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The topic of one of my math courses over the past two weeks has been cryptanalysis and ciphers. Over that time, my professor has passed out numerous letter-related handouts, one of which is a table with the frequency of letters in the English alphabet. Below is that table.
E 0.1304 (i.e. the letter E appears in the sample text 13.04% of the time)
T 0.1045
A 0.0856
O 0.0797
N 0.0707
R 0.0677
I 0.0627
S 0.0607
H 0.0528
D 0.0378
L 0.0339
F 0.0289
C 0.0279
M 0.0249
U 0.0249
G 0.0199
P 0.0199
Y 0.0199
W 0.0149
B 0.0139
V 0.0092
K 0.0042
X 0.0017
J 0.0013
Q 0.0012
Z 0.0008
Unfortunately, I don't know where this letter sample came from. It could've come from texts, newspapers...I really don't know. This table came from a college-level book about cryptanalysis, so I'd believe large samples of text were used.
As you can see from the above list, the five most common consonants are T, N, R, S, and H. Does this mean players on Wheel have put too much faith in L all these years?
Also, at the bonus round, if you don't have an idea about the puzzle, the numbers above say you should pick the H, D, F, and A. I don't watch Wheel as much as I used to, but I don't recall many people picking F's and H's at bonus land.
Do my theories hold water? Feel free to poke as many holes in it as you want.
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Well, the way the puzzles are written nowadays, R S T L E don't always help you out as much as one would think. I've proposed before to have four or five mini-wheels with non duplicated letters and a vowel wheel to be spun that would determine which letters one could use in the bonus, you'd see a different variety of letters and some that might help out more than the ones they now "give" you.
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[quote name=\'Jimmy Owen\' date=\'Oct 21 2004, 08:32 AM\']Well, the way the puzzles are written nowadays, R S T L E don't always help you out as much as one would think. I've proposed before to have four or five mini-wheels with non duplicated letters and a vowel wheel to be spun that would determine which letters one could use in the bonus, you'd see a different variety of letters and some that might help out more than the ones they now "give" you.[/quote]
If I understand what you're saying, the "letters chosen are outside of the player's control" method was used on Wheel 2000, where scoring during a task would give a contestant whatever letter was on the randomizer. If I was the person who spun K, X, Z, Q, J, and U, I'd be quite pissed.
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Not if those letters are in the puzzle. :) Well, if you're a good spinner, you might have a little more control, but I understand what you're saying. Of course, in the main game, I'd rather choose my dollar amount, but that's not the way the game works. For many years, the wheel had nothing to do with the bonus round and that "puzzled" me. I like the way the bonus prize is determined now. It's just a way to make the wheel a part of the bonus and bring some unpredictability to the procedings.
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[quote name=\'Jimmy Owen\' date=\'Oct 21 2004, 10:56 AM\']Not if those letters are in the puzzle. :)[/quote]
True. If my bonus puzzle is QUIZ JUNKIE, I'll prosper. The other eleventy billion times, I'll have to suffice with the main game winnings.
Well, if you're a good spinner, you might have a little more control, but I understand what you're saying.
Even if I was a good spinner, surely there would be a rule in place saying the wheel must make at least one or two full rotations, just to ensure I wasn't purposely trying to land on the best letters.
Is there such a rule for WoF's bonus round or even the main game regarding a minimum number of rotations? (I know the average spin of the big wheel usually makes a full rotation, give or take 3 full wedges.) If there are no such rules, what's stopping anybody from spinning the wheel very lightly, just to pass by a bankrupt or just enough to land on the jackpot space? Similarly, why not spin the bonus wheel the length of a few wedges? It doesn't matter what's landed on, since the contestant doesn't know what's at stake until the prize is revealed.
If there are no such rules and I was on Wheel, that's what I'd do. Pat would have a field day with the big 6'4" guy who couldn't get that little bonus wheel around half a rotation. :-)
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[quote name=\'hmtriplecrown\' date=\'Oct 21 2004, 11:32 AM\'][quote name=\'Jimmy Owen\' date=\'Oct 21 2004, 10:56 AM\']Not if those letters are in the puzzle. :)[/quote]
True. If my bonus puzzle is QUIZ JUNKIE, I'll prosper. The other eleventy billion times, I'll have to suffice with the main game winnings.[/quote]
I think the point Jim's trying to make is that these puzzles are prepared with thought given to the letters. Let's use an obvious example: The bonus puzzle is never going to be TREES. The producers consider the letter distribution in a way that your average newspaper article (or wherever you get your random letter source) doesn't.
Knowing the usual distribution of letters is an advantage when you're playing the regular game. And to answer an earlier question, yes, most cryptographers will tell you that the letter "L" doesn't belong in the top five. But when it comes to the current bonus puzzles, the typical distribution of letters is much less relevant.
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[quote name=\'hmtriplecrown\' date=\'Oct 21 2004, 11:32 AM\']Is there such a rule for WoF's bonus round or even the main game regarding a minimum number of rotations?
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Back when the Bonus Wheel debuted, I think I remember Pat saying that it has to go around at least once. I want to say I even remember seeing somebody have to spin it again, but I'm not certain.
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I think I recall seeing the wheel not being spun all the way around, and they didn't do anything about it.
As for Bonus Wheel, I don't see a reason why they HAVE to go all the way around, its not like they really would want to hit any certain space since the cards are random. But it doesn't seem like its that heavy to spin.
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[quote name=\'Jimmy Owen\' date=\'Oct 21 2004, 05:32 AM\']Well, the way the puzzles are written nowadays, R S T L E don't always help you out as much as one would think.
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But only because the puzzles are written with the knowledge that those letters are automatic. If we had it all to do over again, and for some reason the prevalent letter selection was R S T D N E, then that is probably what would have wound up being the second bonus format, and the puzzles would be written with more L's and less D's. :)
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[quote name=\'Steve Gavazzi\' date=\'Oct 21 2004, 12:29 PM\']Back when the Bonus Wheel debuted, I think I remember Pat saying that it has to go around at least once.
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I remember him saying that, too, and being confused since the contestant doesn't know where the $100,000 is to begin with.
I remember one encyclopedia (I want to say World Book, but I could be wrong) gives frequency rankings to each letter entry, and I remember noticing that H ranked higher than L. I've wondered if that's because H has a tendency to get paired up with S, T, C, and W so often, as opposed to making its own sound in the word. It makes me wonder if H is a useful bonus round pick -- assuming it usually appears in conjunction with one of those other consonants, why not pick C instead? If you see an S or T followed by an uncovered space followed by a vowel, you can guess there's an H there (usually), and C seems more likely to stand as its own letter.
By the way, I'm surprised that the sample text ranked S comparitively low. With all of the plurals possible, I'd think it would rank higher.
--
Scott Robinson
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Also, "the." I have to suspect that little word has a lot to do with H's high ranking, since it tends to be, by far, the most often used word in written English. And with T_E, calling the H isn't really going to help all that much, now is it ;)?
At the same time, S being as low as it is is astonishing, considering all the plurals, and subject/verb agreement, and all that stuff that requires the use of S. Seems Scott thought the same.
"Word endings" is probably what puts D above L. Specifically, the popular "ed" ending for words. L has the "ly" ending, but that really doesn't get as much use.
Honestly, I always thought F was probably the most underrated letter on the show, and that list kinda' supports my thoughts on that. Why so many call B, and so virtually no one ever calls F, I never did understand....
I'm also more than a bit surprised to see Q is more common than Z. I thought surely Q would have to come in dead last.
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I'd think X would come dead last.
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The bonus puzzle is never going to be TREES.
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Of course not. That's a silly puzzle. How about TENNESSEE?
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[quote name=\'whoserman\' date=\'Oct 22 2004, 12:06 AM\']I'd think X would come dead last.
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The bonus puzzle is never going to be TREES.
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Of course not. That's a silly puzzle. How about TENNESSEE?
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Or STREET?
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Q ranks higher than Z thanks to its pairing with the letter U. So, where there's a Q, naturally, you'll find a U after it 99.9% of the time although there are exceptions(Iraq, Qtar).
As far as X goes, very few words start with that letter & should be near the bottom if not there.
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[quote name=\'Craig Karlberg\' date=\'Oct 22 2004, 04:49 AM\']Q ranks higher than Z thanks to its pairing with the letter U. So, where there's a Q, naturally, you'll find a U after it 99.9% of the time although there are exceptions(Iraq, Qtar).
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That would help the letter U, not the Q. (Geez...)
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>>QUOTE(Craig Karlberg @ Oct 22 2004, 04:49 AM)
Q ranks higher than Z thanks to its pairing with the letter U. So, where there's a Q, naturally, you'll find a U after it 99.9% of the time although there are exceptions(Iraq, Qtar).
Nitpick: "Qatar".
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[quote name=\'Craig Karlberg\' date=\'Oct 22 2004, 01:49 AM\']Q ranks higher than Z thanks to its pairing with the letter U. So, where there's a Q, naturally, you'll find a U after it 99.9% of the time although there are exceptions(Iraq, Qtar).
As far as X goes, very few words start with that letter & should be near the bottom if not there.
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But while you're right about the QU- pairing (in fact, the list of 16 legal Q-without-a-U words is the first list of words every budding Scrabble expert ought to memorize...and IRAQ and QATAR, being proper names, are not legal, just as an aside), one would think that the EX- prefix would be at least as prevalent in the language, if not more so. I'm still a little surprised to see the Q and X ranked where they are with respect to each other.
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[quote name=\'clemon79\' date=\'Oct 22 2004, 08:44 AM\']in fact, the list of 16 legal Q-without-a-U words is the first list of words every budding Scrabble expert ought to memorize[/quote]
Nitpick: The second. The list of 2-letter words is useful much more often.
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[quote name=\'gameshowsteve\' date=\'Oct 22 2004, 01:38 PM\'][quote name=\'clemon79\' date=\'Oct 22 2004, 08:44 AM\']in fact, the list of 16 legal Q-without-a-U words is the first list of words every budding Scrabble expert ought to memorize[/quote]
Nitpick: The second. The list of 2-letter words is useful much more often.
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Yeah, but I'd argue that the Q-sans-U list is easier to memorize, it being much shorter, so you can get results from your work sooner. :)
Agreed, tho, that the 2-letter and 3-letter lists are right up there.
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A couple of miscellaneous yet related comments to the discussion:
Although there is not a rule on WoF about getting the wheel all the way around during the main game, there was a rule when I was on the show that basically gave the host/producers the right to rule a spin invalid because it went almost nowhere; I assume that rule is still on the books.
Also, I teach a number theory course which contains a couple of units on cryptography, and yes, Mike, the distribution you show is somewhat of a standard one. Of course, all such distributions are based on a sampling of actual text; however large it may be, it's only an approximation of what the true distribution is. That's why the only part of the distribution that carries much significance is that of the high frequency letters. I tell my students that those stop with the S... that H, D, and L are on the border between high and medium frequency. And yes, the H is on the list because of its pairings with several letters, but primarily T, as TH occurs often, as does THE (not just as a word, but as a part of other words). The students generally enjoy finding out that Wheel of Fortune is "wrong." :-)
As it turns out, the cryptography course I took was not long before my appearance on the show, and had I made it to the bonus round, I would have chosen H instead of L (this was in 1986, when you picked your own five consonants and one vowel). But, 'twas not to happen.