Optimal strategy for the Race Game

This post shall address the optimal strategy for the Race Game as played on The Price is Right. I shall assume that the contestant has zero knowledge of the value of any prize but is a perfect logician. Here is an example of the game.



Here is my strategy.

1. Randomize first guess
2. For all guesses, choose something that has a chance to win, as evidenced by previous scores.
3. If the score on the first guess is 0, then switch tag over one position, or some mathematical equivalent involving one loop. Do not reverse any two tags (it will take longer, on average, to win if you do).
4. If the score on the first guess is 1, then keep one tag the same and switch every other tag over one position (this should go without saying, given rule 2)
5. If the score on the first guess is 2, then reverse any two tags (this should go without saying, given rule 2)

If you're not able to follow this strategy in your head, then label the tags A,B,C, and D and place them according to the following orders given the prior score history:

Play ABCD first.
If 0, then BCDA
If 0-0, then CDAB
If 0-0-0, then DABC (must win)
If 0-1, then BDAC
If 0-1-0, then CADB (must win)
If 0-1-1, then CDBA
If 0-1-1-0, then DCAB (must win)
If 0-2, then BADC
If 0-2-0, then DCBA (must win)
If 1, then ACDB
If 1-0, then BDCA
If 1-0-0, then CABD
If 1-0-0-1, then CBAC (must win)
If 1-1, then BDCA
If 1-1-0, then CABD
If 1-1-0-1, then CBAC (must win)
If 1-1-1, then BCAD (must win)
If 2, then ABDC
If 2-0, then BACD (must win)
If 2-1, then ACBD
If 2-1-0, then DBCA
If 2-1-1, then ADCB
If 2-1-1-0, then CBAD (must win)

Following this strategy will result in the following distribution of total turns:

Turns	Count	Probability	Return
1	1	0.041667	0.041667
2	4	0.166667	0.333333
3	8	0.333333	1.000000
4	8	0.333333	1.333333
5	3	0.125000	0.625000
Total	24	1.000000	3.333333

So, 10/3 turns on average. If you can get in five rounds, which would take nine seconds per round or less, then you can guarantee winning. If you can squeeze in only four rounds, you will have a 87.5% chance of winning.

Comments? Better strategies?

The question for the poll is what do you think of the strategy?

Q: Why do they never serve beer at a math party?

I don't know the specific rules, but could they let you place less than all four price tags and check?

This is one of those polls where there should be more than one answer; I trust the Wiz, TPIR contestants are idiots, and Wiz should write a book!

Quote: rsactuary

I don't know the specific rules, but could they let you place less than all four price tags and check?

I've never seen anybody ask or try, but I'm quite sure it isn't allowed.

Quote: Wizard

I've never seen anybody ask or try, but I'm quite sure it isn't allowed.

I'm pretty sure that it is. You would look foolish, but I don't see a problem with it.

Of course, you're not taking some things into account, like how tired you would get if you had to try to make every "pass" in nine seconds.

Also, you overestimate the logical abilities of most TPIR contestants. The two things that every contestant should know are:
(a) In Secret X, place your first X in one of the corner spaces (so if you win two more, you have a 2/3 chance of winning instead of 1/3);
(b) In Ten Chances, all of the prices end in zero. Considering that the same applies in Safe Crackers and pretty much everybody knows this as well, you would think the Ten Chances rule would be just as well known.

Now on to the next task...what's the strategy for whether or not to roll again on Let 'Em Roll?
(For those of you who have never seen it: the contestant gets 1-3 rolls based on pricing items. There are five dice, each of which has $500, $1000, $1500, and the other three sides have car symbols. On the first roll, all five dice are rolled; after any roll, assuming the player has another roll (or two) remaining, the player can stop and keep the money - cars are worth zero in this case - or set the dice with cars aside and re-roll the others. If all five dice are cars, the player wins - you guessed it - a car.)

Quote: ThatDonGuy

...Now on to the next task...what's the strategy for whether or not to roll again on Let 'Em Roll?
(For those of you who have never seen it: the contestant gets 1-3 rolls based on pricing items. There are five dice, each of which has $500, $1000, $1500, and the other three sides have car symbols. On the first roll, all five dice are rolled; after any roll, assuming the player has another roll (or two) remaining, the player can stop and keep the money - cars are worth zero in this case - or set the dice with cars aside and re-roll the others. If all five dice are cars, the player wins - you guessed it - a car.)

Yahtzee!

https://youtu.be/EKRYrYCCrdU

Quote: ThatDonGuy

I'm pretty sure that it is. You would look foolish, but I don't see a problem with it.

I think we'll have to agree to disagree on that.

Quote:

Of course, you're not taking some things into account, like how tired you would get if you had to try to make every "pass" in nine seconds.

Nine seconds seems like enough time to me.

Quote:

Also, you overestimate the logical abilities of most TPIR contestants.

Surely you're not suggesting they weed out the non-perfect logicians in the screening process?!

Quote:

The two things that every contestant should know are:...

Let's make a new thread for any other TPIR games you wish to discuss.

This is how you play optimally:




And not so optimally....: