Wednesday, September 4, 2019

The Ultimate Price is Right Strategy Guide: Secret X

Secret X

Rules
A main prize is shown and a 3x3 tic-tac-toe grid is revealed. One of the squares in the middle column has an "X" in it, but the contestant does not know which one. The contestant gets one X for free and can win two more by guessing prices of small prizes. After the contestant places their X's, the location of the secret X in the middle column is revealed. If the contestant has three X's in a row, including the secret X, they win the main prize.

Random fact
While this is rarely stated by Bob or Drew, the three X's in a row to win the game must include the secret X. The contestant cannot win by placing three X's all in the left-most column or three X's all in the right-most column.

Win-loss record
  • Actual (seasons 29-47): 132-120 (52.38%)
  • What it would be by random chance: 1/3 (33.33%) (This assumes the contestant doesn't do anything stupid, like put an X in the center row or place their first two X's in the same column.)
The correct guess for the small prize was...(seasons 40-47)
  • The more expensive price: 70 prizes (35.71%)
  • The cheaper price: 126 prizes (64.29%)
The secret X was in which square? (seasons 40-47)
  • Top square: 38 playings (38.78%)
  • Middle square: 51 playings (52.04%)
  • Bottom square: 9 playings (9.18%)
Strategy
Part 1: Small prize pricing
As you can see, the cheaper price is right almost 2/3 of the time, so if you're not sure, go for that one.

Part 2: Where to place the X's

Part 2a: If not playing for a car
As you can see, the producers like putting the secret X in the middle and really don't like putting it at the bottom. So place the X's in this order: top left, bottom right, and top right. Of course, any ordering where you first cover the middle square, then cover the top square will work. Just whatever you do, don't place an X in the middle row--believe it or not, that has happened.

Part 2b: If playing for a car
As Flerbert419 at golden-road.net pointed out, of those 9 playings where the X was at the bottom, 6 came when the game was played for a car. In fact, of the 13 playings for a car from season 40-47, the X was at the top twice, in middle 5 times, and at the bottom 6 times. So if you're playing for a car, you should cover the bottom square first, then the middle. Start with the lower left, then the lower right, then either of the top corners.

Tuesday, September 3, 2019

The Ultimate Price is Right Strategy Guide: Safe Crackers

Safe Crackers

Rules
Two prizes are shown, a main prize and a prize with three digits in the price. The contestant is given the three digits in the smaller prize's price; if they can arrange them correctly to form the price of the smaller prize, they win both prizes.

Random fact
This game has an unwritten rule: the price of the smaller prize ends in 0. This has been true in every playing of Safe Crackers since at least season 34.

Win-loss record
  • Actual (seasons 29-47): 98-95 (50.78%)
  • What it would be by random chance if you follow the 0 rule: 1/2 (50%)
The correct price to choose was...(seasons 40-47)
  • The less expensive price: 32 playings (38.10%)
  • The more expensive price: 52 playings (61.90%)
Strategy
Start by remembering the 0 rule in this game--that narrows it down to 50/50. Then if you're not sure of which price to choose, there are two things that can help you out here:
  • The producers like to use the more expensive option. This means a price like $970 is more likely to be right than $790.
  • Listen to the amount the entire prize package is worth and do some mental math estimates. If the prize package is worth $8,900 and your choices are $790 or $970, then the price of the main prize must be either about $8,100 or $7,900. Depending on the prize, $7,900 sounds a lot more like a price for a prize than $8,100, which would make $970 the more likely option.

Monday, September 2, 2019

The Ultimate Price is Right Strategy Guide: Rat Race

Rat Race

Rules
3 main prizes are shown, usually including a car. Then 3 smaller prizes are shown. The contestant must guess the first prize to within $1 (above or below), the second prize to within $10 (above or below), and the third prize to within $100 (above or below). For each of those they get correct, they get to choose a mechanical rat out of the five on the track. Those rats then are released. If the contestant chose the rat that finished first, they win the largest main prize (again, usually the car); they chose the rat that finished second, they get the middle prize, and if they chose the rat the finished in third, they get the third prize.

Random fact
They once twice* played this game for cash instead of a car. You can see how the contestant did in one of those playings here:
* Thanks to TPIRfan#9821 at golden-road.net for the correction!

Win-loss record (seasons 38-47): 40-68 (37.04%)

Which lane contained the winning rat? (seasons 38-47)
Note: the following list only counts playings where the race was actually run.
  • Lane #1 (the left most lane): 34 playings (32.38%)
  • Lane #2: 18 playings (17.14%)
  • Lane #3: 17 playings (16.19%)
  • Lane #4: 15 playings (14.29%)
  • Lane #5 (the right most lane): 21 playings (20.00%)
Which rat won? (seasons 38-47)
Note: the following list only counts playings where the race was actually run.
  • Blue: 17 playings (16.19%)
  • Green: 20 playings (19.05%)
  • Orange: 26 playings (24.76%)
  • Pink: 23 playings (21.90%)
  • Yellow: 19 playings (18.10%)
What were the values of each of the prizes? (seasons 44*-47)
* I'm choosing season 44 to start with because before that season, they sometimes had second prizes worth less than $30.
  • First prize: $1.49-$7.99
  • Second prize: $40-$90
  • Third prize: $110-$300
Strategy
Part 1: Prize pricing
  • First prize: For the first prize, your guess should be between $2.49 and $6.99, inclusive. Of course it's possible they could expand the range of prices of the prize, but the $7.99 item they used in season 47 was a full $1 more than any other first prize they had ever used, so I doubt they'll expand much further any time soon. Beyond that range, know the price.
  • Second prize: Your guess should be between $50 and $80 inclusive. Beyond that, know the price.
  • Third prize: Guess $200. They have never used a third prize that was strictly less than $100 or strictly more than $300. 
Part 2: Which rats to pick
Pick the endpoints! As you can see, no color has a huge advantage, but one lane does. For whatever reason, the left most lane wins significantly more often than any other lane, so you should choose whatever rat is there. Then go for the right most lane. If you were good enough at pricing to have a third rat, choose your lucky color from the three rats in the middle.

Saturday, August 31, 2019

The Ultimate Price is Right Strategy Guide: Range Game

Range Game

Rules
A prize is shown as is a $600 range for that prize. The contestant chooses a $150 range inside that $600 range. If the range the contestant guesses for the prize contains the price of the prize, they win.

Random fact
The rangefinder is manually controlled by a stagehand. Usually that stagehand behaves, but not always...

Win-loss record (seasons 29-47)
  • Actual (seasons 29-47): 212-189 (52.87%)
  • What it would be by random chance: 1/4 (25%)
The price was how far from the bottom? (seasons 41*-47)
  • $0-$149: 0 playings (0%)
  • $150-$199: 3 playings (2.21%)
  • $200-$249: 17 playings (12.50%)
  • $250-$299: 54 playings (39.71%)
  • $300-$349: 34 playings (25%)
  • $350-$399: 18 playings (13.24%)
  • $400-$449: 9 playings (6.62%)
  • $450-$600: 1 playing (0.74%)
* I'm starting with season 41 because season 40 had some patterns that have not been repeated since--for example, the value of the prize was between $150 and $200 from the bottom of the range 12 times in that season.

The last two digits of the prize's value were...(seasons 41-47)
  • Between 00 and 24: 31 playings (22.79%)
  • Between 25 and 49: 29 playings (21.32%)
  • Between 50 and 74: 40 playings (29.41%)
  • Between 75 and 99: 46 playings (33.82%)
Strategy
Since no price is in the bottom $150, you should make sure the range moves up by $150 before you press the button. Beyond that, know the price, though if you're clueless, let the rangefinder move up $250 from the bottom before you press the button. There used to be a pattern where the last two digits were more frequently between 75 and 99 than the other options, but that has been changed in the last couple of seasons; in fact, there were only 3 playings in season 46 and 4 in season 47 where the last digits were in that range. Thus, a strategy like "make sure two multiples of $100 are covered by the range" is no longer any better than random chance.

Friday, August 30, 2019

The Ultimate Price is Right Strategy Guide: Race Game

Race Game

Rules
Four prizes are shown as are four price tags. The contestant must match up the price tags to the corresponding prizes. The contestant is then shown how many they got correct; if they got fewer than 4, they get to make changes and try again. They keep going until they either run out of the allotted 45 seconds or get all 4 right.

Random fact
The show kicked off its 40th season by playing Race Game for four cars. Here's how it went:

Win-loss record
  • Actual (seasons 29-47): 113-97 (53.81%)
  • What it would be by random chance: N/24, where N is the number of unique solutions the contestant can try in 45 seconds.
Which combinations were correct? (seasons 40-47)
  • 1234: 7 playings (8.05%)
  • 1243: 5 playings (5.75%)
  • 1324: 0 playings (0%)
  • 1342: 2 playings (2.30%)
  • 1423: 0 playings (0%)
  • 1432: 3 playings (3.45%)
  • 2134: 8 playings (9.20%)
  • 2143: 5 playings (5.75%)
  • 2314: 8 playings (9.20%)
  • 2341: 2 playings (2.30%)
  • 2413: 3 playings (3.45%)
  • 2431: 4 playings (4.60%)
  • 3124: 4 playings (4.60%)
  • 3142: 0 playings (0%)
  • 3214: 3 playings (3.45%)
  • 3241: 2 playings (2.30%)
  • 3412: 0 playings (0%)
  • 3421: 4 playings (4.60%)
  • 4123: 4 playings (4.60%)
  • 4132: 4 playings (4.60%)
  • 4213: 4 playings (4.60%)
  • 4231: 2 playings (2.30%)
  • 4312: 7 playings (8.05%)
  • 4321: 6 playings (6.90%)
The way to read the above table is that "1" means the cheapest prize, "2" means the second cheapest prize, "3" means the second most expensive prize, and "4" means the most expensive prize. So 2143 means the prize on the left was the second cheapest, the second prize from the left was the cheapest, the third prize was the most expensive, and the prize on the far right was the second most expensive.

Strategy

DO NOT LOOK AT THE AUDIENCE!!!

You simply do not have time. Your goal is to get 4 tries in the 45 seconds (no one has had more than 4 attempts since at least season 29.) Looking at the audience wastes valuable time. So this really comes down to a "know the prices" game--unfortunately, there's no mathematically clever way to guarantee a win in just 4 tries. Do try to keep track of your previous guesses--they can help you narrow down what prices go where. Also note that if you get two right, switch two, and you end up with none right, you know the correct answer: switch the two back that you just switched, and then switch the other two. For example, let's say you try 4132 and you get two right. You then switch the first two to get 1432 and have none right. Then you know the correct answer must be 4123--switch the first two back and the switch the last two.

Thursday, August 29, 2019

The Ultimate Price is Right Strategy Guide: Push Over

Push Over

Rules
A prize is shown as is a set of blocks with numbers on them. Somewhere in that set is the four or five digits of the price of the prize. If the contestant selects the price of the prize correctly, they win.

Random fact
When Push Over first debuted, it had a red and yellow set instead of the blue and yellow set we have now. Here's the debut playing:


Win-loss rate
  • Actual (seasons 29-47): 254-256 (49.80%)
  • What it would be by random chance: 1/6 (16.67%) for four digit prizes or 1/5 (20%) for five digit prizes. Of course, this assumes all possible prices are equally likely, which is almost always bogus.
Which price was correct? (seasons 40-47)
Four digit prizes
  • x x x x x [X X X X] was right: 0 playings (0%)
  • x x x x [X X X X] x was right: 36 playings (21.43%)
  • x x x [X X X X] x x was right: 51 playings (30.36%)
  • x x [X X X X] x x x was right: 38 playings (22.62%)
  • x [X X X X] x x x x was right: 38 playings (22.62%)
  • [X X X X] x x x x x was right: 5 playings (2.98%)
Five digit prizes
  • x x x x [X X X X X] was right: 0 playings (0%)
  • x x x [X X X X X] x was right: 23 playings (50%)
  • x x [X X X X X] x x was right: 16 playings (34.78%)
  • x [X X X X X] x x x was right: 5 playings (10.87%)
  • [X X X X X] x x x x was right: 2 playings (4.35%)
Strategy
Mostly know the price, but a couple of things can help you here:
  1. The correct price is never the first one. You must always push at least one block over.
  2. Similarly, the very last possible price is rarely correct. Only select that one if you're sure of it.
  3. There hasn't been a prize worth less than $5,000 in this game since the end of season 41. So any prices less than $5,000 can be immediately thrown out.
  4. Since season 44, there haven't been more than 3 prizes in a season in this game that ended in a 5 or a 0. So if you're not sure, throw those prices out. However, prizes that end in 9 do come up with reasonable frequency, so don't throw those out.

Wednesday, August 28, 2019

The Ultimate Price is Right Strategy Guide: Punch a Bunch

Punch a Bunch

Rules
Four small prizes are shown, each with an incorrect price. The contestant must decide if the actual price is higher or lower than the price shown. However many they get correct, they get that many punches on the punch board. The contestant then punches that number of holes. One at a time, Drew reveals how much each punch was worth; the contestant can choose to throw that money away and keep playing or quit with the amount of money shown. The contestant wins whichever amount of money they keep, or the last amount of money revealed if they played until their last punch.

Random fact
When this game first debuted, it was played much differently. You can see an example here:

Win-loss record
  • Actual (seasons 29-47): 22-336 (6.15%)
    (Note: it only counts as a win if the top prize, $25,000, is won.)
  • What it would be by random chance: 1/25 (4%)

The correct choice for the small prizes was...(seasons 40-47)
  • Higher: 239 prizes (43.61%)
  • Lower: 309 prizes (56.39%)
How often was each combination of highers and lowers correct? (seasons 40-47)
  • 4 Higher: 0 playings (0%)
  • 3 Higher, 1 Lower: 13 playings (9.49%)
  • 2 Higher, 2 Lower: 77 playings (56.20%)
  • 1 Higher, 3 Lower: 47 playings (34.31%)
  • 4 Lower: 0 playings (0%)
Stats for each hole (seasons 40-47)
The way to read the following table is for each hole, the first line is how often it contained $10,000 or more, and the second line is how much money it contained on average. For example, the top left corner reads "0/18"--this means that in 18 punches, it contained $10,000 or more 0 times. The average of all the values that were found in that hole was $1,302. Note this excludes the playing where a dream car was offered.

 0/18   0/5    0/11   0/10    0/6   0/7    0/8    0/10   0/5   0/14
$1302  $2200  $1736  $1450   $792  $1121  $1813  $1125  $2350 $1686

 1/5    0/8    1/17   1/13   0/12   0/12   0/9    0/20   0/14   0/4
$2900  $1344  $3059  $1308   $583   $588  $1122  $1183  $2264  $563

 0/3    0/11    0/9   1/10   0/27   0/14   0/11   2/12   0/9    0/0
$1083   $714  $1889  $1950  $1535  $1682  $1114  $3600  $1667   N/A

 0/2    0/11   0/16    0/6   1/8    0/9    0/7     0/9   0/15   1/3
$1375   $632   $916   $767  $4169  $1317  $2571   $761  $1130 $3533 

 0/6    1/10   0/6     0/3    0/2   0/5    0/4    1/10    0/8  0/11
$625   $1345  $1958  $1867   $175  $3700   $588  $2475   $650  $782

Bold means $10,000 or more was found there at least once.

Strategy
Part 1: Small prize pricing
Know the prices. They don't make this part hard because they want people to punch the board. Do note that it's never been all four prices are higher or all four prices are lower, so if the first three have the same answer, you know the fourth will be the opposite answer.

Part 2: Which holes to punch?
DON'T PUNCH THE CORNERS!! The producers know that people like to punch the corners so they never place the big money there--you can see none of the corners has had the big cash since season 40. (To be fair, the dream car was in the top right corner; I excluded that playing because the car replaced a $100 slip. I don't know if the producers placed all the slips, then replaced a $100 they had put in the top right corner with the car or if they intentionally placed the car in that spot.) Otherwise, it's really a crapshoot. I personally would go for the 4th through 7th spots on the bottom row, because very few people punch those spots. If you want to try something no one else has, punch the far right spot in the middle row--no one has tried that since season 39 at least.

Part 3: Should you continue?
The naive analysis would simply be to look at the average amount on the board, which is $2,260 $2,060 (thanks to TPIRfan#9821 for the correction!), and say that if you have more than that you should stop. So that analysis would state that if you get $2,500 or more, stop, $1,000 or less, and you should continue. I'm going to go a little deeper than that, though. Here's another table...

If you   # of picks     Probability of all other picks being
 have       left        strictly less than what you have now
$250         1                        10.20%
$250         2                         0.85%
$250         3                         0.054%

$500         1                        30.61%
$500         2                         8.93%
$500         3                         2.47%

$1,000       1                        51.02%
$1,000       2                        25.51%
$1,000       3                        12.48%

$2,500       1                        71.43%
$2,500       2                        50.60%
$2,500       3                        35.52%

$5,000       1                        87.76%
$5,000       2                        76.79%
$5,000       3                        66.98%

$10,000      1                        95.92%
$10,000      2                        91.92%
$10,000      3                        88.01%

Note: this table assumes that the amount you currently have is the one and only punch you've taken so far. It doesn't change things drastically if you remove that assumption. 

As you can see, I've highlighted the rows where continuing would mean that you'd lose money more likely than not. Here's that strategy in a simple bullet list:
  • If you have $500 or less, continue.
  • If you have $1,000, stop if and only if you have exactly 1 pick left.
  • If you have $2,500, stop if and only if you have 1 or 2 picks left. If you have 3, continue.
  • If you have $5,000 or more, stop. Period. (Yes, I know of the guy in the 1990s who threw away $5,000 when the top prize was $10,000, and then managed to get the $10,000. That's so incredibly unlikely you should not follow suit.)