The Search for a Hot Craps Table
The Effects of Temperature on the Outcome of Fair Dice
Craps with a table.
We here report the first direct scientific test of the concept of a hot
craps table.
Craps is a game with a long history. For over a century players the likes of Sky Masterson, Big Julie, and Nicely Nicely have been performing the technical procedure known as "rolling the bones." Time has replaced the hood- and shark-infested dens of the past with modern casinos. This has given craps a level of respectability. The respectability is well deserved, because as games of chance go, craps is actually not a bad deal.
The accompanying box (see "The Dope on Craps," below) gives a
succinct description for scientists outside our field of study.
After reading many books on the topic, we have come up with a scientifically
testable hypothesis. It is a fact that nearly every craps textbook refers
to the crucial difference between a "cold" table and a "hot"
table.1,2 Brisman clearly states, "Every veteran dice player will warn
you about "cold" tables where the dice only allow for craps and
sevening out."2 Conversely, a hot table has the shooters consistently
successful in making their points. Most of the reported craps strategies
involve methods of determining whether or not a craps table is "hot"
or "cold." These various "methods" are remarkably unscientific
and obviously flawed. This is particularly surprising given that there is
a perfectly straightforward, well established technique to determine "hot"
from "cold." Of course, we refer to the science of thermometry.
With this technique in mind, we set out to determine if temperature has
any effect on the outcome of dice.
Experimental Method
Since there were no local research laboratories we had to move our experiment
to an offsite location, namely the Las Vegas Strip. At the experimental
site we selected craps tables using a two-stage random walk technique, randomly
choosing both the casino and the craps table within. (In order to truly
randomize the process, our "lead" scientist voluntarily ingested
1000 ml of carbonated liquid mixed with 100 ml of ethanol before beginning
the random walk.)
Initial attempts to take direct temperature measurements of the table and
dice were met with failure (casino security) and hence it was deemed that
the temperature of the air surrounding the table would be sufficient. A
digital thermometer (in a watch) was carried throughout the trip. We would
approach a table and note the temperature. Then we would measure the CFOM
(craps figure of merit). We defined the CFOM as the total number of rolls
for 5 shooters. This quantity reflects the number of points made as well
as the number of "good" rolls before sevening out. Finally, after
the 5th shooter had sevened-out, the temperature was checked again. The
two temperature measurements were then averaged. This process was repeated
for several tables and casinos, effectively scanning the so-called CPS (craps
phase space).
Figure 1. CFOM plotted against temperature. Clearly there is an increase with increasing temperature.
Results
Figure 1 shows the CFOM plotted against the temperature of the area immediately
surrounding the table. There is a clear trend of higher CFOM with higher
temperature, confirming our initial hypothesis. A linear fit shows excellent
agreement with these data lending further credence to the result.
Craps lore states that the best time to play is in the middle of the night.
This contradicts common sense. One would expect that the table would be
"hottest" in the mid-afternoon when the ambient temperature reaches
a maximum. However, knowing that most casinos are strictly temperature-regulated,
we performed a series of measurements at a craps table over 24 hours. The
results are shown in Figure 2, and indicate that the highest temperature
is reached in the middle of the night. The thermostat is presumably raised
slightly when it is cooler outside, possibly some form of overcompensation
by the casino. Taken together with Figure 1, this data clearly indicates
that craps lore is, in fact, correct.
We also took it upon ourselves to study another piece of craps lore. It
is believed by all we spoke to that a table with no one playing at it is
inherently "cold." One must wait until some people have gone over
to the table to "warm it up," or else one is certain to lose.
One of the authors (KW) was determined to prove this wrong. We entered the
casino and purposely chose a craps table without any players. We were even
bold enough to announce our plan to the dealers and stickman at the table.
Together, we lost about $200 in 15 minutes, proving to our satisfaction
that the historical lore was again correct.
Figure 2. Temperature as a function of time of day.
Further analysis explains this phenomenon. The average human being is about
the equivalent of a 100 W heater. A craps table with 10 people around it
will therefore have approximately 1 kW of excess heat being radiated into
the air. For a relevant air volume of 4 m3 (5kg), a specific heat of air
equal to 1000 J/kg-oC, and a thermal diffusivity of air equal to 2.4 10-5
m2/s, one finds that it will take approximately 15 minutes for 10 people
to warm the air by 1 oC, thereby changing it from a cold to a hot table.
We want to emphatically restate that one should never to go to an empty
craps table.
As a final test of our hypothesis we requested that the casino turn the
temperature in the casino up to 100oF. This got us escorted out of the building.
We have obviously stumbled onto something that casino management does not
want us to know about.
Conclusions
While the precise mechanism of the thermal effects is still open to explanation, temperature has a clear effect on the outcome of a craps game.
The terms "hot" and "cold" are probably from observations
(conscious or subconscious) made by early craps players. Over the years
the original meaning has been forgotten, but the terms have stayed as part
of the lore surrounding the game.
As a result of this research, we now know basic principles:
1. The best time to play craps is in the late night; and
2) You should never go over to an empty craps table.
We encourage other researchers to study the lore surrounding other games
of chance to find previously observed, but now-forgotten truths.
The authors are currently seeking funding to continue these studies. Fortunately,
given our now-proven system, we only need to borrow the money for a little
while, and it should be paid back within the week, along with a large portion
of our winnings. Any interested funding bodies (or investment houses) should
get in touch with us as soon as possible.
References
1. Forever
Craps, F. Scoblete, Bonus Books, Chicago, 2000.
2. American
Mensa Guide to Casino Gambling, A. Brisman, Sterling Publishing,
New York, 1999, p. 140.
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The Dope on Craps
A technical primer for the non-specialist
Craps without a table.
Craps is a simple game. The standard pass line bet has a house take of a mere 1.41% (i.e., the house takes 1.41 cents for every dollar wagered). The bet pays out 1 to 1 if a 7 or 11 are thrown on the first, or "come out" roll. The bet is lost if a 2,3, or 12 are thrown. If any other number comes up, that number becomes "the point." The bet will now pay out (1 to 1) if "the point" number is rolled again before the shooter "sevens out" (rolls a seven). An odds bet (which actually pays true odds) can be placed down after a point number (4, 5, 6, 8, 9, 10 for those not paying attention) has been thrown on a come-out roll. The odds bet further lowers the house take on the overall bet to less than 1%. The size of the maximum odds bet varies with the casino. The authors have seen 100x odds (i.e., the maximum odds bet can be 100 times the pass line bet), lowering the house take to only 0.02%. With such a pittance of a house take, this game seems like a gambler’s dream. The authors have spent much time at the tables with the idea of enjoying the exceptionally small amount of funds that would have to be given to the house. But after much field research, our experimental efforts began to converge on one fundamental question: Why is it that we keep losing all of our money?
© Copyright 2002 Annals of Improbable Research (AIR)
This HotAIR feature first appeared in AIR VOLUME
8-ISSUE 4. For a complete list of strangely fascinating featured articles
elsewhere on this web site, see What's New.