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Gambling games can be divided
into two categories: games of chance, such as lotteries, keno, craps,
roulette, baccarat, bingo and slots; and games of skill, such as horse
race betting, sports betting, poker and blackjack. For example, playing
bingo requires perceptual and motor skills, but winning is purely a matter
of chance. In contrast, winning at poker is dependent on skills relative
to the other players. The number of skills involved and the long-term
prospects of financial return vary for each type of game. In Hold'em poker,
skilled players can make a decent living (Warren, 1996), but in poker
games played against the "house," such as Caribbean Stud Poker, players
cannot beat the house edge, regardless of how skilled they are (Cardoza,
1997). Players of games based on skill are more likely to be male, with
the exception of horse racing, and more likely to be younger (Kelly et
al., 2001).
The relationship between skill
and problem gambling is particular interesting. According to data on problem
gambling treatment collected in Ontario, just over 40% of gamblers in
treatment list a game of skill as their major area of concern (Rush &
Shaw-Moxam, in press). Several researchers have noted that problem gamblers
often have an inflated sense of their own skill (Gadboury & Ladouceur,
1989; Toneatto, Blitz-Miller, Calderwood, Dragonetti & Tsanos, 1997).
Are problem gamblers who play games of skill simply unskilled players?
An alternative view is that some of the "skilled" gamblers in treatment
might actually be skilled but not be as skilled as other players.
Books on how to gamble successfully
often portray games of skill as games in which the player has a chance
of winning in the long run (e.g., Warren, 1996; Patterson, 1990). However,
the mixed skills of gamblers playing these games affect the outcome for
every player. Against novices the first author (Nigel), can play a successful
game of poker, but against experienced players, he most often loses. The
second author (Barry) fairs somewhat better against good players. The
goal of this paper is to measure how skilled players affect the success
of less skilled players, so that the dynamics of a game of skill can be
understood.
Method
The goal of this paper is difficult
since it often takes thousands of games to accurately measure skill in
gambling. Furthermore, tracking enough gamblers for a sufficient amount
of time is time consuming and probably not possible (casinos don't like
people researching on their property). Consequently, this paper relies
upon simulations.
Two games are compared: roulette
(see Wong & Spector, 1996) and Hold'em poker (see Warren, 1996). One
hundred thousand simulations on both poker and roulette were conducted.
Conducting these simulations at exactly the same skill level is not particularly
realistic because players do improve (and sometimes get worse). However,
applied to the current moment in time, these simulations allow us to get
an accurate estimate of a player's level of skill and their expected financial
return.
Roulette is a game in which
a little ball is thrown around the edge of a spinning wheel. A player
places a bet on one of the 37 (or 38) numbered slots that they think the
ball will land on. There are many betting options available.
Hold'em poker is a popular
casino poker game where as many as 10 players can play at the same time.
Players play against each other while the dealer merely deals the cards
and handles the money. Each player is given two cards face down; the remaining
cards are community cards that are dealt face up in the middle of the
table. Players make their hands by creating the best five-card combination
of their own two cards and the community cards. There are four rounds
of betting. For the poker simulation, Wilson's Software Turbo Texas Hold'em
was used.
Turbo Texas Hold'em is an elaborate
program that allows players to teach themselves the game. In addition
to basic playing instructions, the game provides extensive statistics
on how players play as well as how the other characters play. The opponents
in this game are not random; they have programmed profiles that react
to the many specific poker situations that they might encounter. These
profiles are designed to match the types of players one might meet around
an average poker table — they have names that are amusing and relevant.
The game comes with 40 pre-designed
profiles. Player profiles can vary from "tight" (folds most hands) to
"loose" (stays in most hands) to "passive" (checks or calls, but rarely
bets or raises) to "aggressive" (often bets or raises). Specific types
of players such as "loose but aggressive," or "tight but passive" can
be selected, and opponents can learn how to counter their styles. Players
can also create their own characters. More to the point, players can set
up a line-up of characters and then run a high-speed simulation to determine
the long-term outcome of various strategic moves.
In the context of poker, an
operational definition of skilled play means that players adjust their
play to their position in the hands (i.e. Are they first or last to bet?);
they gauge the odds of making a particular hand compared to the size of
the pot (the "pot odds"); they try and figure out their opponents hands
by "tells" and betting patterns, and usually tend to play tight and aggressive,
but must occasionally vary their play by bluffing (loose) or checking
(passive) in order to avoid giving away their strength (see Warren, 1996,
for details).
Three simulation studies were
conducted.
Study 1
Poker
First, a line-up was constructed
using an average player, a player that was neither particularly good nor
bad, nor tight or loose — but fairly aggressive. This profile is
called Igor (by the company's software). To see the normal spread of scores
when only average-skilled players were involved, Igor was copied 10 times
into the line-up. That is, Igor played against nine other copies of Igor.
The game played was 10-20 Hold'em, where a blind bet (a forced bet for
the first two players) and the first and second rounds of betting are
in $10 increments, and the third and forth rounds ("turn" and "river")
are in $20 increments.
The "rake" is the casinos way
of making money. They take a percentage of each pot as profit or charge
a per hour fee. The rake in casino card rooms varies from 3% to 5%. We
selected 5%. The simulation data did not include the rake, so we had to
estimate the effect of the rake on each player's net balance, which was
based on the average size of pots and the number of pots won.
In real life, the rake is taken
off in fixed amounts (e.g., $1, $2, etc.) and is capped at a maximum (e.g.,
$4). Thus, sometimes the rake is more than 5%, while other times it is
less. In this simulation, the rake is an exact percentage from each hand.
This inaccuracy somewhat overestimates the size of the rake, but does
not otherwise affect any of the conclusions that we draw from the data.
Roulette
Roulette was much easier to
simulate than poker because there are few decisions to make. One of the
difficulties was to determine how to create a roulette simulation that
would produce the same range of scores as a poker game. To do this we
first conducted 100,000 simulations of poker and obtained from the program
the average investment per hand ($14.80) and average winning pot size
($86.40). It was then determined that the closest roulette bet to these
numbers was a $15 bet on a "six line" or "double street" that pays 6 for
1 (i.e. returns $90).
The double street is a group
of six numbers that are together on the betting table (e.g., 4, 5, 6,
7, 8, 9) but may be scattered around the wheel. The player wins if the
ball lands on any of these six numbers. Poker bets, however, vary from
zero to hundreds of dollars. To mimic this situation, the roulette bets
were varied from $0.50 to $30, averaging at $15. A rake of 5% on a poker
game would produce a house edge in poker of about 2.7%.
To get the equivalent edge
in roulette we used the parameters of the European wheel, (one zero),
which is available in Europe, Quebec and a small number of casinos in
Las Vegas and has a house edge of about 2.7%. These parameters were programmed
into a quick basic program similar to Turner's (1998), and then the simulation
was run.
Results
Figure 1 shows a comparison
of the two games. The poker range is similar, t(18) = .45, ns, but includes
both lower and higher scores due to the greater variability of the bets.
Since all 10 poker players were matched in skill, all of the variation
in their outcomes is random. That is, when a group of players are up against
players of equal ability, the net outcome is random, and in the long run,
only the casino wins.
(click
figure for larger image)
Study 2
A second poker simulation was
conducted where two more skilled poker players were introduced: (1) Tricky
Dicky, a tight player who "slow" plays (i.e. checks acting as if he has
a poor hand then raises, a strategy that is particularly effective against
loose players), and (2) Advisor T., who plays "pump it or dump it" (i.e.
if the hand isn't good enough to raise, he folds it, which is effective
against tight players). Both of these players are tight, but they vary
their strategy depending on circumstances. The roulette data is the same
as the first simulation since skilled roulette play is not really possible.
For comparison, additional
simulations for poker were conducted where the number of skilled players
varied from 20% to 80%. Simulations were also run where even fewer skilled
players were added to the mix.
Results
Figure 2 shows a comparison
of the two games. The poker range is now very different from the roulette
range. The two skilled players have scored large wins, while the remaining
eight average-skilled players ("Igors") have racked up large losses. Since
the eight average players were matched in skill, all of the variation
between them is random. However, the difference between the average-skilled
players and the two skilled players is not random but due to the superior
playing ability of the two skilled players. What this simulation shows
is that when skilled players are introduced into the mix, the average
player may be better off playing a game of chance (e.g., roulette) than
a game of skill, t(16) = 3.3, p<.01. As noted below, the actual outcome
depends on a number of factors including the mix of players.
(click
figure for larger image)
Interestingly, the skilled
players did not come out ahead because they won more often. On the contrary,
the skilled players won between 8,605 and 9,271 pots, while the eight
average-skilled players won between 10,216 and 10,638 pots each. This
illustrates an important rule in poker: skilled poker players are more
selective, and therefore, enter fewer pots. They win less often, but are
more likely to win the pots that they do enter. Average-skilled players
tend to pursue more hands, and therefore, lose more when they do lose.
On average, these poker players
played against an expected return (house edge) of -2.69%; however, when
playing against skilled players the average return was -3.1% for the Igors,
which is a relatively small house edge. The skilled players achieved an
average return of +1.35%, approximately the same advantage card counters
can achieve in blackjack.
Figure 3 shows the effect of
adding additional skilled players to the game. When playing against eight
skilled players, the expected return drops steadily for the average-skilled
players to -7%. Interestingly, the expected return also drops for the
skilled players, because they are playing against each other. In fact,
according to this analysis, skilled poker players only have a positive
expectation if the majority of their opponents are less skilled. If the
final two Igors were replaced with skilled players, the outcome for the
skilled players would be random — identical to the results of the
first stimulation in which all players were of average ability.
(click
figure for larger image)
As stated earlier, the profile/character
used to represent an average player, Igor, was not a particularly bad
player, just a little too loose and aggressive. Other profiles representing
players that were much too loose, too tight, too aggressive or too passive
were also tried. For example, when a very loose player and a very tight
player were played against the Igors, the Igors had an average return
of +1.6%. The very loose player, G.A. Joe, achieved an average return
of -22.3%, and the very tight player, Crusty Jack, played at a return
of -10.1%. Against average players, these two particularly weak players
played with an expected return that was worse than most slot machines.
Alternatively, if Igor played against both weaker players and more skilled
players, he tended to break even, more or less (+0.05%).
The point is that the outcome
of play depends on the mix of players present; against equally matched
players, the game results are random and have a return that is about the
same as European roulette and somewhat better than most slots machines.
However, against more skilled players, the player disadvantage for weak
players can be extremely great. It should be noted that even though many
average-skilled players face a negative return, they often do not have
a gambling problem. They often play poker just to enjoy the game.
Study 3
A final simulation was conducted
to illustrate that these findings are not restricted to poker but also
apply to sports betting and other skills-based games. In sports betting
the house edge averages at around 4.55%, and this is accomplished by a
9.09% vigorish or commission charged on all wins (see www.professionalgambler.com/vigorish.html
for more information). For example, if an $11 bet is made, it pays $21
for a win (a bet of $11 plus a $10 win). The extra $1 is the commission.
The bookie sets a "line" for
the teams that turn the sport game into a situation where the player has
a 50% chance of winning. For example, if the line says that the Yankees
will win by one and a half runs, then a player only wins the bet if the
Yankees score two runs (more than another team). If the bookie places
the line with 100% accuracy, the game is random; but since bookies are
only human, there is usually some opportunity to win. In addition, a bookie
sometimes has to shift the line to encourage bets on an underdog that
isn't getting enough action. A skilled player has to out-think both the
bookies and the other players and look for opportunities.
A relatively simply program
was constructed to examine this situation. In this simulation, a situation
was set up where all players had an equal chance of winning. The next
simulation was conducted in which 20%, 40% or 60% of the players were
5% more likely to guess the winning team than the less skilled players;
but the line was adjusted to maintain the 4.55% overall house edge. This
program does not really take into account the skill of the bookie. But
the skills of the bookie would simply add more random variation to the
data and would not otherwise affect the results.
Results
Figure 4 illustrates what happens
to the expected return of the less skilled bettors as the number of skilled
bettors is increased. The results are nearly identical to the results
obtained in the poker simulation.
(click
figure for larger image)
Discussion
The results of this study illustrate
two important aspects of playing a game of skill. Firstly, if all players
are equally matched in skill, the outcome is random. Secondly, if highly
skilled players are introduced into a game, the less skilled players are
more likely to lose. These rules also apply to horse racing, sports betting
and stock market investing. In each case, players can only make money
if they have better information and strategies than other players do.
If the information is shared and the strategies are the same, the outcome
is random. Andrew Beyer (1983) describes how "speed handicapping" is no
longer a sure-fire moneymaker. He states, "If [speed figures] have become
somewhat less profitable than they used to be, it is only because so many
bettors have discovered what a wonderful device they are (pg. 88)."
In sports and horse betting,
players do not play directly against each other; a player's level of skill
affects other players because pay-out odds in horse racing or the "line"
in sports are adjusted based on the bets of other gamblers. A player's
skill level is also affected by the skill of his or her bookie; a particularly
good bookie will leave fewer opportunities for the astute player. Only
those players who take the time to rationally evaluate all the information
available, watch the races or games for subtle clues, look for games where
the bookies and other bettors have underestimated horses' or teams' abilities
can get an edge. "Trip handicapping" (Beyer, 1983) can help, but knowing
that a second place horse from two weeks ago lost because it was "parked"
in the fifth path around the last turn, and that its speed figures are
underestimated, requires prodigious study and observation.
If all of the players are using
the same information, no one can achieve any real long-term edge, and
like roulette, in the long term, only the house (e.g., bookie, broker,
casino) wins. However, some highly skilled players often have more information,
and as a result, the average-skilled player in each of these games can
be at a tremendous disadvantage.
Blackjack is perhaps the only
game where skilled players do not immediately hurt the short-term success
of less skilled players. However, the successes of card counters forced
the casinos to change the rules and made it harder to win at blackjack
(see Patterson, 1990; Thorpe, 1962).
In interviews with poker players,
Horbay and Fritz (1998) found that poker players in treatment for gambling
problems over-emphasized the luck element and under-emphasized the skill
element. Successful skilled players (those that do not have a gambling
problem), on the other hand, emphasized the skill factor — they see
luck as having a minimal role.
Books by skilled gamblers (e.g.,
Warren, 1996) stress the importance of understanding the short-term influence
of luck in contrast to the long-term influence of skill. This idea is
key to both retaining emotional control during bad beats (e.g., losing
what should have been a sure win) and keeping weaker players in the game.
However, even players with problems do possess some skill. According to
Browne (1989), many players have periods of problem ("tilt") and non-problematic
play.
Are problem gamblers simply
players who have a poor level of skill? Do they all suffer from false
beliefs about their abilities? According to the data presented here, a
person could be reasonably good, and yet, in the long term, still lose
money. A problem gambling counsellor might conclude that a problem gambler
has a distorted belief about his or her own skill, but the reality may
be subtler. Moderately skilled gamblers may be caught in a rather odd
net — they might know that they are above average players, and yet,
may still lose money in spite of winning more often than not.
The counsellor may find that
a slightly different approach is needed for such clients. Telling them,
for example, that they cannot win because winning is random, would not
sit well with clients who know they have the skills. Their self-appraisal
may be, in fact, reasonably accurate. But they may not realize just how
skilled they would have to be to beat the house edge and the edge of other
players (especially in horse racing). However, if they focus instead on
how the house rake and better players take their cuts, this may lead to
an understanding. The point is that a counsellor should consider the game
that a player frequents, and in the case of skilled games, help players
understand how even skilled play does not guarantee winning in the long
run.
There are a number of limitations
to this study. In this simulation, skill was defined in terms of card
playing skills (probabilities, pot odds and the ability to apply strategies).
In real life, emotional upsets, fatigue and other psychological states
also affect the outcome of a game of skill. The ability to read the non-verbal
cues of other players while masking their own is also an important factor
for skilled players. This simulation does not take into account these
specific kinds of skills; however, for the purpose of the simulation,
the specific type of skill doesn't really matter. What matters is the
difference in skill between one group of players and another. Another
limitation is that this simulation treats the two groups — skilled
and less skilled — as if they were distinct. In reality, skills vary
continuously between individuals. It is unlikely that a table exists where
all players are matched in terms of skill.
In addition, the behaviour
of the individuals in this simulation are fixed, whereas the behaviour
of real players vary considerably. Real players with mediocre skills may
become more skilled, drop out of play, play well on one occasion, or get
too emotionally involved in a game on another occasion and play badly.
The goal of this simulation
is not to show how an unskilled player would fair over the course of his
or her life. Instead, the goal is to make a realistic estimate of their
expected return (probable long-term outcomes over three years), given
their current level of skill, and the mix of skilled and less skilled
players at the table. The actual results would only apply to individuals
who continued to play against skilled players without improving their
own skills. These results, however, are consistent with observations of
a player in treatment for poker related gambling problems (Horbay &
Fritz, 1998), who lost $40,000 over a three-year period.
Part of the allure of poker
and other games of skill is that players feel they can win in the long
term. The results of this study show that this belief is often illusory,
especially if the other players are more skilled. In a game of skill,
the less skilled players can be at a greater disadvantage since they are
playing against both the house edge (the rake) and the skilled players'
edge. It should be noted that many social players who play for fun rather
than money are unlikely to develop gambling problems, even if the odds
are stacked against them.
However, consider the plight
of the average horse race bettor. The house edge at the track is at least
17% (see Beyer, 1983) and actually higher for some of the more exotic
bets (e.g., exactas). Apparently, there are horse bettors who win and
have a positive expected return (see Beyer, 1983). This means that the
remaining horse bettors are not only up against a 17% house take but also
contribute to the 1% or 2% positive return that the expert horse bettors
take home. If 10% of the horse bettors are bringing home a positive return
of 1%, then the average loss of the remaining players has to drop to around
-19% to accommodate this 1% profit. Up against 17%, it would take a fair
amount of skill to achieve a return of -10%. This explains why even very
skilled horse bettors may end up losing money. Today, perhaps only 1%
or 2% of horse bettors make money. Consequently, when a player from a
game of skill reports losing consistently, it does not necessarily indicate
a lack of ability, but rather that the player has played against the house
edge and the edge of more highly skilled players.
This study also has implications
for prevention. The types of simulations used in this paper may have a
practical application. Showing gamblers how dismal their long-term prospects
are may facilitate a re-evaluation of gambling as an activity. Simulations
could be used to teach various games as a form of harm reduction. Finally,
simulations could also be used to correct such erroneous expectations
as the belief that one is due to win.
In summary, this paper shows
that an unskilled player is sometimes financially better off in a game
of chance than in a game of skill. However, it should be noted that many
people play poker not because they expect to make a fortune but because
they enjoy playing the game. As long as there are no serious financial
consequences, they will continue to play even though they may lose less
money at games of chance.
References
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Houghton Mifflin company.
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3–21.
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R. (1989).
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B. (1998, June).
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gambling in poker players. Paper presented at the 12th Annul Conference
of the National Council on Problem Gambling, Las Vegas, Nevada.
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Turner, N., Noonan, G., Wiebe, J. & Falkowski-Ham, A. (2001, April).
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Presentation given at the Conference of the Canadian Foundation on Compulsive
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Handbook. New York: Perigee Books.
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R. (in press).
- Treatment of Problem
Gambling in Ontario: Service Utilization and Client Characteristics.
Toronto: Centre for Addiction and Mental Health.
- Thorpe, E.O. (1962).
- Beat the Dealer: A Winning
Strategy for the Game of Twenty-one. New York: Vintage Books.
- Toneatto, T., Blitz-Miller,
T., Calderwood, K., Dragonetti, R. & Tsanos, A. (1997).
- Cognitive distortions in
heavy gambling. Journal of Gambling Studies, 13(2), 253–266.
- Turner, N.E. (1998).
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as strategies for gambling. Journal of Gambling Studies, 14(4),
413–429.
- Warren, K. (1996).
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This article was peer-reviewed.
Submitted: November 2,
2000
Accepted: August 17, 2001
For correspondence:
Nigel Turner,
PhD
Scientist
Centre for Addiction and Mental Health
33 Russell Street,
Toronto, Ontario, Canada M5S 2S1
Phone: (416) 535-8501 Ext. 6063
Fax: (416) 595-6899
Nigel_Turner@camh.net
Nigel Turner received
his doctorate in cognitive psychology from the University of Western
Ontario in 1995. He has worked at the Addiction Research Division of
the Centre for Addiction and Mental Health for the past five years where
he has developed psychometric tools to measure addiction processes.
He is currently focused on understanding the mental processes related
to gambling addiction. He has extensive experience in various research
methods including psychometrics, surveys, experimental studies, computer
simulations, interviews and focus groups. He has published numerous
papers in peer-reviewed journals, including three on problem gambling,
and he has made many conference presentations.
Barry Fritz is
professor of Psychology at Quinnipiac University, Hamden, Connecticut.
He is a member of the board of the Connecticut Council on Problem Gambling.
He graduated with a BA from the University of Vermont, an MA from Connecticut
College, and a PhD from Yeshiva University.
"My current research interests
are focused on understanding the motivation to gamble and those factors
which differentiate between problem gamblers and recreational gamblers.
I enjoy the game of poker and hope that my research will keep me on
the recreational side of the table."
Other research articles in
this issue
Internet
Gambling: Preliminary Results of the First U.K. Prevalence Study
Internet
Gambling Among Ontario Adults
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