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  2. Lucky 7 is a very modern slot game, organized around a simple set of basic rules that will ensure all players, experienced or not, an easy beginning on the reels. The game matrix contains 5 spinning reels and 18 pay lines, which show you where you need to try and align identical reel symbols in.
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'All will be well if you use your mind for your decisions, and mind only your decisions.' Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.

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The game show The Price is Right has so many fun games to analyze.

Tricks

One of my favorites is called “Lucky Seven” or “Lucky $even.” This is a guessing game and the prize is a brand new car.

Here is how the game works. You start out with seven one-dollar bills. You must then guess four digit’s of the car’s price in succession. After each guess, the actual digit of the price is shown.

If your guess was correct, you hold on to your cash. If your guess was wrong, then you have to pay the difference between the actual number and your guess. So if you guessed 5 and the actual was 7, you lose 2 dollars.

You lose the game if you run out of money. You win the game if you have at least one dollar remaining, and you can use one of those dollars to “buy” the car. Pretty cool way to win a car if you ask me!

An example of game play

It’s definitely easier to see how this game works than to read its rules.

Lucky 7 Game Cheats

So here’s a clip of the game, courtesy of CBS:

The strategy on the first three guesses

Lucky 7 Game Tricks

If you watched the above clip, you can see that there’s no easy way to guess the thousands digit, or the hundreds, or the tens. These are dictated more by common sense like whether a car is worth around $12,000 or instead $17,000. It would make sense to guess near the middle if you have no clue, like a 4 or 5 or 6 to minimize losses.

Something that may help is an unwritten rule that the show has not used zeros as digits since the early 1980s (undocumented but written on Wikipedia).

Other than that, it’s something of crapshoot. If you’re skillful or lucky enough to make it to the final digit, then you can use a bit of strategy.

The final digit: think dominated strategies

Suppose you’ve guessed the first three digits right on the nose and you’ve made it to the final guess with all seven dollars. What should you do?

The problem can be solved by thinking about which guesses are sensible. Take the guess of 1. Does it ever make sense to guess 1?

The answer is clearly no. With seven dollars, you can be off by six and still win the game. For a guess of 1, that means you will win if the actual digit turns out to be between 1 and 7. You will still lose the game if an 8 or a 9 show up!

Lucky 7 Slot Games

Notice that instead you could have guessed 2 which wins for digits between 1 and 8. This is definitely better, but you still lose if a 9 shows up.

You can instead guarantee a win by guessing 3. Now the entire range of 1 to 9 is covered by a difference of six from your guess.

This argument shows that 1 and 2 are dominated strategies. Regardless of your beliefs, there is simply no way to justify them. It is always better to guess 3 if you have seven dollars remaining.

By symmetric reasoning, the guesses 8 and 9 are dominated by the guess of 7.

The right guesses–the ones that cover the entire range and win for sure–are therefore 3, 4, 5, 6, and 7.

The final digit: a cheat sheet

I will not belabor the calculations, but it can easily be shown that you can win for sure if you have 6 dollars (and guess 4, 5, or 6) or even if you have 5 dollars (and guess 5). The other choices in these situations are dominated strategies and should never be guessed–though I have seen people guess wrong and lose!

The game is not as simple when you have 4 dollars or less. Now it is not possible to guarantee a win. But it is possible to eliminate bad guesses by considering dominated strategies.

Suppose you have 4 dollars on the last guess. Would you ever want to guess 3? The answer is no. With 3, your range is 1 to 6, and you’d be better off guessing 4, which has a larger range of 1 to 7.

The logic can be extended to consider the other dollar amounts of 3 and 2. You can usually eliminate at least one number and increase your odds of winning.

I’ve compiled a small cheat sheet table below.

Dollars at final guess

Reasonable numbers to guess

7*

3, 4, 5, 6, 7

6*

4, 5, 6

5*

5

4

4, 5, 6

3

3, 4, 5, 6, 7

2

2, 3, 4, 5, 6, 7, 8

1

any number, must guess exactly right

Lucky Sevens Game

*can win for sure

Here’s an example just to reiterate. If you have 3 dollars at the end, you should definitely guess between the digits 3 and 7. You cannot guarantee you’ll win but you will give yourself the widest possible ranges by avoiding the guesses 1, 2, 8, or 9. Any of the remaining guesses are reasonable depending on your instinct.

(And my wildest dream is that this table actually helps someone. Please memorize this table if you’re going to be on the show–and good luck!)

You start the lucky 7 card trick by going through the cards, placing a few of them face down in a pile. You tell the spectator that your lucky number is 7. You locate a 7 and place it face up on top of that pile, then put the remaining cards on top of it. Now the 7 is the only card facing up in the deck. Have the spectator cut about one-third of the deck, then two-thirds of the remaining cards. Now you have two piles. Shuffle the remaining cards and give them a cut. The bottom card of the pile you just cut is the spectator’s card. Put that pack on top of the first pile. After that, you look for the face-up in the deck. You put it on top of the deck, then tell the spectator that you will go for three 7s, just like in a casino. Every time you count, put the seventh card face down on the table, then put the deck aside. Now you take the three cards and move the top one to the bottom 6 times. The 7th card is the selected one.

Explanation of Lucky 7 Card Trick

Lucky 7 card Trick Tutorial

First, count 20 cards from the bottom of the deck, then place a 7 in closely after them. Then, you have to place 20 cards on the table, as you look for the 7. The spectator must not know that there are 20 cards on the table. After locating the 7, place it face up on that pile and put the rest of the deck on top. Then the spectators cuts one-third of the deck, then two-thirds of the remaining. The second cut will include the lucky 7. Their card will be selected out of the remaining cards and put on the first pile. The remaining cards out of that pile go under the ‘7’ pile, then that on top of the first.All you have to do now is locate the 7, bring it, along with the following cards on top of the deck, and the trick will work.