The Ultimate Price is Right Strategy Guide: Any Number

Any Number

Rules

Two prizes are shown: a car and a prize with three digits in its price. A board is shown with three rows: one for the car, one for the 3 digit prize, and one for the piggy bank. The first number of the car is revealed. In the remaining 10 squares, each number 0-9 inclusive appears exactly once. The contestant picks digits one by one; after each selection, the location of that digit is revealed. The contestant wins the prize whose digits they fill in first.

Random fact

In addition to being the first game in alphabetical order, this is the first game that was ever played on the current iteration of the show. You can see it, and the entire first episode of the show, here:

(Note the still picture is of Bonus Game, not Any Number.)

Key Stats

• Win-loss record (seasons 29-46): 166-285 (36.81%)
• Chance of winning if you pick numbers completely randomly: 9/35 (25.71%)
  (Note I calculated that by enumerating all orderings of choosing the numbers 0-9. Later, I found this mathematical analysis of the game. Thankfully, we both ended up with the same result.)
• Which digit appears where? (Seasons 40-46)
  
                   % in 3 digit  % in piggy
  Digit  % in car      prize         bank  
    0      16.07       47.62        36.31
    1      45.24        8.93        45.83
    2      44.64       16.67        38.69
    3      58.92       12.50        28.57
    4      39.88       23.81        36.31
    5      29.76       46.43        23.81
    6      50.00       33.33        16.67
    7      35.71       32.14        32.14
    8      40.48       35.71        23.81
    9      39.29       42.86        17.86
  
  Let me explain how to read that table with an example. The first entry, 16.07, means that the number 0 was in the car 16.07% of the time, which is less than 1/6. By random chance, you would expect it to be in the car 40% of the time. (Actually, you could argue that the first digit of the 3 digit prize and the first digit of the piggy bank are never 0, so it should be in the price of the car 50% of the time based on random chance. But I digress.)
• The ordering of the piggy bank digits (seasons 40-46):
  
  Order    %  
  $3.21  38.69
  $3.12  48.81
  $2.31   4.76
  $2.13   7.14
  $1.32   0.00
  $1.23   0.60
  
  This table is referring to the ordering of the digits in the piggy bank. "$3.21" means the largest digit that appears in the piggy bank is first, the middle digit is second, and the smallest digit is last; a piggy bank price of $9.42 would fit that example. Similarly, $2.31 means the largest digit is in the middle of the piggy bank, the second largest digit is in the first spot, and the smallest digit is in the last spot; a piggy bank price of $4.92 would fit that example.
  

Strategy

The strategy comes out of those tables above, along with the paint and fabric protection rule. Cars in Any Number almost always have paint and fabric protection in order that the last number won't be 0. In fact, in those 168 playings of Any Number, the last digit of the car was a 0 eight times. That's less than 1 in every 20 playings. The 5 was the last digit only 11 times. So here is the strategy to this game:

1. Start by trying to find the second digit of the car, as you should be able to get that in just a couple of tries. If the first digit is a 2, go for a 1, 2, or 3 as the second digit if you're not sure. And this is where you can try a 0 if the first digit is a 2. Of the 27 times a 0 was in the price in the car from seasons 40-46, 18 times it was the second digit. 
2. Once you've found that, pick the 3 and the 6 if you haven't already. You have at least a coin flip chance of those being in the car.
3. At this point, you've probably found at least one number in the 3 digit prize and/or the piggy bank. Note the largest digit in the piggy bank is the first digit 87.5% of the time, so if you see _ 6 _ in the piggy bank, pick numbers less than 6. But if you have 6_ _ in the piggy bank, guess numbers greater than 6. Update: jhc2010 pointed out at golden-road.net that the first digit of the piggy bank has been its largest digit in every playing since October 29, 2015. So you should really follow this piece of advice.
4. If at any point the above tips don't help, and you can't figure out which numbers would appear in the 3 digit prize, then pick the remaining numbers in the order they appear most frequently in the car. That order is 3,6,1,2,8,4,9,7,5,0. But don't just pick them haphazardly in that order--after each digit, look to see if you can apply the piggy bank concept in rule 3 or if you got any clues to what the 3 digit price prize might be.
5. Speaking of the 3 digit prize, thanks to pannoni1 at golden-road.net, I realized there hasn't been a prize under $500 offered since season 42. So feel free to try the lower numbers a bit if you only have the first number to go in the second prize.
6. If you can't remember that order, just remember this: don't pick the 5 or the 0. Those are by far the least frequent numbers in the car, which is not surprising, since those are the numbers contestants pick the most frequently thinking they're the last number in the car. But they almost never are.