It seems that some people may not be aware that the groundbreaking and definitive piece of research on the question of the efficacy of guessing “three” was done more than 15 years ago now. The short-sighted snobs at The Annals of Improbable Research turned it down for publication at the time, so I posted a link to it here many years ago so that the world might know the results. I just discovered that that link no longer works, so I am posting the text of it below as a public service. As you can see, it is a bit dated in places ("NTN," "Wipeout," "Bennigan's," "Damon's," "more than three thousand dining and drinking establishments," etc.), but I believe the vital findings of this immensely important study still hold:
“The Super-Frequent-Three”—Myth or Reality?: A Quantitative Analysis of a Popular NTN “Countdown” Strategy By Anon
ABSTRACT A statistical analysis of the frequency of answer number “3” in NTN “Countdown” games was performed to test the hypothesis that this answer occurs more frequently than other answers. This hypothesis was not proved, but potential ways in which this analysis may be used to enhance game-playing strategy and one’s quality of life are discussed.
INTRODUCTION The National Trivia Network (NTN) is a popular pastime among tens of thousands of people in the United States and Canada. In more than three thousand dining and drinking establishments throughout North America, NTN players attempt to answer trivia questions for points, competing not only against other patrons in their own establishment, but players across the continent as well. Most NTN games are half-hour, 15-question contests in which trivia questions appear on a television screen with five multiple choice answers. Using a computerized “playmaker,” players choose answers for each question, having the ability to change their answers at any time. As the potential points count down from 1000 points, clues are offered to the correct answer. Thus, in answering questions, a premium is placed speed, and a good strategy rests on selecting the correct answer faster than your opponents, even if one’s first guess is incorrect. Among dedicated players of these games, one of the most popular strategies is that of relying on “the three-hole”—in other words, choosing answer “3” at those times when one has no idea what the correct answer might be. This strategy is based on the widely-held perception that answer number “3” occurs significantly more frequently than the three times (20%) expected in a fifteen-question game. The purpose of this research was to test statistically the validity of this belief in the “super-frequent-three.”
METHODS The NTN system hosts a number of different games, but the most frequently-featured are “Countdown” and “Wipeout.” As “Countdown” is by far the most common game (appearing more than a fifteen times a day as opposed to three or four times for “Wipeout”), and in order to control for any error that might result from combining data from different types of games, only “Countdown” games were considered for this analysis. In order to maintain consistency and eliminate the possibility of inter-observer error, only one person recorded the data from all games. Furthermore, because this data-collector was required to pay close attention to playing and recording data for every game, it was determined that he must refrain from consuming all but the smallest amount of intoxicating beverages. As these guidelines necessitated the voluntary participation of someone with no appreciable social life, the author was chosen to fulfill this function.
A total of 74 “Countdown” games were recorded between the dates of 8 July and 12 August 2002 at five NTN-hosting establishments in the greater Akron area (Annabell’s, Bennigan’s, Buffalo Wild Wings, Scorcher’s in the Valley, and a North Canton Damon’s). Cases were thrown out only when one of the answers in the game was demonstrably false. Two cases were eliminated in this manner, one because of an untrue final answer (which was also contrary to the final clue), and one because there was no correct answer among the given choices. These cases represented less than 3% of the total sample size. Because of the nature of the data and the directional nature of the hypothesis, a paired, one-tailed student’s “t” test was chosen as the main analytical tool for this experiment.
RESULTS A table showing the cumulative totals and percentages for each number is presented below (Table 1). In the 72 cases studied, “3” appeared 225 times, compared with 205 times for “1,” 225 times for “2,” 214 times for “4,” and 211 times for “5.” In percentage terms, answers “2” and “3” appeared 21% of the time, answers “4” and “5” appeared 20% of the time, and answer “1” appeared 19% of the time.
Table 1 Frequency and Percentage of Each Answer for NTN “Countdown” Games (n=72)
Answer 1 205 19% Answer 2 225 21% Answer 3 225 21% Answer 4 214 20% Answer 5 211 20%
The per-game averages and standard deviations of each answer appear in Table 2. The means range from 2.85 to 3.13, and the standard deviations from 1.46 to 1.56. A student’s-“t” test revealed that there was no statistically significant (∂=.05) difference between the frequency of answer “3” and any of the other answers (Table 3). The null hypothesis thus held, and the “three-hole thesis” was not proved.
Table 2 Mean and Standard Deviation for Each Answer in NTN “Countdown” Games (n=72)
Answer 1 mean: 2.85 sd: 1.46 Answer 2 mean: 3.13 sd: 1.54 Answer 3 mean: 3.13 sd: 1.50 Answer 4 mean: 2.97 sd: 1.56 Answer 5 mean: 2.93 sd: 1.43
Table 3 Student’s “t” Tests for Answer “3” Versus Other Answers in NTN “Countdown” Games (paired, one-tailed, n=72)
3 vs. 1 "t"-value: 0.16 3 vs. 2 "t"-value: 0.50 3 vs. 4 "t"-value: 0.30 3 vs. 5 "t"-value: 0.25
Despite their nearly total disproof of the “three-hole” hypothesis, these data nevertheless might tempt the reader into believing that some answers occur significantly more or less frequently than should be expected. Answers “2” and “3,” for example, appeared 9 times more than the expected value of 216, and fully 20 times more often than Answer “1.” Such minor deviations (no more than 4% off of the expected value in all cases) are to be expected in any statistical analysis, but to cover all of our bases and appease the potential whiners in the crowd, a z-test between the actual frequency of all answers and their randomly-expected frequency of 3.0 revealed that no answer deviates significantly (P ≥ .95) from the expected (Table 4).
Table 4 Z-Test for Each Answer Versus Expected Value in NTN “Countdown” Games (two-tailed, sample standard deviation used, n=72)
Answer 1 P value: 0.813 Answer 2 P value: 0.245 Answer 3 P value: 0.240 Answer 4 P value: 0.560 Answer 5 P value: 0.660
DISCUSSION Although this analysis did not prove “the three-hole” hypothesis, potentially valuable information regarding strategy may still be gleaned from these findings.
First, these data indicate that having a standard answer on which to fall back is not necessarily a bad idea. If one plays often and consistently chooses the same number for unknown answers, then as much as 21% of the time he or she will be rewarded with a “gift” correct answer. This is predicated on the assumption, of course, that the given number is not one of the possible answers that may safely be eliminated before the clues are given. This study demonstrates that any answer from “1” through “5” will do in pursuing this strategy, with no statistically significant difference between any of these answers. Furthermore, the now disproved, but still overweening perception of the “super-frequent-3” may ironically prove to be useful strategically as well. Even though “3” does not come up more frequently than the other numbers, good strategy may still insist as using this number as one’s standard answer, particularly if one is leading the game. As this is already the strategy of many dedicated players, one can take advantage of this knowledge when a particularly difficult question comes up. If there is a good chance most of one’s close competitors are stumped by this question as well, one is less likely to give up points to the rest of the field if he or she guesses “3” along with the rest. Conversely, if one is behind, choosing any number other than “3” may be in order for the same question, as the person in the lead might be more likely to be guessing “3” as well, and this presents a challenger with the opportunity to gain points if a number other than “3” is the correct answer.
CONCLUSIONS This analysis has conclusively demonstrated that answer number “3” does not occur with greater than expected frequency in NTN “Countdown” games. Nevertheless, the current study argues persuasively for several conclusions that may be useful to frequent NTN players.
First, having a standard answer for unknown questions is a sound strategy. Consistent choice of a particular number will reward the player with “gift” answers up to 21% of the time over a prolonged period of time.
Second, precisely because of the faulty perception of the “super-frequent-3,” choosing “3” as a fallback answer may still be a good idea if one is leading in a game. As the other players are more likely to be guessing this number as well, one is less likely to lose ground to one’s competitors if all are guessing the same number. Conversely, if one is behind, he or she may wish to risk guessing a different number in order to take advantage of the 79% chance that answer “3” is incorrect.
Last, this study emphatically confirms a final conclusion that has been suggested to the author by several independent sources--including fellow NTN players, family, and friends alike--both before and during the current research. If the reader understands the concepts presented herein; if he or she has read this research closely from beginning to end; if he or she is planning on using the results of this research to enhance game-playing strategy; then this is probably a very strong indication that the reader (like the author) ought to consider very strongly getting a real life already.
Acknowledgements: The author would like to acknowledge and sincerely thank Dana, Emily, Kelly, Kendra, Tiffany, and Trish at Annabell’s; and Amy, Heather, Kim, and Sandy at Scorcher’s; who cheerfully served him endless “Cokes-with-no-ice” while he conducted this research.
_________________ Anon "He may seem like Mr. Rogers but a dark spirit lies beneath."
Last edited by ANON on Fri Jul 13, 2018 9:15 pm, edited 1 time in total.
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