Sunday, November 9, 2008

Reciprocity of a Drinking Game

Yesterday evening, my friends played a drinking game before heading out to the bar. Because I wasn't planning on going out, but still wanted to enjoy their company, I decided to monitor the tendencies of their drinking game.

The rules of the game were pretty simple. It is a game that involves cards and decisions by the players. When cards are dealt, players will either have to "take," or drink for a specified amount of time based on the round, or "give" a specified amount of time to drink based on the round.

The first couple rounds go swiftly. Cards are dealt one-by-one to players in a counterclockwise order. The cards are dealt face up and in each round a player receives only one card.

During the first round, players are asked
 to guess whether the card is red or black. If they guess correctly, they can "give" the value associated with the first round (2 seconds) to another player, but if they are wrong, then they have to "take" those 2 seconds. In the second round, players are asked if their next card will be higher or lower than the card they already have. The same rules apply if they are right or wrong, except now it extends to 4 seconds. 

The third round asks players to determine whether the card will be inside or outside of the range of cards that they have. For instance, if a player has drawn a 7 of spades and an 8 of hearts, it is likely that the next card will be outside of the range, whereas, a player with a 2 of diamonds and a king of clubs would probably guess inside. The same rules apply for being right or wrong, except now it is 6 seconds. 

The fourth and final round of the preliminary rounds asks players to guess which suit their card will be. If players are correct, they can "give" 8 seconds, but have to "take" 8 seconds if they are wrong.

After the preliminary round, the game enters into a phase called, Fireworks. The picture above gives the breakdown of how Fireworks is setup. As you can see there are several cards used in Fireworks, all face down to begin with. There are two columns of cards, one "take" and one "give" that increase in their intensity from 2 seconds to 8 seconds, similar to the opening rounds (this is represented in the illustration by the number following the word Card). On the wings are four more cards that raise the level of intensity. On the left side, there are two cards, one "take" and one "give" for half a beer. On the right side, there are two cards, one "take" and one "give" for a whole beer. The order in which Fireworks occur is by starting with "Card 2" in the Take Column, and then "Card 2" in the Give Column. This continues through "Card 8" for both Take and Give. Then Take and Give is done for Half and then Full.

The way in which this portion of the game works, is if any of the four cards you received during the preliminary round match in value (8's, Kings, Jacks, 4's, etc.) to those that get flipped, you must "take" or "give" depending on the card's designation. 

It's a phenomenal game and a lot of fun to play or watch. 

I thought it would be interesting to map out some of the decisions that were made in terms of "giving" drinking quotas to other people. Though this is a friendly game, harsh decisions have to be made at times as to who has to drink. I've also considered that as the game progresses, participants are most likely becoming further inebbriated, which may effect their decision-making processes, but this effect is inherent to the system. I was interested if any patterns would emerge based on some sort of reciprocity, and as I expected, something quite concrete can be deduced from this very simple but telling game about social networks.
  • Explanation
Above is a visual representation of the decisions made by participants in their first game of play recorded. There were five total participants, each depicted as a "Smiling Face." The boxes either above, below, or to the side of the faces are how I will make reference to distinctive actions made by that player. The visual representation is supposed to give scope as to the actual seating arrangements of the individuals playing the game, which I assert makes significant impact on the decisions of the players. I was seated between JG and SS and was not participating in the game.

I propose that seating is the most important factor determining decisions in the game. Starting from the left side: ZS was sitting on a chair by himself. JG, Tyrone Schiff, and SS were sitting on a couch together. MK and MB were sitting on a seperate couch perpendicular to JG, Tyrone Schiff, and SS, facing ZS. There is a rectangular table between the groups.

There are clear trends that can be noticed from the outset. SS and ZS engaged in a "war" during the game, consistently being given decisions (which is based on luck), and consistently "giving" the designated value to one another. SS and ZS were also seated quite far away from one another, at least on opposite sides of the table. 

SS was given several opportunities to "give," but made them consistently towards ZS. He could have just as easily "spread the wealth" by "giving" to JG, MK, and MB, but chose to direct his efforts to a member farthest away from him.

There are several underlying causes of this. One consideration is mere comradary. ZS and SS may be good buddies and want to get each other "wasted" to have a fun night at the bar. However, all the individuals playing the game are all trying to get "wasted" and are equally good buddies. This is not a qualifying argument. 

Another cause could possibly be based on the Feedback effect. As SS makes more decisions to "give" to ZS, ZS comes back at SS and "gives" to him in order to "level the score." This argument has slightly more merit. However, one must realize that the players are all reasonable people and wouldn't intentionally engage in "war" with another if they had other options available. "War" is undesirable, and none of the players at the table would choose to wage it rationally.

This leaves us with the prevailing theory that decision making was based on seating arrangements. This is well evidenced by SS's decisions. While SS had 5 decisions to make, more than any other person, he directed his "giving" to only one person, and that person was farthest away. He did not "give" to MK, who was very close but on another couch, or MB, slightly farther away, but not the farthest, nor did he "give" to JG, a member of his same couch. SS clearly looked for a member of an outgroup in which he could get others to gang up on.

And they did. In closest proximity to SS was MK. MK, with only 3 decisions, decided to spend one of them on ZS, influenced by the actions of SS and feeling comfortable with the distance between them. 

The distance and seating argument is further evidenced by actions of MK and MB on JG. MK and MB are members of the same couch. MB, with only 1 decision, chose to spend it on JG, and MK spent 2 out of 3 of his decisions on JG. MB and MK were located equally as far away from JG as SS and ZS were. The fact that they were working together and the "extreme" distance between the parties made it okay to gang up on this one player.

MK and MB also attacked each other by "giving" one decision to each. However, once the decision was reciprocated, the two never "gave" to one another again, indicating a truce of sorts, and an understanding of using their strength elsewhere on farther targets.

The decision by JG may seem a little incongruous with the proposed theory of distance being the most important factor, but a brief analysis makes sense of his decision.

JG had no reason to "give" to SS. They are members of the same couch and SS had never targeted JG before. It is then likely that JG would attack either MK or MB, because they "gave" to him and JG would like his revenge. However, JG was only provided with 1 decision, and it would have been futile to "give" to either MK or MB. There are two reasons for this.

First, by "giving" to only one of the members, MK or MB, the revenge isn't sweet at all. JG can only make one of his attackers suffer. The full effect of the decision is thus inconsequential; there is no statement made by JG's decision. Second, JG, realizing that he was a target of attack, didn't want to further annoy or anger MK or MB by "giving" to them. JG was already being targeted for being far away from MB and MK, an attack on them would just motivate MK and MB to "give" to JG more frequently.

Thus, JG "gave" to ZS, a fellow member of attack. There are several reasons why this may be the case. JG could try to win support from SS or MK, so they would both view JG as an ally. JG does this for MK so that he would no longer attack him, based on their mutual agreement to attack ZS. JG does this for SS so that if ZS, MK, or MB "gives" to JG, SS may counterattack on behalf of JG, due to the fact that they have a mutual understanding of attacking ZS and because they are members of the same couch. 
  • Conclusion
The object of this study was to try and understand the decision making processes involved in playing a drinking game. 

After excluding alternative hypotheses, decision making during this drinking game can most accurately be attributed to the location in which someone sits relative to the other players.

ZS was thus a "sitting duck" from the start. He was farthest away from three of the four players, not including himself, and also sat in a chair with no other person. SS and JG were "members" of the same couch, just as MK and MB were "members" of a different couch. This team-like or shared experience as "members" of the same couch is remarkably strong in shifting decisions. Allegiances were tested, as MK and MB reveal, but ultimately, the majority of the decisions were based on how far someone was located away from the decision maker.

Saturday, November 8, 2008

Word Frequency Measurement

I came across a fascinating product today that Google operates. The product is Google Trends and visually displays information relating to search queries that could be entered into a Google search. It's unbelievable comprehensive. Aside from providing a line graph of the relative search volume since 2004, it also provides you with the ability to narrow your search to particular regions of the world or even singular countries. For a person who wants to use Google as their advertising medium on the Internet, this feature is without doubt a must. Understanding where and why people are searching for the terms they are is a critical feature that sets Google apart from the rest.

You can also localize your search term trend for a particular span in time. So, if you are only interested in how people have been searching for these words within the past 30 days, you can set that option very easily. If you are particularly interested in how many times that search term was queried in a particular month since January 2004, Google Trends will allow you to set that.

The graph has an interesting dependent variable called Search Volume Index. On Google Trend's About page they define it as "how many searches have been done for the terms you enter, relative to the total number of searches done on Google over time."

Just below the graph are three columns at are unbelievably helpful in understanding how exactly the search term you're looking at is used. There is a column for regions, which specifies the rank of usage by country. Then, next to that column is an even more specific look at where the search term is being queried by ranking the cities by usage. As you will see later, the city in which the search term is queried the most is quite intuitive. Finally, the last column is what language that term is most queried in. Most of the tests that I've performed have had the most usage in English, however, it is fascinating to see how the rest of the queries not in English relating to the search term rank by language.

Probably one of the coolest features about Google Trends is its pairing with relevant news articles. Below the primary graph that reveals search volume there is a another graph called New Reference Volume. "This graph shows you the number of times your topic appeared in Google News stories." When there are spikes in the search term volume, Google Trends automatically flags the occurrence and links the spike to an actual news article, which probably explains the spike in search term volume.

It's an amazing feat of computational engineering. When it comes to understanding how people are using the Internet in terms of what their searching, I cannot think of a better source than Google Trends. Google has approximately 60% market share of all search queries, and this data is contigent on that sample. Google Trends is comprehensive and provides the user with the relevant information that he or she is looking for.

In order to gain further understanding of Google Trends, I ran a quick study in order to familiarize myself with the options and processes available.
  • Google Trends Study
This study was conducted on November 8, 2008 at approximately 7:30pm. The purpose of the study was to gain familiarity with Google Trends and make comparisons of search term usage for a randomly sampled set of search terms across regions.

The study sampled three words from three randomly sampled individuals living in my house. Participants were asked to, "provide three words that could be possible search queries in a well known search engine, like Google." The individuals choosing the words sat together and were asked to recite them aloud. This would ensure that participants didn't provide duplicate words.

After the participants gave me three randomly selected words each, they were asked to, "provide a country somewhere in the world aside from the United States." Each participant then selected the country in the same fashion that they provided the words. Some participants took longer than others; one participant was still selecting words while another had already provided both their words and country. The time length in which the participants finish their selections is not terribly important, however, it should be done in a reasonable amount of time.

Participants were also asked to predict the relative search volume of their three words from highest to lowest across the world.

The following table summarizes each participant's selections and the order in which they expect their search volume to be from highest to lowest:
As you can see, there was a rich diversity in the words that were selected. Participant 2 focused on more Proper Nouns than regular nouns like the other participants involved, yet, still a sufficiently random sample.
  • Participant 1
[To see worldwide results please click each of these respective words: Drugs, Cowboy, Cardboard]

Upon requesting search volumes for the three words provided by Participant 1 in Djibouti, Google Trends was unable to provide search volume information citing the following:
Your terms - ????? - do not have enough search volume to show graphs.
Suggestions:
  • Make sure all words are spelled correctly.
  • Try different keywords.
  • Try more general keywords.
  • Try fewer keywords.
  • Try viewing data for all years and all regions.
The subsequent 6 search terms provided by Participant 2 and 3 were then also searched for in the Djibouti database rendering the same message. Unfortunately, there does not appear to be sufficient search queries of these provided words from Djibouti to elicit graphs. This is an unfortunate finding based on our study. It appears as though Google Trends, while comprehensive, is indeed fallible.
After trying to insert search queries that I thought would have sufficient volume to represent graphically (United States, Barack Obama), I eventually input "Djibouti," which finally elicited results. The search term, "Djibouti" is most commonly searched for in Djibouti, Djibouti, when narrowing the results to just Djibouti results. The most common language that Djibouti is searched for in Djibouti is French. There was a spike in search volume for "Djibouti" in Djibouti on June 12, 2008 when an article was published entitled, "UN council condemns Eritrean attack."

This can be compared to search queries for the term "Djibouti"
from all regions around the world. "Djibouti" is most commonly searched for in Regions like Djibouti, United Arab Emirates, Morroco, and France. Some cities where "Djibouti" is most commonly searched for include Dubayy, UAE, Ottawa, Canada, and Rennes, France. French, English, Swedish, and Dutch are most common languages when searching for "Djibouti."

Participant 1 correctly predicted the order in which the search terms provided would be relative to one another across the world. It is interesting to note that the order the participant gave the words is the same order that was predicted for highes
t to lowest search volume. The graph visually depicts the relationship between Drugs, Cowboy, and Cardboard in terms of their worldwide search volume.
  • Participant 2
[To see worldwide results please click each of these respective words: Synthesizer, Rex Grossman, Mr. Feeney]

Similar to the Participant 1, the words provided by Participant 2 did not have enough search volume in Malta for a graph to be displayed. This is again another unfortunate occurrence. The same technique was used for Participant 2 as was for Participant 1 in attempting to find some sort of graph. The other 6 search queries did not provide any sort of graphical depiction either.

In order to gather some results, I input the search query, "Malta" to elicit some sort of results within the Malta Google Trends database. Fortunately, this was able to provide some sort of graph with relevant news articles that coincided with spikes in the volume.

In Malta, the search term, "Malta" is most frequently searched for in Msida, San Gwann, and Valleta, all cities in Malta and in that order. The most common language "Malta" is searched for in Malta by frequency is German, English, and Maltese. One of the highest peaks in News Reference Volume within the Malta database when searching for the query "Malta" was on November 20, 2007, when an article entitled, "Queen to Celebrate in Malta," was published on News24.com.

Compare these results to worldwide trends for searching "Malta." Some of the most popular regions searching for "Malta" are Malta, Ireland, United Kingdom, Italy, and Austria. Some of the most popular cities are the three Maltese cities already mentioned, followed by, Poznan, Poland, Dublin, Ireland, and Thames Ditton, United Kingdom.

Participant 2 was correct in the predictions made about the order in which relative search volume would occur. Synthesizer has a higher relative search volume to that of Rex Grossman, and by virtue of there not being enough data on Mr. Feeney, one can deduce that Rex Grossman has a higher relative search volume than Mr. Feeney. This is visually represented below.
  • Participant 3
[To see worldwide results please click each of these respective words: Arsenic, Stencil, Magician]

Similar to the past two participants, all word choices by Participant 3, arsenic, stencil, and magician elicited no graphical results in the Belgium Database of Google Trends. Upon further review, some words provided by Participant 1 (Drugs & Cowboy) elicited results, but for fairness to each participant, I will conduct the same analysis as I have done for the prior two.

Therefore, I will share results from quering the search term "Belgium" in the Belgium database. The most prominent subregions that query the search term "Belgium" are Flemish Brabant, East Flanders, Brussels, and Luxembourg. Major cities querying "Belgium" include Leuven, Gent, and Brussels. The language that "Belgium" is usually queried in is English, Dutch, and French (in that order).

Recently, there was a surge in the News Reference Volume relating to the search query of "Belgium" within Belgium that linked to a story entitled, "First Industrial to Invest in New State-of-the-Art Logistics Facilities in Belgium." The story was published on October 6, 2008 and led to the highest New Reference Volume in the Belgium Database of Google Trends for the search query "Belgium" ever.

Compare this to worldwide searches for the search query "Belgium." The major regions in which "Belgium" is searched for occur in Belgium, Luxembourg, Ireland, the United Kingdom, and the Netherlands. Cities outside of the Belgium that most frequently query the search term "Belgium" include London, United Kingdom, Amsterdam, Netherlands, Syndey, Australia, and New York, New York. Around the world, the most commonly used language to query the search term "Belgium" is Dutch, French, English, German, and Italian (in that order).

Participant 3 incorrectly predicted the relative search volumes of the three randomly selected words provided. Based on worldwide Google Trends data, the relative search volumes of the words Arsenic, Stencil, and Magician are correctly ordered as Stencil, Magician, and Arsenic. Stencil is relatively searched for 2.65 times more than arsenic, and Magician is searched for approximately twice as much as arsenic. The graph below reveals this relationship.
  • Conclusion
The purpose of this study was to gain familiarity with the product Google Trends and make comparisons between the relative search volume of randomly selected words.

While Google Trends contains a wide breadth of data on search volumes, there is desperate need for its regional databases to contain more comprehensive data. Search queries in the Djibouti, Malta, and Belgium databases hardly provided any results when inputting some randomly selected words. Either these databases should not be provided to begin with, or they need to be more comprehensive in nature.

Two of the three participants in the study were correctly able to predict the relative search volume of their provided terms. This suggests that Google Trends provides intuitive knowledge. However, it is well evidenced by Participant 3 that the relative search volumes for particular words may be harder to predict.

Overall, Google Trends is a phenomenal resource that provides superb measurements of the relative search volumes of typical search queries performed on the Internet.