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Subject: On the Application of Basic Tactical Decision Making on the Card Game Fluxx rss

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Ryan Hackel
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On the Application of Basic Tactical Decision Making on the Card Game Fluxx
Ryan Hackel, 4 April 2008

Abstract

This experiment continues the study undertaken in Hackel, 2006 with attention to the effects of basic decision making practices upon the likelihood of victory. Two hundred test games were conducted in which players alternated the roles of first player and of playing with only basic tactics. It was found that the fully-tactical player won 71% of the games, while the basic player won 29%. The starting player won 56% of all games. Combined with the results of previous study, this concludes that Fluxx players greatly benefit from basic tactical decision making, with considerable advantage over making decisions purely by random methods.

Objective

The purpose of this experiment was to determine the magnitude of effects due to basic tactical decision making on the outcome of a game of Fluxx, and compare those results to previous studies of random play effects. A secondary objective was to determine and compare the amount of first-player advantage in a game of Fluxx.

Background

Fluxx (ISBN #1-929780-01-X) is a non-collectible card game published by Looney Labs in 1998. The object of the game is to meet the victory conditions listed on the current Goal card. Most goals give victory to a player who has collected a certain set of Keeper cards. The basic rules, "draw 1 card then play 1 card", are modified by playing New Rule cards. As a sum of these characteristics, the objective, pace of play, and restrictions on play frequently change during the match.

In the study "On the Effects of Tactical Decision Making on the Card Game Fluxx" (Hackel, 2006), the effects of tactical decision making were quantified. (Readers of this article should be familiar with that study before continuing further with this one.) Many of the criticisms of those results inquired about the purpose of studying purely random behavior. Even novice Fluxx players can identify an individual card play that will either immediately win them the game or guarantee their loss. Multiple commentators suggested a repeat of the 2006 study with such basic tactical decision making included. This study is simply the Hackel 2006 study redone with the random player able to identify obvious plays that would lead to a win or loss.

One game behavior characteristic that was also measured in this experiment is "first player advantage", a property by which the player who makes the first play in a game will have a strategic benefit and thus have a higher likelihood of winning. First player advantage is commonly a problem with purely strategic games, and can be mitigated with the incorporation of random chance through dice or cards. As Fluxx has a significant luck factor due to the sole use of cards, the likelihood of victory favoring the first player should be slim. First player advantage was measured here for comparison with the results of the Hackel 2006 study.

Hypothesis

A player who uses full tactical decision making ability in a game of Fluxx will have a significantly greater chance at winning than a player who plays using only basic decision making ability. A player using basic decision making ability will have moderately greater chances than a player who plays only at random. The first player will have less than 5% likelihood of victory over the second player.

Procedure

The experiment was conducted with 200 games of Fluxx, played between February 15 and December 26, 2007. All of these games were two-player games using the same two individuals.

All games were conducted with the same standard Fluxx v2.1 deck with the following modifications:
* The card Government Cover-Up was omitted.
* The promo card Tarts was added. "Counts as both Cookies or Bread."
* The promo card To Sleep or Not to Sleep was added. "The player who has The Moon and either Sleep or Coffee on the table wins."

In each game, one player played Fluxx normally, having the proper amount of information and making informed decisions (designated hereafter as the 'thinking player'). The other player played generally at random, making decisions in an arbitrary manner (blind selection, die-rolling) when necessary (hereafter designated the 'basic player'). However, the basic player was able to examine their play hand at all times, and were allowed to take any specific action that would result in their immediate victory. That player was also allowed to omit from random selection any specific action that would guarantee a defeat.

In practice, the basic player had difficulty at times in defining what an 'obvious' victory or defeat was. For example, is playing Scramble Keepers, when the possibility exists, however slight,
that the opponent could acquire all Keepers needed to satisfy the current Goal, an obvious defeat? Does counting cards, using statistics, or taking advantage of knowledge of the opponent's hand, and other such advanced methods, violate the spirit of being a 'basic' player? Whenever questionable situations arose, the game was suspended and both players discussed the particular question and how the operating rules applied, and play resumed after a unanimous decision on how to proceed. This occurred in approximately 5% of the games played.

The basic player's hand was shuffled if the thinking player had knowledge of the order of contents of the basic player's hand.

Games were played in sets of 4, following the below schedule:
* Game 1: Player A starts. Player A is basic.
* Game 2: Player A starts. Player B is basic.
* Game 3: Player B starts. Player A is basic.
* Game 4: Player B starts. Player B is basic.
This was done so that each player started 50% of the games, and each player played 50% of the games with 'basic' tactics. Each group of 4 games repeated this schedule.

If the card Secret Data was played, both players chose not to exercise the card's rules. The basic player always chose to exercise the effects of Bonus cards if that player was eligible for those bonuses.

Results

Out of the 200 games played, the basic player won 58 of them, or 29.0%. The thinking player won the remaining 142 games, or 71.0%. The basic player started first on 35 of the 58 games he or she won, and the 'thinking player' started first on 77 of the 142 games he or she won. Combined, the starting player won 56.0% of all games played.

Conclusions

The primary objective of measuring likelihood of victory through basic tactical play was achieved. In this experiment, the thinking player won 71.0% of games played, or 21% more than they would have expected if Fluxx were purely random. The basic player won 29.0% accordingly. In comparison, the result for the 'random player' in Hackel 2006 was 14.0% [1]. By using basic decision making skills instead of purely random chance, a Fluxx player is able to more than double his or her chances of victory. This outcome illustrates that the ability to make basic tactical decisions significantly increased the basic player's likelihood of success.

Many behavioral results observed in Hackel 2006 were also observed in this study. A low number of cards in hand significantly impaired the thinking player's likelihood of victory. Many of the basic player's victories came from the "X, no Y" Goals, where the player with Keeper X wins if Keeper Y is not present.

However, some behavioral differences were noted. In previous study, the 'random player' received little benefit from having extra cards in his or her hand. As the only person to gain from it, the thinking player often attempted to do increase hand sizes [1]. However, in this study, with the ability of the basic player to observe for obvious victories, the thinking player was more hesitant to increase hand size, although still preferred to do so.
Also, more so than in the previous study, the thinking player, through the use of New Rules, encouraged both a high Draw and high Play value. By doing so, the thinking player hoped to force the basic player into making a losing play, while attempting to capitalize on having the advanced tactical skills necessary to fully utilize a large hand during a turn.

The secondary objective of measuring first player advantage was also met. The first player won 56% of games played. This is close to the 50% mathematical expectation for most games. In comparison, Hackel 2006 determined the first player advantage to be 54.0%, two percent lower than the results of this study. The difference in measured first player advantage may be attributed to the ability of both players to spot easy victories early in a game, rather than just one player being able to do so.

There was also a noted disparity in first player advantage (FPA) when separated by player. 60.3% of the basic player's wins came from games he or she started, while the thinking player won 54.2% of the games he or she started. This cause of this disparity is still unknown. Note that this is similar to those found in Hackel 2006, with 60.7% for the 'random player' and 52.9% for the thinking player. The 'random' or basic player's FPA is reduced by 0.4%, while the thinking player's FPA increased 1.4%. This illustrates that as tactical ability among players becomes more balanced, so does the first player advantage. By extension, players of equal ability should have equal amounts of first player advantage.

Recommendations for Further Work

The results of this experiment should be compared to a similarly sized sample group of games that were played randomly by both players. This will help validate the results of this study, and help measure the amount of first player advantage that is inherent to the design of Fluxx, not just that attributed to player ability.

Also, this experiment should be repeated with the v3.1 Fluxx deck, without promo cards. The changes made between v2.1 and v3.1 were significant. Each Keeper was reviewed to be just as useful as the other Keepers, and underused Keepers were omitted. A few Keepers were added, along with new Goal cards for them. Also, the Bonus rules were completely rewritten and many Action cards were replaced. Overall about 25% of the deck was modified, and this may have a significant impact on the results of this experiment.

References

[1]: Ryan Hackel. "On the Effects of Tactical Decision Making in the Card Game Fluxx" BoardGameGeek, April 2006.
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Doug Orleans
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I'd really like to see someone implement some intelligent Fluxx bots for Volity. That would make it much easier to do these sorts of experiments.
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Red Dragon
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There is a flaw in thinking that there should be no first player advantage. You would only expect precisely 50% of games to go either way if every game was of infinite length with an infinitesimal chance of winning on each turn. If the average game lasts 20 turns, then you have an average of 5% chance of winning on each turn, and that would translate into a clear advantage to the first player. I believe this is the explanation for the small difference between 50% that you expected to get and the 54% or 56% that I think should have been expected.
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Doug Orleans
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But the second player has a better chance of winning on his first turn than the first player does, since he can take advantage of the new rules put in play.
 
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Chris Flood
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Although this study thoroughly debunks the argument that tactical decisions play absolutely no part in Fluxx, I feel like the comparison to purely random play (50-50 split of who wins a two-player game) does not really get at the heart of the criticisms of Fluxx. Even though critics claim that a player making random choices will do as well as a "thinking" player in Fluxx, I wouldn't expect that anyone really belives this.

What they really mean is that a player's decision-making has far less impact relative to other games. A win rate of 14% for purely random play seems ridiculously high to me; I'd expect that rate to be less than 1% for a game like Chess and far below 14% for most of the top-rated games here on BGG. That's where the real comparisons--and complaints--lie, rather than with the strawman of "totally random play."
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Spencer C
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I suspect the random win rate of your earlier article increases dramatically the more players you add. Perhaps even to the point where the tactical player has equal odds of winning as any other player.
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