Monday, July 15, 2019

The Ultimate Price is Right Strategy Guide: Dice Game

Dice Game

Rules
A car is shown and the first digit of the car's price is revealed. The remaining four digits in the car's price are guaranteed to be between 1 and 6 inclusive. The contestant rolls four dice one at a time, representing the second through the fifth digits of the car, in that order. For each roll, the host checks if the value on the die is correct; if it is, it is lit up. If it is not, the contestant must guess whether that digit in the car's price is higher or lower than the number rolled. After all dice are rolled, the actual digits are revealed, and if the contestant's higher/lower guesses are all correct, they win the car.

Random fact
Believe it or not, a contestant did once roll all the numbers in the price of the car in spite of the 1/1296 (0.08%) chance of that happening:


Win-loss record
  • Actual (seasons 29-46): 179-184 (49.31%)
  • What it would be by random chance: 625/1296 (48.23%)
    Note: That assumes the digits of the car are equally likely to be 1, 2, 3, 4, 5, or 6, and that you go with the odds on every roll.


Which digit of the car had which value? (Seasons 40-46)

                                                                 Actual value                  
Digit of car    1       2       3       4       5       6   
 2nd digit    23.21%  16.96%   8.93%  16.07%  14.29%  20.54%
 3rd digit    16.07%  18.75%  13.39%  17.86%  15.18%  18.75%
 4th digit    13.39%  14.29%  18.75%  19.64%  17.86%  16.07% 
 5th digit     1.79%  15.18%  16.96%  13.39%  42.86%   9.82%
 Overall      16.07%  18.75%  13.39%  17.86%  15.18%  18.75%

Strategy
When I first saw that the actual win-loss record was just barely better than the random chance record, I figured it would be because the producers were using 1s and 6s all over the place, but this turned out to not be true. It's really more a testament to the fact that the producers can add whatever options they want to turn car pricing into a crap shoot (pun not intended.) So here's the strategy:
  • 2nd digit: The show rarely offers cars less than $15,000, so if the first number is a 1, feel free to say higher for anything you roll besides 6. Yes, that means if you roll a 5 and the first number is a 1, you should seriously consider saying "higher." On the flip side, if the first digit is a 2 and you roll a 2, you should seriously consider saying "lower."
  • 3rd & 4th digits: Go with the odds. Period.
  • 5th digit: Go with the odds unless you roll a 4. Look how often the last digit is 5--by saying "higher" on a 4, you're more likely to win than if you say "lower."

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