(Image credit: Flickr user Simon Huggins)
The Effects of Temperature on the Outcome of Fair Dice
by Jason Zweiback, Photonics Division, General Atomics, San Diego , California
and Ken Wharton, Department of Physics, San Jose State University, San Jose, California
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.
Craps with a table. (Image credit: Flickr user Alan Kotok)
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).
[caption id="attachment_68855" align="alignleft" width="250" caption="Figure 1. CFOM plotted against temperature. Clearly there is an increase with increasing temperature."][/caption]
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.
[caption id="attachment_68856" align="alignright" width="250" caption="Figure 2. Temperature as a function of time of day."][/caption]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.
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.
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.
The Dope on Craps
A technical primer for the non-specialist
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?
Craps without a table. (Image credit: Flickr user Bernard Delmundo)
Craps without a table. (Image credit: Flickr user Bernard Delmundo)
_____________________This article is republished with permission from the July-August 2002 issue of the Annals of Improbable Research. You can download or purchase back issues of the magazine, or subscribe to receive future issues. Or get a subscription for someone as a gift!
Visit their website for more research that makes people LAUGH and then THINK.