However, Small warned that roulette "is a game of chance. Even if the odds are in your favor, there is still a probability of losing, and losing big. In the long run you would come out ahead but you may first need very deep pockets."
And Small also has some advice for casino owners.
"Train the croupiers to spin the ball when they release it, and make sure that the tables are level and the air conditioning is working," Small said, to allow for any influence of air resistance.
Small insists that his interest in gambling is purely theoretical. He has broken even in casinos by refusing to gamble there.
"Drilling the pips...gives the symmetry in the die but symmetry is not enough" to make it random, he said. "[The] top face will always be more probable."
If not random, is the die roll chaotic--the popular concept that originated in the second half of the 20th century, in which small differences in starting conditions can lead to large differences in end results? The most common example is the hypothetical picture of a butterfly flapping its wings in South America changing air circulation patterns to influence the weather halfway around the globe. The end result is knowable only if you have precise knowledge of the starting conditions of the world's weather.
A die roll is chaotic only if it bounces on the table an infinite number of times, according to Kapitaniak. But this is far from attainable, due to the fact that the die loses energy with each bounce due to friction.
With the high-speed camera images and the new theoretical treatment, this paper provides a new contribution to the question of the true randomness of dice throws and coin tosses. It contributes to an increasingly sophisticated understanding of what can be considered fully random in everyday life.
And in a more practical vein, if you're playing Dungeons and Dragons tonight, it probably wouldn't hurt to start your roll with the coveted 20 on top--it may occasionally give you the desired results, while Dungeon Masters could insist on playing on the roughest, highest-friction table they can find.
Be sure you know the bet requirements at a particular slot machine or table game before you sit down. On slots or video poker, the denomination is either painted on the machine's glass or displayed on a video screen. You've probably heard of "comps" in a casino. Maybe you saw a casino manager use the word in a movie to pacify an upset guest at his hotel, but did you really understand what the word meant? Also, tipping is an awkward subject no matter what situation you are in, but do you have to tip in a casino? Aren't they getting enough of your money already? Well, you've come to the right place. Read on to learn about both of these casino conundrums.
Casino "Comps"
Casinos want to keep their best customers coming back. Players who have shown they will give the house a shot at their money are treated like royalty. Free beverages for customers while they are playing, discounted rates on hotel rooms, and free meals are the most common complimentaries given by casinos. For high-rollers -- people who bet hundreds of dollars a hand -- the casino might give free airfare, room, food, beverages, or limousine service.
"Comps" are most frequently distributed through player rewards clubs. Members are issued credit-card-sized plastic cards, usually with an encoded magnetic strip on the back. The card is inserted into a magnetic reader on the machine the member is playing, and the amount and duration of play are tracked via computer.
In most player rewards clubs, players earn points for play and can redeem the points for comps. When the card is inserted into a reader at a slot or video poker machine, a display on the reader might say something like, "Welcome, member. You have 42 points. Coins to next point: 24." After the required number of coins have been played, another point will be added to the player's total. A list is issued detailing the comps available for various point totals. Some clubs allow players to redeem points for cash; others offer meals, rooms, or merchandise.
Other slot clubs don't issue a point table but require the player to ask an attendant at the player rewards club booth. The attendant will check the computer, and if the player qualifies, the attendant will issue the comp.
Comps work similarly at table games. At most casinos a player may use the same card issued to slot club members as identification to be rated for comps at table games. The pit boss overseeing the table takes note of the player's buy-in (the amount of currency exchanged for chips at the table), the average bet size, and the duration of play.
It's common for casinos to kick back in the form of comps an average of 10 percent to 40 percent of the amount it expects to win from the player.
The basic formula for the player's expected loss combines the amount of time played, the number of hands per hour, the average bet, and the house percentage. So if a blackjack player bets $5 a hand for an hour at a busy-table speed of 60 hands per hour, and the house figures it has a 2 percent edge, then the player is betting $300 per hour, and the house, on the average expects to win $6, or 2 percent of $300. If the house is issuing comps at a generous rate of 40 percent of the player's expected loss, the customer's play for an hour is worth about $2.40 in comps, regardless of the actual win or loss, whether he's won $50 or lost $50.
A side benefit of being rated for comps is that the casino puts you on its mailing list for special offers. Rated players frequently get free or discounted rooms and tournament invitations from casinos. Cash vouchers by mail are an often-used incentive for players to return.
Tipping Dealers