My Masters Thesis, Now Online
Nov. 18th, 2008 05:38 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
le_bebna_kamniFor all of you who didn't know I was working on a thesis, I've finally completed it today and am posting it online for all to read. [Warning: Extreme Silliness(TM) ahead]
Statistical Verification of a Curse Cast Upon a Player During the Kingsburg Board Game
by L.B. Kamni, Miskatonic University
Curses have long been part of the folklore of human history, with evidence of curses spanning disparate cultures and across many millennia[1]. While curses were once a preferred method of attack among our predecessors, the art form seems to be disappearing from common use as modern technology becomes a more effective option for destruction of one's enemies.
It has been noted that examination of the validity and effectiveness of curses is largely absent from modern scientific research. This may be in part due to their diminishing use, but it is also because of recent movements such as "empiricism" and "rationalism" that tend to disregard older and better-established forms of inquiry. While it could be argued that more traditional methods like entrail-reading and divine revelation still have their place in the scientific method[2], empiricism via statistical analysis is often useful when human sacrifice is illegal under local laws, or if the preferred deity is not immediately available for petitioning.
Potential evidence of curse activity was detected during the play of a board game called "Kingsburg" conducted at a coffee shop in downtown Ann Arbor, Michigan. It is the purpose of this paper not only to confirm that this was, in fact, a curse – most likely uttered under the breath of the opponent to ensure the victim's defeat – but to demonstrate that statistical methods are a valid way to study curses that should be used in addition to more traditional methods.
Background of Modern Cursing
A curse can be defined as "a formula or charm" intended to cause "misfortune, evil, doom, etc." on a group or person[3]. Evidence of magical or divine calamity being called down on a transgressor or a rival can be seen as far back as The Epic of Gilgamesh, where Enki eats the fruit created by Ninhursag in the garden of the gods, and she curses him to a slow and painful degenerative death[4].
More well-known curses come from the Egyptian tombs, which promised to bring trespassers such things as death, impotence, sexual violation by donkey, and even complete nonexistance[5]. Curses abounded among the ancient Greeks and Romans, Hindus, Chinese, and Celts. And curses linger even to this day – albeit in humorous fashion – in the modern office voodoo doll[6].
Some scientists have questioned the whether curses are still potent in this day and age; however, recent advancements in other branches of science seem to confirm that in principle curses are still effective. Theories in quantum mechanics state that phenomena on a micro level can be influenced by the very act of measurement[7],[8], and recent scholars have posited that this obervation/expectation effect may extend even to the macro level[9]. Similar effects of belief on the realm of faerie were discovered over a century ago[10], and modern philosophers even posit that our belief may alter the existence of the gods themselves [11].
It is then reasonable to conclude, then, that it is belief itself that is waning[12] -- not the potency of curses. Provided that a modern person calls on one of the more effective gods[12],[13],[14], or if the person has a sufficient belief fueled by a desire for victory or revenge, curses can and still are an effective weapon even in the technological world.
Methods
The opportunity for studying curses in an empirical fashion was provided by two complete play-throughs of a board game known as "Kingsburg". Kingsburg is set in a medieval-style realm, with each player enacting the role of a noble landowner who is protecting his or her lands from a series of raids. The game consists of five "years", or rounds, in which players take turns using dice to influence members of the King's court to gain resources and protection from the coming onslaught. At the end of each "year", a randomly drawn enemy is faced. Victory for each player is determined by a total of defensive points acquired either through building permanent structures that carry across multiple rounds, or hiring mercenaries that only count toward the defensive total for the current round. In addition, a single die is rolled before the attack to determine how many "reinforcements" the king will send to add to the defensive total.
The game itself allows up to five players, but has rules that can be adapted to as few as two players. The two-player version was chosen because it allowed for a more tight control. Many studies in the past have attempted to analyze gameplay between groups of three people or larger, but did not accurately control for the effects of multiple people cursing a single [often annoying] player, cross-cursing, or shifting curses that follow whichever player is currently in the lead.
The two-player version was made significantly easier to analyze by the presence of only one player doing the cursing (hereafter referred to as the "opponent") and one player being cursed (the "victim"). Care was taken to insure that the opponent was selected for a highly competitive nature and love of cut-throat board games such as "Puerto Rico". The victim was chosen for a relative dislike of competitive board games and an aversion toward returning curses.
Additionally, the game itself was chosen for a study on curses because it not only has a skill component, but a randomized component that is easy to test. Most curses that effect skill, such as mind control or generalized "bad luck" spells, tend to be fairly complex to cast or rely on deities that are frequently fickle or unreliable. Due to the internalized and subjective nature of the skill-oriented curses, previous studies of games where mind control curses have been used have been difficult to analyze statistically, as there is currently no quantitative way to rule out other factors that might influence performance. Only more sophisticated divination methods such contact with the recently departed[15] have consistently demonstrated that the curses did, in fact work.
However, a randomized die roll can easily be compared to a known distribution, ruling out other factors without having to resort to more time-consuming methods. Therefore, this study focuses on a sampling of the "reinforcement" roll made at the end of each of round.
Hypothesis
When examining curses, we would expect that the die rolls would perform well below the mean. Therefore, the experiment will be given a directional (one-tailed) analysis. To decrease the probability of a Type I error – i.e., rejecting the null hypothesis incorrectly and risking the wrath of any deities who do not wish to accept responsibility for the presumed curse – an Alpha of .01 was set. Therefore, the critical z-score value that must be met is -2.333 in order to reject the null hypothesis:
The null hypothesis and the alternative hypothesis are as follows:
Setup
Two complete play-throughs of the board game "Kingsburg" were made, and at the end of each round the "reinforcement" roll was made using a 6-sided die. Five rolls were recorded for each game (one for each "year" of game play), for a total of ten rolls, and the same die was used for each roll to ensure that it was the player and not the die that had been cursed. The first game's rolls were conducted solely by the player who had been cursed (the "victim"); the second game acted as a control, and its rolls were carried out by the person doing the cursing (the "opponent"). The two sets of rolls were then compared with a standard distribution of five die rolls and analyzed for statistical significance.
Care was taken to rule out astrological effects related to both of the players, and consideration for astral and geolocation lines, alphanumeric association, and color of the dice used by each player was made prior to conduction the experiment. No significant alterations or portents were discovered in the survey (please see Alhazred, 1938[16] for a more detailed analysis).
Data
The rolls for each game can be summarized in the following table:
It is clear to see that during Game 1, the victim rolled entirely 1's, while during Game 2 the opponent had a much more varied roll.
In Kingsburg, die rolls affect the number of "reinforcements" that are received from the King, with a higher number considered more optimal. During the course of the victim's game, only 5 reinforcements were received from rolling the die, whereas during the opponent's game, 22 reinforcements were received.
Analysis
In order to tell if the victim was, indeed, cursed, we must first look at a normal distribution of reinforcements that a player can expect to receive during a game:
The mean score is 17.5, with a standard deviation for the population of 3.82. Therefore, in a typical game a player might reasonably expect to get between about 14 and 21 reinforcements (~1 standard deviation away from the mean), with less likely but still reasonable ranges between 10 and 25 reinforcements (~2 standard deviations).
In the first game, which acted as the test case, the number of reinforcements was 5, so the Z-score is:
Conclusion
This experiment has shown within reasonable probability that statistical analysis can be used to confirm curses in an empirical manner. Further confirmation was needed that the curse had indeed only affected the random die rolling by the victim (as opposed to the victim's skill-based actions), and this was demonstrated when the victim successfully won both games despite obviously poor dice rolls.
Other unofficial confirmation of the curse's effectiveness came when the opponent took over rolling the die in Game 2. With no other die rolls to act on, the curse began acting on the victim's three "resource rolls" that precede the "reinforcements roll". The victim consistently rolled below 7, even when 4 dice were being rolled. While statistical analysis of those rolls is beyond the scope of this current paper, a full exploration of their implications may be undertaken in a subsequent publication.
Scrying was used to confirm the figures found; however other follow-up may be necessary, such as eviscerating the opponent and reading his entrails or using necromancy on the corpse to make it reveal the exact curse used.
It is true that statistical analysis remains less accurate than more traditional methods, in that it has the potential to miss subtle effects – such as the minor blessing detected during Game 2. Nevertheless, statistical analysis tends to be significantly less time-consuming than full-moon rituals, more cost-effective than the exotic animal sacrifices required by many gods, and avoids many of the legal hassles when human subjects or demons are involved. An argument may also be made that statistical analysis does not need to rely on the capriciousness of spirits or the alignment of portents and planets (and is therefore more reliable).
While the experimenter should not be so hasty as to abandon these time-honored traditions, it is the conclusion of this paper that statistical analysis and other empirical methods should be studied further and be considered as at least a supplement to the other noble traditions currently in practice.
** Based on real world data – I kid you not! However, the analysis is solely for amusement and did not actually involve curses... ;P
Statistical Verification of a Curse Cast Upon a Player During the Kingsburg Board Game
by L.B. Kamni, Miskatonic University
Curses have long been part of the folklore of human history, with evidence of curses spanning disparate cultures and across many millennia[1]. While curses were once a preferred method of attack among our predecessors, the art form seems to be disappearing from common use as modern technology becomes a more effective option for destruction of one's enemies.
It has been noted that examination of the validity and effectiveness of curses is largely absent from modern scientific research. This may be in part due to their diminishing use, but it is also because of recent movements such as "empiricism" and "rationalism" that tend to disregard older and better-established forms of inquiry. While it could be argued that more traditional methods like entrail-reading and divine revelation still have their place in the scientific method[2], empiricism via statistical analysis is often useful when human sacrifice is illegal under local laws, or if the preferred deity is not immediately available for petitioning.
Potential evidence of curse activity was detected during the play of a board game called "Kingsburg" conducted at a coffee shop in downtown Ann Arbor, Michigan. It is the purpose of this paper not only to confirm that this was, in fact, a curse – most likely uttered under the breath of the opponent to ensure the victim's defeat – but to demonstrate that statistical methods are a valid way to study curses that should be used in addition to more traditional methods.
Background of Modern Cursing
A curse can be defined as "a formula or charm" intended to cause "misfortune, evil, doom, etc." on a group or person[3]. Evidence of magical or divine calamity being called down on a transgressor or a rival can be seen as far back as The Epic of Gilgamesh, where Enki eats the fruit created by Ninhursag in the garden of the gods, and she curses him to a slow and painful degenerative death[4].
More well-known curses come from the Egyptian tombs, which promised to bring trespassers such things as death, impotence, sexual violation by donkey, and even complete nonexistance[5]. Curses abounded among the ancient Greeks and Romans, Hindus, Chinese, and Celts. And curses linger even to this day – albeit in humorous fashion – in the modern office voodoo doll[6].
Some scientists have questioned the whether curses are still potent in this day and age; however, recent advancements in other branches of science seem to confirm that in principle curses are still effective. Theories in quantum mechanics state that phenomena on a micro level can be influenced by the very act of measurement[7],[8], and recent scholars have posited that this obervation/expectation effect may extend even to the macro level[9]. Similar effects of belief on the realm of faerie were discovered over a century ago[10], and modern philosophers even posit that our belief may alter the existence of the gods themselves [11].
It is then reasonable to conclude, then, that it is belief itself that is waning[12] -- not the potency of curses. Provided that a modern person calls on one of the more effective gods[12],[13],[14], or if the person has a sufficient belief fueled by a desire for victory or revenge, curses can and still are an effective weapon even in the technological world.
Methods
The opportunity for studying curses in an empirical fashion was provided by two complete play-throughs of a board game known as "Kingsburg". Kingsburg is set in a medieval-style realm, with each player enacting the role of a noble landowner who is protecting his or her lands from a series of raids. The game consists of five "years", or rounds, in which players take turns using dice to influence members of the King's court to gain resources and protection from the coming onslaught. At the end of each "year", a randomly drawn enemy is faced. Victory for each player is determined by a total of defensive points acquired either through building permanent structures that carry across multiple rounds, or hiring mercenaries that only count toward the defensive total for the current round. In addition, a single die is rolled before the attack to determine how many "reinforcements" the king will send to add to the defensive total.
The game itself allows up to five players, but has rules that can be adapted to as few as two players. The two-player version was chosen because it allowed for a more tight control. Many studies in the past have attempted to analyze gameplay between groups of three people or larger, but did not accurately control for the effects of multiple people cursing a single [often annoying] player, cross-cursing, or shifting curses that follow whichever player is currently in the lead.
The two-player version was made significantly easier to analyze by the presence of only one player doing the cursing (hereafter referred to as the "opponent") and one player being cursed (the "victim"). Care was taken to insure that the opponent was selected for a highly competitive nature and love of cut-throat board games such as "Puerto Rico". The victim was chosen for a relative dislike of competitive board games and an aversion toward returning curses.
Additionally, the game itself was chosen for a study on curses because it not only has a skill component, but a randomized component that is easy to test. Most curses that effect skill, such as mind control or generalized "bad luck" spells, tend to be fairly complex to cast or rely on deities that are frequently fickle or unreliable. Due to the internalized and subjective nature of the skill-oriented curses, previous studies of games where mind control curses have been used have been difficult to analyze statistically, as there is currently no quantitative way to rule out other factors that might influence performance. Only more sophisticated divination methods such contact with the recently departed[15] have consistently demonstrated that the curses did, in fact work.
However, a randomized die roll can easily be compared to a known distribution, ruling out other factors without having to resort to more time-consuming methods. Therefore, this study focuses on a sampling of the "reinforcement" roll made at the end of each of round.
Hypothesis
When examining curses, we would expect that the die rolls would perform well below the mean. Therefore, the experiment will be given a directional (one-tailed) analysis. To decrease the probability of a Type I error – i.e., rejecting the null hypothesis incorrectly and risking the wrath of any deities who do not wish to accept responsibility for the presumed curse – an Alpha of .01 was set. Therefore, the critical z-score value that must be met is -2.333 in order to reject the null hypothesis:
The null hypothesis and the alternative hypothesis are as follows:
H0: Statistical analysis of the rolls carried out while under the curse show no differentiation between random variation found in normal die rolls. Z is greater than -2.33.
H1: Analysis of the die rolls reveal a significant difference in performance between what would normally be expected by chance. Z is less than -2.33.
Setup
Two complete play-throughs of the board game "Kingsburg" were made, and at the end of each round the "reinforcement" roll was made using a 6-sided die. Five rolls were recorded for each game (one for each "year" of game play), for a total of ten rolls, and the same die was used for each roll to ensure that it was the player and not the die that had been cursed. The first game's rolls were conducted solely by the player who had been cursed (the "victim"); the second game acted as a control, and its rolls were carried out by the person doing the cursing (the "opponent"). The two sets of rolls were then compared with a standard distribution of five die rolls and analyzed for statistical significance.
Care was taken to rule out astrological effects related to both of the players, and consideration for astral and geolocation lines, alphanumeric association, and color of the dice used by each player was made prior to conduction the experiment. No significant alterations or portents were discovered in the survey (please see Alhazred, 1938[16] for a more detailed analysis).
Data
The rolls for each game can be summarized in the following table:
| Round # | Roll for Game 1 | Roll for Game 2 |
| 1 | 1 | 4 |
| 2 | 1 | 6 |
| 3 | 1 | 3 |
| 4 | 1 | 3 |
| 5 | 1 | 6 |
It is clear to see that during Game 1, the victim rolled entirely 1's, while during Game 2 the opponent had a much more varied roll.
In Kingsburg, die rolls affect the number of "reinforcements" that are received from the King, with a higher number considered more optimal. During the course of the victim's game, only 5 reinforcements were received from rolling the die, whereas during the opponent's game, 22 reinforcements were received.
Analysis
In order to tell if the victim was, indeed, cursed, we must first look at a normal distribution of reinforcements that a player can expect to receive during a game:
The mean score is 17.5, with a standard deviation for the population of 3.82. Therefore, in a typical game a player might reasonably expect to get between about 14 and 21 reinforcements (~1 standard deviation away from the mean), with less likely but still reasonable ranges between 10 and 25 reinforcements (~2 standard deviations).
In the first game, which acted as the test case, the number of reinforcements was 5, so the Z-score is:
(5-17.5)/3.82 = -3.27In the second game, which served as the control, the number of reinforcements was 22, so the Z-score is:
(22-17.5)/3.82 = 1.18The control falls just outside one standard deviation to the positive side of the mean, which is well within statistically expected norms (although the slight advantage indicates a mild blessing that the opponent invoked upon himself, as indicated by a later follow-up with scrying that confirmed both the figures for the test case and the control). However, it can clearly be seen that the test case falls well outside the -2.333 minimum required by the null hypothesis, and in fact occurs in less than 0.13% of cases. Therefore, this paper rejects the null hypothesis and contends that statistical analysis can, in limited cases, be considered a valid form of inquiry.
Conclusion
This experiment has shown within reasonable probability that statistical analysis can be used to confirm curses in an empirical manner. Further confirmation was needed that the curse had indeed only affected the random die rolling by the victim (as opposed to the victim's skill-based actions), and this was demonstrated when the victim successfully won both games despite obviously poor dice rolls.
Other unofficial confirmation of the curse's effectiveness came when the opponent took over rolling the die in Game 2. With no other die rolls to act on, the curse began acting on the victim's three "resource rolls" that precede the "reinforcements roll". The victim consistently rolled below 7, even when 4 dice were being rolled. While statistical analysis of those rolls is beyond the scope of this current paper, a full exploration of their implications may be undertaken in a subsequent publication.
Scrying was used to confirm the figures found; however other follow-up may be necessary, such as eviscerating the opponent and reading his entrails or using necromancy on the corpse to make it reveal the exact curse used.
It is true that statistical analysis remains less accurate than more traditional methods, in that it has the potential to miss subtle effects – such as the minor blessing detected during Game 2. Nevertheless, statistical analysis tends to be significantly less time-consuming than full-moon rituals, more cost-effective than the exotic animal sacrifices required by many gods, and avoids many of the legal hassles when human subjects or demons are involved. An argument may also be made that statistical analysis does not need to rely on the capriciousness of spirits or the alignment of portents and planets (and is therefore more reliable).
While the experimenter should not be so hasty as to abandon these time-honored traditions, it is the conclusion of this paper that statistical analysis and other empirical methods should be studied further and be considered as at least a supplement to the other noble traditions currently in practice.
** Based on real world data – I kid you not! However, the analysis is solely for amusement and did not actually involve curses... ;P
