube.com/watch?v=q5jAXcqzCCk

In my strategy, assign the prizes letters, say A, B, C, and D. Then number the positions. A pattern will represent which position to put which prize in. For example, 3421 would mean put prize A in position 3, B in position 4, C in position 2, and D in position 1. The history column shows a record of how many you got right, starting with the first turn.
History Play First turn 1234 0 2143 0,0 3421 0,0,0 4312 0,0,2 3412 0,0,2,0 4321 0,2 2341 0,2,0 4123 0,2,1 2413 0,2,1,0 3142 1 1342 1,0 2431 1,0,0 3124 1,0,0,0 4213 1,1 1423 1,1,0 2314 1,1,0,0 3241 1,1,0,0,0 4132 2 2134 2,0 1243 2,1 1324 2,1,0 4231 2,1,1 1432 2,1,1,0 3214

The next table shows the probability of the number of turns needed to win. As you can see, a win is always guaranteed within five turns.

probability 4.2% 16.7% 33.3% 37.5% 8.3% 100.0%
Turns count
1 1
2 4
3 8
4 9
5 2
Total 24


The average turns needed is 3.29167.

The question for the forum is can you find a better strategy? It would be very easy to find ones that are equally as good. My strategy just takes any combination that might win.

The question for the poll is how would you play the Race Game?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
AZDuffman
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October 3rd, 2019 at 8:12:28 AM permalink
Quote:

The question for the poll is how would you play the Race Game?



First, I would only care about going on the show when Holly Hallstrom was there and in her prime. But that out if the way....

What I did not see, and I am kind of working on a project as I do this, is that one part of this is distance. 3-4 is further than 1-2. Thus one should make as few trips to 3-4 as possible.

I would put them out A-B-C-D. And see how many I got right. Then I switch A-B and see if I improve. If so then I switch C-D. If not then I switch B-C. Then if I improve I switch C-D. If not then A-D. Something like this. Idea switch 2 at first then keep trying to narrow it down.

Then I would try to get a date with Holly.

Here is one thing, how many trips do you think a person would be able to make?

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Wizard
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October 3rd, 2019 at 9:51:47 AM permalink
Quote: AZDuffman

Here is one thing, how many trips do you think a person would be able to make?



Most make three but some get off only two. It's worth noting that if you're in the middle of a round when time runs out, Bob lets you place any tags still in your hand.



Holly was my favorite of the classic three too. A blonde, brunette, and a red head. The blonde was Diana, right? I can't remember the brunette's name.
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AZDuffman
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October 3rd, 2019 at 10:50:32 AM permalink
Quote: Wizard

Most make three but some get off only two. It's worth noting that if you're in the middle of a round when time runs out, Bob lets you place any tags still in your hand.



Lots seem clueless as to strategy IIRC. They used to do season tix for LA based teams. The strategy there was put the lowest price on the Rams/NFL as they had just 10 games. (I assume included exhibition season.) Then make a guess as to the NHL/NBA/MLB. Bob would tell losers this after.



Quote:

Holly was my favorite of the classic three too. A blonde, brunette, and a red head. The blonde was Diana, right? I can't remember the brunette's name.



The "classic" Barker's Beauties were:

Janice Pennington, who handed Bob the mic at the opening
Holly Hallstrom, who we all know
Diane Parkinson, the other Blonde

A few years back I was waiting for a Doc appt and TPIR was on. They had a male model! What is this world coming to?

Wiz, if you did not see it yet there is (or was) a Netflix video called "The Perfect Bid" or something like it.
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Wizard
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October 3rd, 2019 at 1:51:56 PM permalink
Quote: AZDuffman

Wiz, if you did not see it yet there is (or was) a Netflix video called "The Perfect Bid" or something like it.



That has been discussed here a few times.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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October 3rd, 2019 at 2:11:58 PM permalink
Quote: AZDuffman

A few years back I was waiting for a Doc appt and TPIR was on. They had a male model! What is this world coming to?





Do you mean him?
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smoothgrh
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October 3rd, 2019 at 2:23:47 PM permalink
I think I like Bob with white hair better—it gives him a more distinctive look.

Barker's Beauties, on the other hand—flawless!
AZDuffman
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October 3rd, 2019 at 2:40:43 PM permalink
Quote: Wizard



Do you mean him?



Don’t remember. I just shook my head and moved on. Male models on TPiR is just wrong.
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avianrandy
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October 3rd, 2019 at 3:08:50 PM permalink
I remember when Dian posed for playboy and she was on Geraldo I think and he asked her why she posed? She quipped,'the price was right'....lol But yea, definitely all 3 were beauties.
Lovecomps
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October 3rd, 2019 at 3:18:19 PM permalink
Quote: avianrandy

I remember when Dian posed for playboy and she was on Geraldo I think and he asked her why she posed? She quipped,'the price was right'....lol But yea, definitely all 3 were beauties.



Yeah, but now it's male models?? Gimme a break!

That game was best when they had some old woman in her 70's trying to run to and fro. They rarely call elderly people to contestants row now because the demographics of the audience and who they pick for them to see has changed. F.Y.I., the selection isn't random. The contestants are carefully chosen before they are even let into the studio.
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michael99000
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October 3rd, 2019 at 3:44:43 PM permalink
Always wondered exactly how big of an advantage it was, mathematically , to go 3rd in the spinning of the big wheel portion of the game. Too bad there’s no stats on how often each position 1st, 2nd 3rd, won.
AZDuffman
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October 3rd, 2019 at 4:26:15 PM permalink
Quote: michael99000

Always wondered exactly how big of an advantage it was, mathematically , to go 3rd in the spinning of the big wheel portion of the game. Too bad there’s no stats on how often each position 1st, 2nd 3rd, won.



As a guess I would sat about the same as the dealer going last in BJ.
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michael99000
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October 3rd, 2019 at 4:41:40 PM permalink
Quote: AZDuffman

As a guess I would sat about the same as the dealer going last in BJ.



Maybe. Although in this case you never go over the $1.00 mark and bust when you go first
Joeman
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October 3rd, 2019 at 5:19:41 PM permalink
Quote: michael99000

Maybe. Although in this case you never go over the $1.00 mark and bust when you go first

Actually, I have seen multiple episodes where both the 1st and 2nd players 'bust' and the 3rd player is automatically in the showcase.
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Wizard
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October 3rd, 2019 at 6:43:51 PM permalink
Quote: michael99000

Always wondered exactly how big of an advantage it was, mathematically , to go 3rd in the spinning of the big wheel portion of the game. Too bad there’s no stats on how often each position 1st, 2nd 3rd, won.



I have written about this extensively.
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michael99000
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October 3rd, 2019 at 7:23:21 PM permalink
Quote: Joeman

Actually, I have seen multiple episodes where both the 1st and 2nd players 'bust' and the 3rd player is automatically in the showcase.



I shouldn’t have said never bust going first.
Lovecomps
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October 3rd, 2019 at 9:09:29 PM permalink
Quote: michael99000

Always wondered exactly how big of an advantage it was, mathematically , to go 3rd in the spinning of the big wheel portion of the game. Too bad there’s no stats on how often each position 1st, 2nd 3rd, won.



You can't gain a mathematical advantage because (and I guess this shows that I watched this show to much) you don't decide which posistion to take. You spin in order, starting with the losers first and whoever won the most last.
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EdCollins
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October 3rd, 2019 at 10:25:03 PM permalink
Getting back to Mike's original post...

I'm a big fan of the game Mastermind, and basically that's what this game is, with just four peg colors, four columns (slots), and the stipulation that duplicate peg colors are not allowed in the code.

After placing your first selection randomly, you will either have zero right, one right, or two right.

You can't have exactly three right, and if you have four right you've immediately won, so you don't need to worry about how you play next.

If you have zero right, there are just nine codes remaining.
If you have one right, there are just eight codes remaining.
If you have two right, there are just six codes remaining.

If you are fast enough to run back and forth to get in FOUR different guesses, then it might be wise for your second (or third) guess to be a sequence that you know is NOT possible, in order to get more feedback on this guess than you otherwise would.

The reason I say this is because many years ago I wrote a program that played Mastermind. I was unhappy with all of the programs and apps I found, and so I wrote my own. (I wanted many more features than what all of the other apps offered. I specifically wanted the computer to be able to play against itself in batch mode, for any number of desired games, which no other program could do.)

After writing it, I discovered that at times the program would play a NON possible code, to lower its overall solution rate. By playing a non possible code it got more constructive feedback on what codes were remaining than it did if it had just played a possible code.

And if you happen to get two right on Guess #1, which reduces the number of possibles to just six, you should be able to play optimally to solve it on or before Guess #4. No way should it take you a full five guesses in this case. But again, to solve it by Guess #4 you might have to play a non-possible code for the additional feedback it brings.

However, I suspect most people aren't fast enough to run back and forth in the time allowed to get in four different guesses. And if you only have three guesses, I suspect choosing a non-possible guess on Guess #2 would not at all be ideal. It wouldn't give you enough extra feedback to justify wasting a full guess on a solution that you know could not work, and only having one guess remaining.

Alas, I just looked for this old program I wrote and I can't find it. I did have a hard drive crash a half dozen or so years ago, and I lost a few things that weren't fully backed up. I now suspect I lost this program. Too bad, because I could have set up these parameters and watched it play against itself a few million times, to see how what it's average solution time was with these parameters, (just four colors and no duplicate colors) and how often and when it may have played a non-possible code.
AZDuffman
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October 4th, 2019 at 2:35:42 AM permalink
Quote: michael99000

Maybe. Although in this case you never go over the $1.00 mark and bust when you go first



No, but it is a huge advantage to be able to stand on 0.65 and make the other players bust.
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Wizard
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October 4th, 2019 at 5:13:50 AM permalink
Quote: EdCollins

The reason I say this is because many years ago I wrote a program that played Mastermind. ...



I wrote a Mastermind game too once. You could even play it online. I had the computer just play any code that might win. Always wondered if a faster way to a win was to pick a non-possible code. Thanks for addressing that.
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EdCollins
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October 4th, 2019 at 9:57:13 AM permalink
Quote: Wizard

I wrote a Mastermind game too once. You could even play it online. I had the computer just play any code that might win. Always wondered if a faster way to a win was to pick a non-possible code. Thanks for addressing that.

Yea, and a simple (albeit extreme) example will help to prove that.

Assume you're playing a Mastermind game with four pegs (columns) but with 100 colors, not six, as in the standard game. And further assume you've figured out that the code (for the sake of simplicity) is red-red-red-?. You don't know that fourth peg color, nor have you eliminated any colors it might be

Well, there are then exactly 100 possible codes left. And if your guesses are possible guesses each time (red-red-red-blue, red-red-red-yellow, red-red-red-orange, etc.) it might take many guesses before you stumble upon the right code. You're not getting any feedback when you miss, other than to know that color wasn't the correct color for that fourth slot. (I believe the average solution is 50.5 rows from this point forward.)

But yet if your guess is four different colors each time, which isn't a possible code of course, you can lower your average solution per row considerably.

For example, your first guess might be brown-purple-white-black and then if that reveals no keypegs, try magenta-green-blue-yellow, etc.

This way you are certain to try all 100 possible colors in as little as 25 rows, and are certain get a black or a white keypeg by then. Once you do, you either immeidately know the code (if you drew a black keypeg) or at most, another three guesss to narrow down which color drew that white keypeg.

In practice, making non possible codes reduces the average solution by a much smaller margin, but it is there.
EdCollins
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October 4th, 2019 at 10:44:18 AM permalink
Quote: Wizard

I wrote a Mastermind game too once. You could even play it online. I had the computer just play any code that might win.

I think just about every programmer has written their own Mastermind game.

And that's exactly why so many of them are horrible. Because the programmer usually codes them early in their career, when they are just starting out, when their skill set is minimal. And because of that most of the programs have no polish, they have no cool features, they often contain bugs, etc. (More than once I've seen programs that don't reveal the proper keypeg information, usually when a double color is introduced.)

And soon after the programmer begins this Mastermind project he/she gets bored with it and moves on to something else, before ever finishing it.

There have got to be thousands of different Mastermind programs out there, for all operating systems and platforms. I used to collect screen captures of every one I could find, and I think at one point my folder had more than 200 such images.

I've probably downloaded and played with dozens and dozens and dozens of such programs. And yes, MOST of them are/were horrible.

And most did what yours did not do... allow the computer to solve one of YOUR codes. Most, of course, are just written so that the computer will give YOU a code to solve and give feedback for each guess you make, but that's it.

I wanted to go a few steps further. Not only did I want to play the computer and have it solve a code I created (along with me attempting to solve a code it created), I wanted the option for the computer to play against itself, game after game, unattended, and keep track of all of the results. I also wanted to be able to go into EDIT mode and enter a problem from one of my Mastermind puzzle books, and have it instantly spit out the solution.

And I did all of this. It was sweet. My four different game mode options were

Computer Codebreaker vs. Human Codemaker
Human Codebreaker vs. Computer Codemaker
Computer vs. Computer
Human vs. Human

I had lots of features, like the ability to click a button to reveal exactly how many codes, and WHICH codes were still possible, given the game state so far.

I had an option for different levels of computer strength. Strength 1 for the computer was just selecting a random (but possible) guess each time, as you mentioned. Strength 2 was selecting a possible guess, but not random, as some possible guesses are better than other possible guesses. Strength 3, as I described earlier, selected, at times, non-possible guesses, if it determined that was the best move.

My program had the ability to change the number of available colors (probably from 2 to about 10) and to change the number of columns. (From 3 to 6 as I recall.) Recall "Super Mastermind" has 5 columns and 8 colors while regular Mastermind has 4 columns and 6 colors.

I had an option to allow guesses that contained an empty slot, an option to allow or not allow doubles in the code, etc.

It really kills me that I seem to have lost this program. I had no idea until last night that it was gone and that I didn't have a copy of it anymore. I looked and looked and looked and just couldn't find it. I thought it was in one of my folders on my home PC and those folders show VERY early versions of the program... but NOT the finished product.

And right now I simply don't have the energy to want to begin from scratch and start coding it all over again. (Maybe someday when I retire.)

Anyway, sorry to hijack your thread with this boring Mastermind story. Obviously, I used to love Mastermind. When I was a teenager I could be heard running around the house, "Someone give me a code to solve!" I taught my kid sister how to play and give proper feedback for guesses so she could set me up with a code to solve. She had to be no more than seven or eight years old at the time.

Remember the scene in "Conspiracy Theory" when Mel Gibson's character had to purchase "The Catcher in the Rye" each time he saw that book in a bookstore? That's sort of how I feel about "The Official Mastermind Handbook" by Leslie H. Ault. (I don't even have to look up the author's name... I know it by heart.) I used to LOVE this little book, and I always wanted to buy another copy of it each time I saw it in a bookstore. (I never did... but I really wanted to.)

Finally, I think I own every commercial copy of every version of Mastermind that exists. Tip: All versions from the mid 80s up to now stink. The parts and quality are terrible. The best version is the Super Mastermind game that came out in the late 70s/early 80s.
Last edited by: EdCollins on Oct 4, 2019
ThatDonGuy
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October 4th, 2019 at 12:14:48 PM permalink
Quote: AZDuffman

Lots seem clueless as to strategy IIRC. They used to do season tix for LA based teams. The strategy there was put the lowest price on the Rams/NFL as they had just 10 games. (I assume included exhibition season.) Then make a guess as to the NHL/NBA/MLB. Bob would tell losers this after.


Except that there were some years when the Kings owner gave out really cheap seats, so the bottom two prices were pretty much next to each other.

Also, the "original" two were Janice (trivia: she was the May 1971 Playboy Playmate of the Month), and Anitra Ford; Dian Parkinson (yes, that's how her first name is spelled) was added later. Holly was brought on to replace Anitra.

As for Race Game strategy, you have to take into account the time limit - I don't think I have seen anybody get more than three guesses.
If the first guess has none right, move the prices one to the right, and put the rightmost price on the leftmost prize as you are running back to the display.
If the first guess has one right, assume it is the rightmost one, and rotate the other three. Similarly with having two right.
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