Reigning "Jeopardy" champion Arthur Chu has lit up the Internet with his smart play, clever strategy, and game theoretical reasoning—concepts that can be used on other game shows, as well. Which made us wonder: What if Arthur Chu had mistakenly put his contestant application in the "Wheel of Fortune" bin?
Strategizing for "Wheel of Fortune" is considerably easier than it is for "Jeopardy." With "Jeopardy," you have to worry about how others will wager their money. On "Wheel," you can safely ignore how your opponents act most of the time and instead focus solely on puzzle solving. If anything, your greatest competition is the producers of the show, who are working hard to make sure you won’t bring down the house during the bonus round.
But let’s not get ahead of ourselves. First, you need to win the main game to reach the bonus round. Here’s your game plan:
Win the Tossup Rounds
Each episode of “Wheel of Fortune” has three tossup puzzles, worth $1,000, $2,000, and $3,000. The board automatically reveals letters one by one until a player rings in with the correct solution. The tossups tend to reward better puzzle solvers, not clever strategists. However, occasionally the tossup reaches a point where almost all letters are on the board. Here, the interaction resembles what game theorists call a duel. Ringing in immediately following a letter—but before you actually know the answer—might be smart. You have to be careful—"Wheel of Fortune" requires you to answer almost immediately after ringing in—but going a split second early ensures that you have first shot on what will (hopefully) be an obvious puzzle.
Stay in Control of the Wheel
In the main game, contestants have three options: spin the wheel and call a consonant, buy a vowel for $250, or solve the puzzle. Each consonant is worth the cash value of the wedge the wheel lands on. Contestants can continue spinning the wheel until they miss a letter or spin a Bankrupt or Lose a Turn.
These rules imply that you should focus on maintaining control over the wheel and mostly ignore your opponents. Unfortunately, staying in control involves guess work—you will not always know for certain that a letter will be in the puzzle—and some luck in spinning. The table below provides some guidance. It looks at how frequently a calling a letter will allow you to keep your turn, using data from more than 3,000 historical puzzles (excluding tossups and the bonus round):
If you have no clue what else to do, begin the round by spinning and selecting the T. Following that, if you cannot figure out any other letters, buy the E. Vowels are criminally undervalued in “Wheel of Fortune”—they cost the same as they did in the show's first season despite inflation and much, much larger dollar values on today’s wheel.
If you still cannot deduce any other consonants from the puzzle, buy the A. Then buy the I. Then spin and guess the R. Continue down the list until you are confident about a missing letter (selecting known and moneymaking consonants before known and costly vowels) or have enough money to solve.
Having a hard time remembering the safest letters? Note that the top eight in order conveniently spell out EAT IRONS.
Know Your Categories
The above list is a guide, not a rule. Some puzzle categories have different letter configurations that should prioritize other letters. “What Are You Doing?”—frequently the category of the all-important prize puzzle—always has a word ending in –ING, like “OPENING THE VAULT” So start with the N, follow with the G, buy the I, and then go through the list as normal.
The category “Things” usually has an S to pluralize the solution. It should be your first consonant. Be careful when the puzzle contains a three-letter word between two others, though. The “Things” might not actually be plural but instead be something AND something else.
“Same Name” always has AND, as in “ELEPHANT AND SWIMMING TRUNKS.” (Sometimes, the AND is an ampersand; the show is really inconsistent on this point.) Go with the N and then the D before buying the A.
The category “Star & Role” is uncommon but always features AS, as in “DANIEL DAY-LEWIS AS ABRAHAM LINCOLN.” Start with the S then buy the A.
Lastly, “Song & Artist” and “Title & Author” has BY in it, as in “THE OLD MAN AND THE SEA BY ERNEST HEMMINGWAY.” This gives you two consonants to grab before dipping into the vowels.
Know Your Letter Strings
You might also deviate from the list when you spot a string of letters, either as you go down the list yourself or after you inherit the board from another player. THE is perhaps the most common word on "Wheel of Fortune." After you guess T with your first spin, you might have a three-letter word appearing as T _ _. Since you are very likely to buy an E down the line, play it safe and take the E here before spinning for the H.
AND is another common word. Seeing _N_ should push you toward buying the A before the E and then spinning for the D.
If the puzzle has a one-letter word, you should buy the A (and then the I) before the E.
–ING words are common outside of “What Are You Doing?” puzzles. So if you see –_N_, be safe and buy the I. If it is where you expect it to be, then spin for the G.
–’_ appears sometimes. These are usually possessives, so the S before the T is appropriate. However, be careful with _’_. Unless the puzzle is about the Oakland A’s, you are probably looking at I’M.
Lastly, –T _ _ N shows up occasionally. This is likely –TION. You should consider skipping A and E and buy first I and O instead.
Some wedges on the wheel require special consideration:
Million Dollar Wedge
If a contestant lands on the Million Dollar Wedge, and then successfully calls a consonant, solves the puzzle for the round, never spins Bankrupt for the rest of the game, has the most money at the end of the game, lands on the million dollar envelope on the bonus wheel, and solves the bonus round puzzle, he wins a million dollars. (Well, he wins an annuity for a million dollars, anyway.) While the Million Dollar wedge makes for exciting television, it is not exceptionally valuable. The number of hurdles that a player has to jump through to actually win the million dollars plus the fact that it is an annuity drops the wedge’s expected value to $5,000 or so, though it becomes more valuable later in the game since you will have fewer spins remaining to hit a Bankrupt. The wedge might be nice to land on, but it should not dramatically affect how you play.
The Mystery Wedge is worth $1,000 for each consonant revealed or a 50/50 shot between $10,000 (and no money from the consonants) and Bankrupt. When deciding, consider how much money you have and how much money you will have by the end of the round. Imagine you had $2,000, hit the Mystery wedge, and called a letter that appeared three times in the puzzle. The wedge grants $1,000 for each of those. Thus, you could take $5,000 with certainty or forgo the $3,000 for a 50 percent chance of going up to $12,000. While that seems worth the risk, you might well accumulate another $3,200 before the end of the round. All things considered, the true gamble is $8,200 or a 50 percent chance of $15,000. That is a risk not worth taking.
New to the current season, the Express allows contestants to call consonants (worth $1,000 each) and buy vowels without having to spin the wheel. The risk is that a missed letter results in Bankrupt. While contestants can pass on hopping aboard the Express, you never should. You might wind up Bankrupt, but it is unlikely you will solve the puzzle if you forfeit control over the round anyway. Also, don’t solve the puzzle if you haven’t called all the consonants in it: Otherwise, you’ll be leaving free money on the table. For some unfathomable reason, three contestants have abruptly stopped to solve prematurely.
The Free Play wedge allows a player to choose any letter without losing his turn if that letter is not in the puzzle; vowels are free and consonants reward the player with $500 apiece. If you are unsure of the puzzle’s solution, consider calling a letter less likely to be in the puzzle. You will maintain your turn even if you are wrong, and the more common letters will still be around when you must take a risk.
The Wild Card allows players to replicate the value of their previous spin or spend it during the bonus round to call an extra consonant. Wild Card holders win the bonus round 7.35% more frequently than non-holders. With the bonus round paying out roughly $37,000 on average, the Wild Card’s added value is about $2,700. Thus, even the overall leader should often use the Wild Card to match a big value spin like $5,000 rather than save it for the bonus round.
This is the least valuable cash wedge on the wheel. While you should still be sure to select letters that you know are in the puzzle, choose letters that are less likely to appear within the puzzle frequently. For example, if you start a “What Are You Doing?” round by landing on $300, call the G first. Save the N for the next spin.
To make this more concrete, imagine an extreme example where the puzzle was “BASKING IN THE WARM SUNSHINE.” Your first spin was worth $300, and your second spin was worth $3,500. If you call N and then G, you end with $4,100 because N appears twice and G appears once in the puzzle. But if you switch the ordering, going with the less common G before the N, your score jumps to $7,300.
Don’t Solve without Money
Some contestants have a bizarre compulsion to solve puzzles regardless of how much money they have accumulated for the round. Perhaps they are worried that spinning again could result in Bankrupt or Lose a Turn, depriving them of guaranteed money. Indeed, "Wheel of Fortune"’s house minimum ensures you will receive $1,000 even if you solve without any money.
Still, this is misguided for two reasons. First, the first $1,000 you win is the least valuable $1,000. In addition to the per-round minimum, "Wheel" also has an overall $1,000 minimum for the entire game to cover the players’ travel expenses. So a person who solves a puzzle for $1,000 and does not accumulate any other money on the show wins the same amount as people who hit Bankrupt every time they spin the wheel.
Second, you need money to advance to the bonus round. Many games are won by the player who solved Round 3’s prize puzzle simply because the prize adds an extra $7,000 or more to the player’s overall score, which smokes opponents who are consistently solving for the $1,000 pittance. An overly conservative player thus has no chance of winning unless they happen to solve the prize puzzle.
Speaking of Round 3, the prize puzzle is an exception to this rule. Since the prize is worth so much, you should solve the puzzle once you know it. Spinning might accumulate a few thousand dollars more but is not worth the risk.
A second—though rare—exception is if you are leading in the overall standings and one of your opponents has a large sum of money for the round. Solving with a minimal amount of money protects your lead and keeps you on track for the bonus round. Spinning might bring you more money for the round, but it could cost you the match.
Bonus Round: Beating the Producers
In the bonus round, players must solve a small puzzle with a very limited supply of letters. The contestant is always given RSTLNE and may pick three additional consonants and one additional vowel. After those are revealed, the contestant has ten seconds to solve the puzzle.
While the goal of the main game is to beat your opponents, the goal of the bonus round is to defeat the producers. Although the producers want the players to win some of the time, they have a vested interest in keeping costs down. They are succeeding, too: only 37.76% of contestants solve the bonus round puzzle.
The producers have the advantage for two reasons. First, RSTLNE is a sham—they know they have to give you those letters and thus choose puzzles in which they appear far less frequently. I analyzed all bonus round puzzles from 2007 to January 2014. The difference between main game and bonus round puzzles is staggering. For example, E makes up 11.32% of all letters in the main game but only 7.87% in the bonus round; T goes from 7.94% to 5.31%.
Second, the producers know historically which letters players tend to select more often. Here is a table with the most frequently called letters and how frequently they show up in the puzzle:
The four most popular letters are C M D A (called 65.20%, 58.77%, 56.90%, and 46.64% of the time, respectively). Knowing this, the producers can select puzzles that under-represent these letters. Indeed, A is the third most common vowel, D is the ninth most common consonant, C is the eleventh, and M is an atrocious eighteenth.
Interestingly, however, the next four most commonly called are also the three most common consonants and most common vowel to appear in bonus round puzzles. They are P H O G (called 38.05%, 34.87%, 32.27, and 21.30% of the time and account for 3.54%, 4.73%, 9.67%, and 4.21% of letters in the puzzles, respectively). If you want to cover the most real estate, these are your go-to letters. (The difference between D and P is not significant, though.)
While you might know to call P H G O, you have no need to rush through it. Wheel of Fortune is very generous in how much time you take to call the letters. Use this time to think about what the puzzle might be. You will still have ten seconds after they reveal your called letters.