On the Effects of Tactical Decision Making on the Card Game Fluxx
Ryan Hackel, 04 April 2006

Abstract

This experiment measured the effects of tactical decision making on the likelihood of victory in the card game Fluxx, and gauged the amount of first player advantage. Two hundred test games were conducted in which players alternated the roles of first player and of playing randomly. It was found that the tactical player won 86% of the games, while the random player won 14%. The starting player won 54% of all games. This concludes that Fluxx players greatly benefit from tactical decision making, but that first player advantage is negligible.

Objective

The purpose of this experiemnt was to determine the magnitude of effects due to tactical decision making on the outcome of a game of Fluxx. A secondary objective was to determine 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.

Strategy is commonly defined as "a long term plan of action designed to achieve a particular goal, as differentiated from tactics or immediate actions with resources at hand.[1]" Tactics is commonly defined as "a procedure or set of maneuvers engaged in to achieve an end, an aim, or a goal.[2]" In the context of a game, strategy is a player's overall plan of how to win the game, while tactics are the discrete decisions made in the prosecution of that strategy.

One of the most frequent criticisms of Fluxx is that it is too random. Many Fluxx detractors claim that the game is so chaotic that the execution of strategy is nearly impossible, and that tactical decisions are of little or no assistance. A few critics pose that Fluxx could be played just as effectively by blindly playing cards at random. While Fluxx may not reward long-term strategic planning, the effects of tactical decision making on winning is unknown.

In a purely random game with only two outcomes, such as a coin toss, the outcome would favor each outcome 50% of all games played. However, the addition of tactical decision making affects the outcome in favor of the player who makes those decisions. From the ideal 50% value, the magnitude of effects of tactical decision making are measured.

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.

Hypothesis

A player who makes tactical decisions in a game of Fluxx will have a greater chance at winning than a player who plays randomly, but this margin of victory will be minor. The first player will have a negligible likelihood of victory over the second player.

Procedure

The experiment was conducted with 200 games of Fluxx, played between November 11, 2005 and February 17, 2006. All of these games were 2-player games using the same two players.

All games were conducted with the same standard Fluxx v2.1 deck with the following modifications:
* The card Goverment 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. The other player played at random, making decisions in an arbitrary manner (blind selection, die-rolling) when neccessary. Cards where played from the 'random player's' hand in the order at which they were drawn, unseen to both players prior to play. The 'random player's' hand was periodically shuffled if the 'thinking player' had knowledge of the order of contents of the 'random player's' hand.

Games were played in sets of 4, following the below schedule:
Game 1: Player A starts. Player A is random.
Game 2: Player A starts. Player B is random.
Game 3: Player B starts. Player A is random.
Game 4: Player B starts. Player B is random.
This was done so that each player started 50% of the games, and each player played 50% of the games randomly. 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 'random 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 'random player' won 28 of them, or 14.0%. The 'thinking player' won the remaining 172 games, or 86.0%. The 'random player' started first on 17 of the 28 games he or she won, and the 'thinking player' started first on 91 of the 172 games he or she won. Combined, the starting player won 54.0% of all games played.

Conclusions

The primary objective of measuring likelihood of victory through tactical play was achieved. In this experiment, the 'thinking player' won 86% of games played, or 36% more than they would have expected if Fluxx were purely random. This outcome illustrates that the ability to make tactical decisions significantly benefitted the 'thinking player's' likelihood of victory. However, the 'random player' did manage to win approximately 1 out of 7 games, showing that even a randomly-acting player still has a non-trivial possibility of winning a game of Fluxx. This margin of victory for tactical decision making was much higher than expected.

During gameplay, it was noted that the 'random player' received little benefit from having extra cards in his or her hand. The diversity of options has no advantage for a player who disregards all those options on his or her turn by making a 'blind play'. As the only person to gain from it, the 'thinking player' often attempted to do increase hand sizes. This behavior helps explain the high likelihood of a tactical player victory.

Conversely, if the 'thinking player' had no cards in hand, he or she was effectively playing like the 'random player', with the inability to choose which cards to play. Although the 'thinking player' still was able to make limited decisions as part of individual plays, a lack of cards in hand significantly impaired the 'thinking player's' likelihood of victory.

It is lastly noted that many of the 'random player's' victories came from the "X, no Y" Goals, where the player with Keeper X wins if Keeper Y is not present. These Goals are achievable with fewer cards, and are thus simpler for a random player to statistically come across.

The secondary objective of measuring first player advantage was also met. The first player won 54% of games played. This is close to the 50% mathematical expectation for most games. A 4% margin for the first player is small, and would have a neglibile impact on a small number of Fluxx games. It is interesting to note from the results that the 'random player' had a 60.7% chance of winning on games he or she started, while the 'thinking player' had a 52.9% chance of winning on games he or she started. This difference in first player victories is unexplained at this time.

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.

Lastly, a similar study could be done with multiplayer games of Fluxx.

References

[1]: Wikipedia online encyclopedia ( http://www.wikipedia.org)
[2]: Dictionary.com online dictionary ( http://dictionary.reference.com)

Brilliant! Though i'm disappointed at the lack of chi-square analysis to show that the difference is indeed significant.

-MMM

Wow, interesting stuff.

Something that would be intersting to see was the effect of playing random EXCEPT for A) always playing a card that will win me the game right now, and B) Never (if possible) play a card that will lose me the game right now.

Very interesting. I was confused by the following:
This might be better worded as "60.7% of the random player's wins came from games he started", etc.

I agree. These results are worthless without this modification.

The study was testing the assumption that Fluxx was truely random. Those modifications add decision making to it and thus tainting the test of random play.

From the article:



The article cleary shows the above quote to be false.


With that said, a similar study which address those two decisions would be interesting and would simulate more accurately what would happen in many games.

So, is someone pushing for an appearance in the Journal of Irreproduceable Results/an Ignobel Award or what?

I think the randomess comes out more with a greater number of players. A two player game of Fluxx is fun. When you get up to 5 or 6, the game can change so much before it gets back to your turn, there is no effective planning. I have played with as many as 9 players and will do so again. Nice article, I look forward to volume 2, more players and the ability to notice a winning or losing play.

http://www.looneylabs.com/OurCommunity/Rosters/Rabbit/index....

Nice article! I too am more interested in the effect of "planning" vs. "non-planning" rather than "thinking" vs. "not thinking." If you can muster the motivation to play another 200 games this way, I'd love to hear about it.

Thanks for the feedback, everyone!

The comments first made by Thomas Tholen and echoed by many others have got me interested in more experiments. I'm working on a testing method and hypothesis, but it might take over 3 months to run 200 games, since constantly switching between "check for winning or losing plays" and "make random decision" will slow the game down.

I do think that benchmarking with both players playing completely at random is more important, and I may be able to incorporate that into another project.

That's some dedication, Ryan, nice article. This is screaming out for some computer simulations of these results, maybe I'll get around to coding that up someday.

I really enjoyed this article. As someone who has played a lot of Fluxx and enjoyed it, I am glad to see some of my own experiences and opinions supported.

I have found that playing against experienced Fluxx players (like the woman I have been dating for the last two years), the game becomes much tighter and much more tactical.

Awesome article. Though I have played way more than 200 games of Fluxx, I am certain I do not have the patience to play 200 games randomly, even if it would prove that Fluxx is a game involving some skill, especially two player Fluxx. I tend to agree (as I said in a another post) that the skill goes away as the number of players increase. I played a six player game of fluxx once that lasted a painful number of hours. The ten minute two player games are much more pleasant to my mind.

Ryan,

An important distinction that has to be made here is between tactics and strategy. You do so in the introduction to your article, and then (obviously correctly) find that tactical play gives a significant advantage over totally random play.

An interesting study, and admirably carried out. However in your introduction, you mention that:



You then goes on to show the falsity of the latter proposition, but don't investigate the former. I think this is what would be most interesting to explore.

When most people criticise games like Fluxx for their apparent randomness, they usually mean only that the execution of strategy is very limited. Few reasonable people would disagree with the advantage conferred by good tactical play over pure random play (though there are some unreasonable people around, judging by what gets written to these forums!).

It would be very interesting to study the different success rates between players who used predefined long term strategic plans and/or immediate tactical differences, and tease out what their contributions were to the chances of vistory - if long term strategies can indeed be defined for Fluxx. The fact that it isn't easy to define them is an indicator that we might already know the answer to that one...

The sequel to this study has been posted on BGG:
http://www.boardgamegeek.com/thread/305020