=Paper= {{Paper |id=Vol-2282/EXAG_117 |storemode=property |title=Desire Path-Inspired Procedural Placement of Coins in a Platformer Game |pdfUrl=https://ceur-ws.org/Vol-2282/EXAG_117.pdf |volume=Vol-2282 |authors=Anurag Sarkar,Riddhi Padte,Jeffrey Cao,Seth Cooper |dblpUrl=https://dblp.org/rec/conf/aiide/SarkarPCC18 }} ==Desire Path-Inspired Procedural Placement of Coins in a Platformer Game== https://ceur-ws.org/Vol-2282/EXAG_117.pdf

Desire Path-Inspired Procedural Placement of Coins in a Platformer Game

Anurag Sarkar, Varun Sriram, Riddhi Padte, Jeffrey Cao, Seth Cooper
Northeastern University, Boston, Massachusetts, USA
{sarkar.an, sriram.v, padte.r}@husky.neu.edu, jhccao@gmail.com, scooper@ccs.neu.edu

Abstract
Many games feature collectible items that are manually
placed by a designer. In this work, we developed an algo-
rithm, inspired by desire paths, for automatically placing col-
lectible coins in a platformer game. Desire paths are paths
naturally formed where people walk, rather than those laid
down artificially, and are often the shortest or easiest route
between an origin and destination. Our algorithm uses player
trajectories to find paths along which to place the coins
for each level. We ran an experiment comparing path-based
placement to other placement methods. Although we did not
find a difference in total time spent playing or likelihood of
finishing the game, our results suggest that path-based place-
ment leads to players collecting more coins in less time than
with designer or randomly placed coins. Further, we found
that players played similarly when coins were either path- Figure 1: A real-world desire path: the small dirt path lead-
based or there were no coins, and similarly when coins were ing to the crosswalk.
either placed by a designer or randomly.

levels where there are multiple paths from start to finish, ab-
Introduction sent other objectives, some types of players may prefer to
Many games have levels containing collectible items (such quickly achieve progress by following the path that is short-
as coins, bonuses, or power-ups) that may serve different est or easiest to traverse, i.e. a path that allows them to com-
purposes within the game. Often, collecting these items is plete the level quickly while having to contend with rela-
a secondary objective, either related or unrelated to some tively few hazards (Bartle 1996; Yee 2007). Note that such
primary objective (such as completing the level). Thus, au- paths may not necessarily be enforced by the level’s design
tomating the placement of such level elements via procedu- but may be discovered after multiple playthroughs of a level.
ral methods could save the designer’s time in authoring the In nature, paths that are created organically by the footfall
level by allowing the designer to focus on the primary goals of people where they naturally tend to walk, rather than by
of the level, and then automatically adding collectibles after artificial construction, are called desire paths. These paths
the level has been designed. usually represent a shortcut or a route that is less circuitous
However, previous work by Andersen et al. (2011b) has than a constructed sidewalk or other walkway. An example
shown that placing such secondary objectives within levels is shown in Figure 1. Borrowing this concept for platform-
may decrease engagement if the placing is not done in a ers, we use desire paths to refer to the paths through a level
manner that serves the primary objective of the levels. That that players are likely to traverse on account of being sim-
is, to be effective and not cause any side effects detrimental ple, direct routes from start to goal. Thus, placing secondary
to player experience, such procedural placement algorithms level elements, such as collectibles, along these paths may
should take into account the level’s primary objective and help circumvent the issues associated with their placement.
how the player achieves that goal. In this work, we extracted such desire paths for each
Platformer games usually consist of levels where the pri- level in the platformer game Iowa James: Treasure Hunter
mary objective is to traverse through a sequence of platforms (screenshots shown in Figure 2) using player trajectories and
and hazards to reach some goal at the end of the level. For placed collectible coins along these paths. We compared the
path-based method of coin placement with coins placed by
a designer, with coins placed randomly, and with levels hav-
ing no collectible coins. Our findings indicate that placing
and Ontañón 2014), action-adventure missions (Dormans
2010), strategy game maps (Liapis, Yannakakis, and To-
gelius 2013a), and space shooter weapons (Hastings, Guha,
and Stanley 2009). One of the primary motivations, among
many, for such procedural techniques is to assist or save the
designer’s time in authoring game content (Smith 2014b).
While much PCG work focuses on generating entire levels,
in our work, we focus on placing collectibles within existing
levels. By automating the design or creation of secondary
or tertiary game artifacts, the designer can then focus more
thoroughly on the principal components of a game’s design.
Data-Driven PCG. Smith (2014a) defines a data-driven
PCG system as one that “uses external data to inform
the generation of content.” Data-driven approaches have
Figure 2: Examples of Iowa James on his adventures.
found wide use for player modeling. Zook et al. (2012)
use data-driven player models for generating missions while
Zook and Riedl (2012) do so for dynamic difficulty ad-
coins along paths leads to players collecting more coins in
justment. Closer to our work is that of Pedersen, Togelius,
less time than with designer or randomly placed coins. When
and Yannakakis (2010) who build data-driven player mod-
compared to having no coins, designer placed coins led to
els, which can then be utilized to inform level design. Simi-
fewer levels being completed with more time spent in each
larly, Jennings-Teats, Smith, and Wardrip-Fruin (2010) used
level, while we did not find such differences for path-placed
players playing through platformer level chunks to train a
coins. Overall, we found no differences in player behavior
model of player experience rather than craft one by hand.
when coins were placed along paths or when there were no
The model was then used to generate platformer levels of de-
coins. Similarly, we found no differences in player behavior
sired difficulty. Such work falls more squarely in the field of
when coins were placed manually by a designer or placed
PCGML (Summerville et al. 2017), where generative mod-
randomly, indicating that in some cases it may be possible to
els trained on existing game data are used for creating new
save designer time simply by placing collectibles randomly.
content. Our data-driven model differs from most traditional
models in that rather than having a model of each individ-
Related Work ual player, we utilize a model of player movement with all
Desire paths in design. While most often directly used in players considered in aggregate. More recently, data-driven
the context of urban planning, desire paths have received approaches have been applied not just to inform level design,
attention in more general design as representative of what but to generate entire adventure games (Barros, Liapis, and
people actually do rather than what designers might prefer Togelius 2016).
or expect (Kohlstedt 2016). Desire paths have been used as Mixed-Initiative PCG. While purely automated content
a metaphor in areas like product design (Myhill 2004), soft- generation systems are useful, we often require procedu-
ware interaction design (Zhang, Padman, and Levin 2014), ral systems that afford authorial control during generation.
and more general social behaviors (Nichols 2014). These systems enable a human designer to guide the PCG
Secondary Game Objectives. Secondary objectives form system towards content with certain desired properties. Such
a fundamental component in the design of many games. Ini- systems are categorized as mixed-initiative PCG since they
tial work by Andersen et al. (2011a) found that the inclusion combine the creativity and judgment of a human designer
of secondary objectives, such as coins, could negatively im- with the ability of a generative system to quickly produce
pact engagement. However, further work (Andersen et al. a large amount of output. Smith, Whitehead, and Mateas
2011b) found that secondary objectives that supported the (2011) developed the mixed-initiative generator Tanagra,
game’s main objective could positively impact player behav- which uses reactive planning and constraint satisfaction to
ior. Specifically, placing coins along the main path through create 2D platformer levels that a human designer can then
levels in a platform game led to players completing more edit. Smith et al. (2011) also created the Launchpad level
levels and spending more time playing than having off-path generator, which uses a grammar-based method and the no-
coins in the levels. This informed our use of player trajecto- tion of rhythm groups to generate playable platformer levels
ries through levels to procedurally determine desirable paths that the designer can then tune to define player paths through
for levels and place coins along these paths. the level as well as frequency of level components. Similarly,
Procedural Content Generation. Procedural content Shaker, Shaker, and Togelius (2013) created Ropossum, a
generation (PCG) (Shaker, Togelius, and Nelson 2016) may level generator for Cut the Rope that takes into account de-
be defined as the process of automatically creating content signer input. Another such system, Sentient Sketchbook (Li-
using procedural or algorithmic techniques. Different types apis, Yannakakis, and Togelius 2013b), generates playable
of such methods—e.g. search-based techniques (Togelius levels from simple maps sketched out by a human designer.
et al. 2011) or constraint satisfaction (Smith and Mateas Baldwin et al. (2017) also described a mixed-initiative sys-
2011)—have found widespread use in the generation of a va- tem that uses game design patterns to create dungeons using
riety of game content, such as platformer levels (Snodgrass genetic algorithms. Our coin placement algorithm can con-
Inputs: The inputs to the coin placement algorithm are the number of coins to
place, grid cell definition, starting and ending locations, and list of player trajec-
tories from players who won the level.

Step 1: For each grid cell c = (xc , yc ), count the proportion wc of winning tra-
jectories that pass through that cell. Thus, if no winning trajectory went through
a cell, wc = 0 and if all winning trajectories went through a cell wc = 1.

Step 2: Find the lowest cost path through the grid (via A*) from the starting grid
cell to the ending grid cell. It is possible to move to any 8-connected neighbor,
|t−s|
and the cost to move from grid cell s to t is max(w t ,)
2 , where is some small

number.

Step 3: Place the required number of coins evenly spaced along the path.

Step 4: For each grid cell pi along the path, compute a priority value ri , using an
estimate of the local deviation from a straight line as ri = |pi − 0.5 ∗ (pi−1 +
pi+1 )|2 + |pi − 0.5 ∗ (pi−2 + pi+2 )|.

Step 5: Given a coin at pi , if ri+1 > ri and there is no coin at pi+1 or pi+2 ,
move the coin to pi+1 ; or if ri−1 > ri and there is no coin at pi−1 or pi−2 , move
the coin to pi−1 . Iterate through all coins, moving each if needed, until no coin
moves.

Outputs: The algorithm outputs a list of coin locations.

Figure 3: Steps in the coin placement algorithm. |v| denotes vector magnitude.
stitute a part of a mixed-initiative PCG system such as the An illustrated overview of the algorithm is shown in Fig-
ones above since the coin placement is automated while the ure 3. We used several heuristics to guide this coin place-
remainder of each level is hand-authored. ment. The main heuristic we used was:
• Coins should be on a single path through the level; the
Game and Recruitment path should have been traversed by successful players
(Steps 1 and 2). This is motivated by the work of An-
For this work, we used a platformer game we developed in dersen et al. (2011b).
Unity called Iowa James: Treasure Hunter (Figure 2). The
We used additional heuristics that were based on our subjec-
player controls an avatar that can move and jump. The goal is
tive experience from playing games with collectible coins.
to navigate a level to reach a treasure chest at the end. Upon
It is possible other heuristics could work just as well or bet-
reaching the chest, the player wins the level and moves on
ter (for example, simply placing coins randomly along the
to the next one. There are several types of hazards that can
path). We consider further study of such additional heuris-
be encountered along the way, including pits, spikes, timed
tics as future work.
retracting spikes, and moving spike balls. The player dies
upon touching a hazard and starts the current level over from • Coins should be well distributed throughout the level
the beginning. The player has unlimited lives, so the only (Step 3). This is motivated by making it more likely for
way to lose the game is to stop playing. players to have coins to collect all along the path through
The game has 14 levels that cover a variety of layouts and the level.
usually contain several ways to navigate from the start to • Coins should be clustered near curves and arcs in the path
the goal. The first level is meant to be a simple introductory (Steps 4 and 5). This is motived by the groupings of coins
level. If the player completes all the levels, they are taken in games such as Super Mario Bros.
to a game over screen. The game also features collectible To gather player trajectories, we ran a HIT that recruited
coins, which the player can collect by touching. Each level 200 participants through MTurk, of which 160 played the
contains 10 coins. A UI element displays how many coins game. The version of the game used to gather trajectories
out of the total possible the player has collected so far in had no coins or associated UI. In order to distribute plays
the level. If the player restarts a level due to encountering a across the levels, after the introductory level, the remaining
hazard, the coins they had collected so far remain collected. levels were served to players in a random order. In this HIT,
The coins do not have any effect on gameplay. we gathered trajectory data from players at high temporal
To recruit players, we posted Human Intelligence Tasks resolution (10 Hz) and filtered out winning trajectories with
(HITs) on Amazon Mechanical Turk (MTurk). Prior work missing events, as well as gaps within individual winning
has shown that players recruited through MTurk respond trajectories. For the introductory level, which was served to
similarly to game design experiments as volunteer players all players, we used 77 winning trajectories for coin place-
do (Sarkar and Cooper 2018). The HIT was titled Platformer ment. For the remaining levels, we used from 8 to 22 win-
Game with the description Play a platformer game! Run and ning trajectories for coin placement. The data from this HIT
jump to collect treasure at the end of each level! and paid was only used for coin placement, and was not used for the
$0.50. The HIT provided the payment code upfront, thus not evaluation described below.
requiring the game to be played at all for payment. Hence,
any time spent playing the game on the HIT could be consid- Experiment
ered voluntary. We found that three-quarters of people who
To evaluate different coin placement methods, we ran a sec-
accepted the HIT, went on to play the game, with the rest
ond HIT that recruited 1600 participants through MTurk, of
simply taking the payment and not playing. Before play-
which 1226 played the game. In the versions of the game
ing, players were given a short set of instructions on how to
used in this experiment, levels were served in a fixed or-
play. To ensure that the same information could be provided
der. To place levels in rough order of increasing difficulty,
across different versions of the game, there was no mention
the ordering was based on the player success rate from the
of coins in the HIT details or instructions.
previous HIT, with levels having lower success rates placed
later in the order.
Path Coin Placement Players were randomly assigned into one of four versions
The coin placement algorithm we developed generates coin of the game with different coin placement, based on the fol-
locations in a level based on winning player trajectories. The lowing conditions:
algorithm places coins based on grid cells; in this work, we • NONE: No coins were in the game. The coin count was
used a tile-based game and each tile was a grid cell. The hidden from the UI.
algorithm takes as inputs the number of coins to place, the • PATH: Coins were placed using the path coin placement
grid cell definition, starting and ending locations, and a list algorithm described above and depicted in Figure 3.
of player trajectories from players who won the level. Note • DSGN: Coins were placed manually by a game designer
that the algorithm does not know which grid cells are im- working with our research group. We asked the designer
passible to the player (although this could be incorporated), to place the coins wherever he wanted, as long as the
instead relying on player paths to determine where the player coins were reachable by the player. The designer spent
can go. The output is a list of coin locations. around 4 hours placing coins.
PATH DSGN RAND

Figure 4: Examples of coin placement for each method used in the experiment.

NONE PATH DSGN RAND 100
†
Levels Won 5a 4ab 4b c 3c NONE
80
Finish Rate (%) 8 10 6 6 PATH

Percentage of Players
Total Time (s) 224 216 226 174 DSGN
60
Per-Level Time (s)† 38a 37a 47b 41ab RAND

Total Coins† 38a 25b 26b 40
Per-Level Coins† 8a 6b 6b
20
Table 1: Summary of data and statistical analysis. Medi-
ans are given, except for Finish Rate. A significance level 0
of α = .05 was used. Daggers† show significant omnibus 1 2 3 4 5 6 7 8 9 10 11 12 13 14
tests. Superscriptsabc show significance groups in post-hoc Levels Won
tests; i.e, conditions that share a superscript were not sig-
Figure 5: Survival plot showing the percentage of play-
nificantly different. Significant comparisons had p < .001,
ers who won a given number of levels. Note that although
except for the post-hoc comparisons in Levels Won: NONE–
PATH and DSGN have the same median value for Levels
DSGN, p = .003, and RAND–PATH, p = .031, and Per-Level
Won, the distributions are different.
Time: NONE–DSGN, p = .009.

tion with no coins (NONE) in the analysis. A summary of the
• RAND: Coins were placed randomly in any cell that had at results of our analyses is given in Table 1. A survival plot for
least one winning trajectory pass through it. In this condi- Levels Won is shown in Figure 5.
tion, each player had the coins placed in different random
locations.
Examples of coins placed by each method for one level of
Discussion
the game are shown in Figure 4. Of the 1226 participants In terms of coin collection, we found that players collected
who played the game, 209 were randomly assigned to NONE, more coins in PATH than in DSGN and RAND. This makes
391 to PATH, 318 to DSGN and 308 to RAND. For each sense, as to collect all coins in this condition, players simply
player, we measured the following variables: had to follow the desire path. Since the desire path is meant
• Levels Won: The number of levels won by the player. to be a natural route in the level from the start to the goal,
• Finish Rate: 1 if the player finished the game (completed by following this path, players could collect all coins while
all 14 levels), else 0. Presented in Table 1 as percentage also progressing naturally toward the primary objective (i.e.
of players per condition who finished with value 1. the treasure chest) of the levels. In other words, players may
have naturally collected more coins on their way to the goal,
• Total Time: The total time the player spent playing the
or the coins along the desire path acted as a guide that play-
game, in seconds.
ers could follow to reach the goal. In the other conditions,
• Per-Level Time: The mean time the player spent playing players had to go off the desire paths to collect the coins.
each level attempted, in seconds. That is, DSGN and RAND required them to temporarily ig-
• Total Coins: The total number of coins collected by the nore the primary objective of moving towards the chest, to
player. achieve the secondary objective of collecting all coins.
• Per-Level Coins: The mean number of coins collected by Additionally, players spent more time playing each level
the player in each level attempted. in DSGN, than in NONE and PATH. This is likely because
For statistical analysis, data were not normally distributed DSGN required players to backtrack or take multiple paths
as determined by a Shapiro-Wilk normality test. We thus ran through a level to collect all coins, unlike PATH where the
an omnibus Kruskal-Wallis test for each variable, and if sig- coins were placed along the same desire path towards the
nificant, ran post-hoc pairwise Wilcoxon rank sum tests with goal or NONE where there were no coins to collect. Simi-
the Holm correction. For the variables looking at coins (Per- larly, we did not find a difference in time spent playing each
Level Coins and Total Coins), we did not include the condi- level between DSGN and RAND, possibly because randomly
placed coins might also require players to backtrack.
Our findings in relation to the platformer game studied
by Andersen et al. (2011b) are particularly interesting. If we
consider DSGN and RAND to have off-path coins and look at
levels won and time played, we only found that PATH out-
performed RAND in terms of levels won. A possible expla-
nation for this may be that the coin placement in DSGN and
RAND was not far enough off-path to have as large an im-
pact on gameplay. Similar to Andersen et al. (2011b), we
did not find significant differences between no coins (NONE)
and on-path coins (PATH). However, while they saw a gen-
eral trend upward for time played with on-path coins, we
saw a trend downward for time played and levels won. It is
possible that our game was too short, or the levels in our
game were simply not challenging enough for the players to
benefit from having a path of coins as a guide. This is partly
supported by the survival plot in Figure 5. Though for the
first 12 levels, more players keep playing in NONE than in Figure 6: Example of a shortcut found by players used in
PATH, for the last 2 levels, PATH’s survival rate catches up coin placement. Many players dropped in the gap between
with that of NONE. It is possible that if there were harder lev- the third and fourth platforms to bypass the designer’s in-
els beyond level 14, PATH would further overtake NONE in tended path through the level. Note that the two platforms
terms of survival rate. If true, this implies that a path of coins near the bottom move vertically and horizontally.
helps the player only if the levels are sufficiently hard. Ex-
ploring this is fertile ground for future work.
Based on our overall statistical results of player behavior,
the coin placement strategies appear to fall into two group- coins (such as “challenge” coins that are intentionally hard
ings, for which we did not find any significant differences. to collect), or other collectibles that impact gameplay (such
NONE and PATH did not show differences from each other, as powerups or extra lives). We also only looked at player
and DSGN and RAND did not show differences from each behavior and not subjective experience.
other. That is, discounting the fact that players could not col- The algorithm itself was guided by our own heuristics, but
lect coins when there were none, players in PATH behaved other heuristics may do better, possibly improving the im-
similarly to those in NONE, while players in DSGN behaved pact of coin placement. Our algorithm requires some play-
similarly to those in RAND. We note, however, that signifi- ers to win the level (although used as few as 8), which may
cance might have been found with a larger sample size. be a problem for especially difficult games, though in such
Overall, our findings imply that each of NONE, PATH, cases, it could be possible to use trajectories of players who
DSGN and RAND has its own benefits. Absent of other utili- make the most progress through the level in place of win-
ties, secondary objectives like collectibles do not necessarily ning trajectories. The algorithm does not incorporate losing
incentivize players to complete more levels and thus, in such trajectories or direction of player movement between cells,
cases, not having any collectibles in the level (i.e. NONE), if which may be useful (for example, to prevent a path from
possible given a game’s design constraints, is a reasonable being found between two neighboring cells that is actually
choice. However, if such items are desired, then placement impossible to move between).
strategy depends on the designer’s goals. If the primary pur- We noticed that in some cases our algorithm used ex-
pose of collectibles is to help players in completing the lev- treme “shortcuts” that players had discovered through the
els, then PATH is preferable whereas if the goal is to make level (e.g. the early drop in Figure 6). This is a natural re-
the player explore as much of the level as possible and spend sult of using desire paths, but if the designer does not prefer
more time in each level, at the risk of completing fewer lev- coins in such shortcuts, they could be moved afterwards, us-
els, then DSGN or RAND are suitable alternatives. ing the path placement as an initial suggestion of locations
for further manual refinement.
Conclusion
Finally, in this work we used player trajectories to gen-
In this paper, we introduced a desire path-inspired algorithm erate a single path for coin placement. Future work can ex-
that uses player trajectories to place coins in platformer lev- plore sampling multiple paths, based on player trajectories,
els, and studied how different placement methods affected to generate many possible coin paths through a level.
player behavior. We consider many avenues for future work.
In this work, we only looked at one game and game genre.
Future work could study other games and genres, including
2D top-down or puzzle and 3D games. We also examined Acknowledgements
a narrow design space: there were only 10 coins to place,
and only one type of coin, which had no impact on game- The authors would like to thank Liam Fratturo for the de-
play. Designers may want to place more coins, other types of signer coin placement, and the MTurk workers for playing.
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