1. Abstract:“Emperors and Scum” is a card game utilising one or more standard 52-card playing decks. The game is based on the premise that players of different rankings will swap good and bad cards with each other after the first round. There are many variations on the game, some of which may be fairer than others.
To determine whether there may be an optimal set of rules, a statistical study of “Emperors and Scum” using both accepted rule sets and variational rule sets has been undertaken. Common games with four, five, and six players have been studied, as well as more extreme versions of the game with eight and three players.
The results obtained from this analysis show that the initial positions determined after the first round are highly unlikely to change, regardless of the rule set used to define the number of decks and cards swapped. This proves that no form of the game is fair and balanced, nor does the lack of statistical variation suggest that the game is fun. Instances of a new psychological condition known as E & S rage have also been observed.
Based on these observations, it is recommended that all forms of the game cease immediately and the initiation of further games be banned.
2. Introduction:2.1. The Rules of “Emperors and Scum”:
“Emperors and Scum” (E & S) is a card game usually played using standard 52-card playing decks. The game has many variations, but the basic premise is that good and bad cards are swapped after the first round based on the positional ranking of players.
The official rules of “Emperors and Scum” are difficult to define (see Section 2.2). The most accepted rules to date use all the cards taken from one or more decks. The exact number of cards in a hand depends on the number of hands that need to be dealt. This may also affect the number of decks that are used. It is also accepted practice among all forms of the game to trade cards between most players.
The cards used are shuffled and dealt successively to each player, until all cards have been dealt. The aim of the game for each player is to be the first to discard all of the cards that they have been dealt.
Whoever holds the 3 of clubs (or, if more than one deck is used, whoever plays a 3C card first) during the first hand dealt leads the first round. All other players must play higher cards, equalling the number of cards initially played. (For example, if two 3’s are first played, then only pairs may be played.) All cards must be played face up. Players may pass at any time, but once they have done so, they may not play again until the next round.
The card rankings are generally accepted to be (from lowest to highest) 3-4-5-6-7-8-9-10-J-Q-K-A-2. Only one 2 needs to be used to beat any number of other cards (a single 2 may be played on a pair, for example). However, if jokers are also used, they rank higher than a 2. This means that Jokers may be played singularly while 2’s must be played in groups. Suits are of equal value and therefore have no impact on the game.
The winner of the hand is deemed to be the person who plays the highest card/s, or the card/s upon which no one else is willing to beat. The winner then leads the next hand. This continues until all but one player has discarded all of their cards. This is known as “going out”. The order in which players have “gone out” is noted.
Generally, the first person to go out is said to have “come first”, the next player to have “come second”, etc. Based on these rankings, the players are split in half. The top half (those who ranked higher) are ruled to be “Emperors”, and the bottom half (those who ranked lower) are ruled to be “Scum”. In other words, whoever has come first is ruled to be “First Emperor” (or some other title of equal prestige, such as “Top Emperor”), second place is ruled to be “Second Emperor”, etc. Likewise, players who ranked low are “First Scum”, “Second Scum”, etc.
The cards are shuffled, and the next round is dealt. Before the round begins, players trade cards. The highest ranking player trades one or more of his or her least useful cards for the lowest ranking player’s highest cards. Lower ranked Emperors and Scum may also trade cards in a similar fashion in some version of the game. If this occurs, they will always trade a lower number of cards than those ranked in more extreme positions.
The exact number of cards traded and the number of trading players may vary, and it is common practice not to trade any more than three cards between players (a situation that occurs with more than 6 players). Players who do not trade cards are known as “Neutrals”. Neutral players will always occur if playing with an odd number of people.
Once the trading has taken place, the lowest ranked player leads the first hand, and the game continues as described above.
2.2. E & S and its Variants:
As stated in Section 2.1, the official rules of E & S are difficult to define. The reason for this is that rigorous research does not turn up a set of officially written rules that matches those described in Section 2.1. In fact, there is some debate as to whether the game is actually called “Emperors and Scum” [5].
It is more common to see the game referred to as “Asshole,” or “President” [1] [5] [8-10]. This is a source of some confusion, as at least on other well-known card game is also referred to as “Asshole” [3]. Further confusion arises from the fact that while E & S goes by many names, some variants use the same name, while some uses their own separate name.
For example, the game “Winner” [10] follows the same rules as E & S, but players discard mainly by poker hands, rather than singles, pairs, etc. The winner and loser of this game exchange only one card, and they are exchanged face up.
Interestingly, “President” is often referred to as a drinking game, and that the non-drinking version of the game is actually “Dai Hin Min” [9]. The general rules of “President” and “Dai Hin Min” are essentially the same. In “President” orders are apparently given out as to who has to drink. In a variation of “Dai Hin Min”, any type of orders may be administered to lower ranking players.
Other common elements in all these variations include no more than 2 cards being swapped at any one time, and having all players move seats so that they are arranged in order of rank. Some variations state that the highest ranking player starts the round, rather than the lowest, and that if a player passes during a round, they may still play again during that round.
None of these elements are present in the rules for E & S as described above. This has raised question as to whether the rules as described in Section 2.1 are as fair and balanced as they could be. Indeed, it is also possible that the rules of variants as described here are no more fair and balanced than the rules of E & S. A comprehensive statistical study of the game, including examinations of rules closer to accepted variants, is required in order to determine these factors.
3. Methods And Materials:Over 100 games were played using various numbers of individual players, based on the rules as described in Section 2.1. No more than three cards were swapped during a game.
Standard 52-card decks were used to play each game, either by using one on its own or by combining two decks together. The choice between using one and two decks was made at the discretion of those involved in the games based on the number of individual players involve. This factor affects the number of hands dealt, and thus the number of cards available per hand. Various numbers of jokers were also utilised, again at the discretion of those involved, based on the number of decks used.
A standard Dastoor Knowledge Kit (i.e. pen, paper, and brain) was used to record and analyse the statistical results. The statistical relationship between old and new rankings, and seating positions (in terms of ranking) were both recorded. Microsoft Excel was also used to provide graphical output of the results.
4. Results and Discussion:4.1. Common Variations:
The most common variations of E & S that are most likely to occur naturally are games that contain four or five players. The players and number of cards swapped may vary, but one of the most accepted rules is that the top and bottom players swap two cards, and the second and second last players swap one card. In the case of five players, the third ranked player is neutral.
The case of five players is shown in Fig 1. The statistics based on 31 games show that the chance of the Top Emperor remaining in his or her position is over 70%. There is very little chance of this player being unseated once the position has been determined. The chance of the Second Emperor remaining in that position is also the most likely situation to occur.
The same is true for the Scum positions. There is a nearly 50% chance of the Bottom Scum remaining in that position, well above the probabilities of moving up to any higher position. Interestingly, the chance of remaining in the Second Scum position is almost equal to falling down to the Bottom Scum position. There is a less than 1/5 chance of moving up to a higher position.
As expected, the Neutral position displays a reasonable degree of variation between all positions. It is more likely for the neutral player to remain as the neutral player, but there is also a comparable probability that they will either move up or down a position. The chance of becoming the Top Emperor is quite unlikely, even if the neutral player manages to move up to Second Emperor.
Figure 1: The probability of entering a specific new position based on old position (each colour represents a specific old position), with 5 players using 1 deck and 2 jokers.Similar trends are displayed in the statistics of the four-player version of the game based on 21 games, as shown in Fig 2. The chance of the two extreme positions (Top Emperor and Bottom Scum) remaining where they are is over 50%. There is also a high chance of all other positions remaining the way they are. There is, however, also a considerable chance that the Second Emperor will move up to the Top Emperor position.
Unfortunately, there is very little chance that this player was previously in one of the two Scum positions. Therefore, the expected variation in a game of E & S with four players will be the switching of the two Emperor positions, and possibly also of the two Scum positions.
Figure 2: The probability of entering a specific new position based on old position, with 4 players using 1 deck and 2 jokers.The lack of variation in position (for both the four and five player versions of the game) can most likely be explained by the use of the jokers, which provide a huge benefit to whichever players are holding them. In both cases, only two jokers were used. Any jokers that are dealt to players ranked as Scum will be handed over to the corresponding Emperor. There is no way that the Bottom Scum can ever hold any jokers, and the Second Scum will only hold a joker if they are dealt both (a highly unlikely occurrence).
One of the justifications for using neutral players is that they will not have to give away the jokers if they are dealt to a neutral hand. Only using one neutral player in the five player version of the game reduces significantly the chances of a joker being dealt to a neutral player. It is possible that using two neutral players in the four player arrangement and three neutrals in the five player arrangement may introduce a higher variation in positions, due to the higher chance of a neutral player being dealt a joker.
Figure 3: The probability of entering a specific new position based on old position, with 6 players using 1 deck and 2 jokers. The error is due to an uncertainty in the exact number of games played.
Figure 4: The probability of entering a specific new position based on old position, with 6 players using 2 decks and 3 jokers. The error is due to an uncertainty in the exact number of games played.Another relatively common arrangement is to have six players, but there has been some debate as to whether the use of either one or two decks is more beneficial to gameplay. Both situations have been examined, utilising an appropriate number of jokers.
The results of one deck (based on 32 games) and two decks (based on 16 games) are shown in Figs 3 and 4 respectively. They suggest that neither mode of gameplay is more beneficial than the other, as both game types display a high probability of remaining in the same position. (The error in these results is due to an uncertainty in the exact number of games played.)
Both game types also display trends similar to the four and five player games. The less extreme positions (Third Emperor and First Scum) have a much larger variation in terms of previous position than the more extreme positions. In fact, in both cases the probability of the Top Emperor remaining in that position is well over 50%.
The move from one to two decks is based on the notion that more cards in a player’s hand will allow for a larger number of high cards. The impact of swapping the cards should therefore have less of an effect. Fig 4 shows that the opposite is in fact true. With two decks, the probability of any Emperor position changing is extremely low. The only variation is in the Scum positions.
While it is likely that further games would lower the probability of remaining in these positions, it is unlikely that the over all trends will change dramatically. Like the four and five player versions of the game, it is the use of jokers that causes this imbalance in gameplay. Introducing a third joker with the second deck does little to increase variation.
With only one deck and two jokers, there is now no possibility of the two bottom Scum positions from holding a joker. Adding a second deck and a third joker only means that the Second Scum can, at most, hold only just joker.
The problem arises before the swap takes place. There is an equally likely chance that an Emperor will be dealt a joker as a Scum is to be dealt one. This means that the Scum will be giving away other high cards, which will further weaken their hand. If the jokers were to be removed, and the 2’s used as the highest card instead, then the large number of 2’s present in two decks may allow for a more balanced game.
It may also be possible that seating position also contributes to this inherent imbalance. One possible way that seating position could present a problem is if a certain rank is repeatedly positioned after another rank. This would be a problem especially if a low ranked player continually has to play after a high ranked player.
Figs 5 – 7 show the effects of seating position on games using four, five, and six players with one deck (based on 10, 13 and 9 games respectively). Even with such a small sample size, it is quite easy to see that in most cases, there is no tendency for one rank to always end up beside another. A larger sample size may further support this analysis.
Figure 5: The probability of a specific position being seated to the right of another position, with 5 players using 1 deck and 2 jokers.
Figure 6: The probability of a specific position being seated to the right of another position, with 4 players using 1 deck and 2 jokers.
Figure 7: The probability of a specific position being seated to the right of another position, with 6 players using 1 deck and 2 jokers.As stated in Section 2.2, some rule sets try to offset the effects of the weaker hands by stating that the players must rearrange themselves based on their ranking. This allows the Bottom Scum to play first, followed by the Second Scum, etc, up to the Top Emperor. Rearranging players will mean that lower ranked players have a chance to remove lower ranked cards from their hand first, while higher ranked players are forced to begin with something at least mid-ranged.
The results would appear to indicate that such measures are not necessary, but this is not strictly true. It may be possible for certain rankings to end up continually beside another ranking (a low Scum playing after a high Emperor, for example) during a particular game. This occurrence would not show up when combined with the overall statistics, since they would be averaged out.
4.2. Other Variations:
While four, five, and six player arrangements are the most common variations of E & S, there are many other slightly less common variations that still arise often enough to warrant examination. Versions of the game with eight and three players are examined here. These variations can adequately represent the effects of playing the game with an extremely large number of players or with a low number of players.
Figure 8: The probability of entering a specific new position based on old position, with 8 players using 2 decks and 3 jokers.Fig 8 shows the statistics of the eight player version based on nine games. While the sample size is relatively small, we can see trends emerging that are similar to the trends observed in the four, five, and six player games. Emperors will only swap positions with other Emperors, and Scum will only swap positions with other Scum.
Interestingly, the ranking of the neutrals displays a similar effect, e.g. the Second Neutral is more likely to enter a Scum position than an Emperor position. This demonstrates the need for a large number of neutral positions to be established, rather than use the somewhat extreme rule of swapping three cards. A large number of neutrals proportional to players should provide an adequate means of variation in ranking to occur.
It is also interesting to note that there is a greater chance that the Second and Third Emperors will switch, rather than remain static. There is also an overwhelming probability that First Scum will become Bottom Scum. The reasons for these observations are unknown, but it is possible that a larger sample size would display different statistics.
Figure 9: The probability of entering a specific new position based on old position, with 3 players using 1 decks and 2 jokers.
Figure 10: The probability of a specific position being seated to the right of another position, with 3 players using 1 deck and 2 jokersFigs 9 and 10 show statistics for the version of the game with three players (based on 11 games), the only feasible version of the game below the four player version. The results definitively demonstrate that the game is so unbalanced that it could be argued that a three player version of the game is actually not possible.
It is possible that swapping only one card may reduce the imbalance, as this would give the Scum the chance to retain a joker. However, given that the neutral player appears to be unable to unseat the Emperor with an equal chance of holding jokers, it is far more likely that the three player variant is indeed unplayable.
4.3. Further Observations:
There have been several claims that Emperors and Scum is fun [2] [4] [7]. This is not the case. Such claims are based solely on anecdote and opinion, neither of which are of any scientific merit.
It is a well-known fact that fun is directly proportional to statistical variation in the results. It is generally accepted that a large variation in ranking (or another similar factor) will raise the interest, and therefore fun, of a game. Since Emperors and Scum displays little to no statistical variation, the game can be labelled as “unfun” in its current form.
It has also been observed that once an individual has been subjected to the conditions of the game for an extended period of time, there is approximately a 50% chance that they will start suffering from a psychological disorder known as “E & S Rage”. This is a worrying trend, especially with the possibility of including the ranking-based drinking or social aspects of “President” and “Dai Hin Min”.
Given that the rankings are unlikely to change, the possibility of alcohol related damage (including vomiting, loss of consciousness, loss of memory, loss of inhibitions leading to regretful decisions, injuries due to lack of coordination, and alcohol poisoning [6]) due to peer-induced drinking are extreme. Violations of the Geneva Convention, causing physical and emotional scarring, are also highly likely if playing with social consequences.
Inexperience in the field of psychology, and a strong sense of morals and ethics, has prevented these conditions from being examined further in this study. In fact, forcing people to participate in the standard E & S game may be a violation of human rights due to the high incident rate of E & S rage.
5. Conclusions:The results presented clearly indicate that Emperors and Scum is, under the tested conditions, possibly the most unbalanced and unfair card game known to mankind. Modifying the rules to closer match other known variants of the game displayed similar unfair characteristics to the unmodified rules described in Section 2.1. The complete removal of jokers may act to return some balance to the game.
Further tests with the card swapping removed could be conducted, but are likely to support the conclusions based on the presented results. In other words, playing ability is useless and luck is everything.
The results also show that the game is not fun, due to the lack of statistical variation in results. Furthermore, preliminary reports suggest that it may even be unsafe, due to the onset of E & S rage. It is therefore highly recommended that all forms of the game, including known variants, cease immediately and that no further games take place in order to preserve humanity’s fragile emotional and psychological state.
6. Acknowledgements:The author wishes to thank all those who became a statistic by playing games, especially those who recorded their own statistics as well. There are too many of you to list individually (and no doubt at least one person would be forgotten) but you should know who you are.
7. References:- Caron, J., “Asshole Drinking Game”, DrinkingGame Rules.com, available online at http://www.drinkinggamerules.com/view_game.php?id=55, last accessed 4/12/07.
- Carraro, T., (2007), Personal correspondence.
- Lang, K., (2006), Personal correspondence.
- Lang, K., (2007), Personal correspondence.
- McLeod, J., (2006), “President”, available online at http://www.pagat.com/climbing/asshole.html, last accessed 4/12/07.
- Mutkins, K, (2007), Personal correspondence.
- Pritchard, J., (2007), Personal correspondence.
- Wikipedia, “Asshole (game)”, available online at http://en.wikipedia.org/wiki/Asshole_%28game%29, last accessed 4/12/07.
- Wikipedia, “Dai Hin Min”, available online at http://en.wikipedia.org/wiki/Dai_Hin_Min, last accessed 4/12/07.
- Wikipedia, “Winner (card game)”, available online at http://en.wikipedia.org/wiki/Winner_Card_Game, last accessed 4/12/07.
.jpg)
Figure 1: The Maitland Art Gallery.jpg)
Figure 2: Our Shrine.jpg)
Figure 1: The Maitland Art Gallery.jpg)
Figure 2: Our Shrine.jpg)
Figure 3: Here we see a faded-pink Horse-like sculpture. Notice the raised tail, as a symbolic gesture representing the imminent future of this town.jpg)
.jpg)
Figure 5: This is certainly a divine garden of unfettered beauty!.jpg)
Figure 6: This face of beauty moved the photographer to tears..jpg)
.jpg)
.jpg)
.jpg)
.jpg)
.jpg)
.jpg)
.jpg)
.jpg)
.jpg)
.jpg)
