Here in Mexico gambling is prohibited, yet we have casinos. To circumvent the prohibition, the casinos have some odd games, all of them computerized: a nice example is a roulette that operates with dice.
Because it is not operated by any human, it is not a gambling device, therefore, it can be used in a casino that is not a casino despite being a place where gamblers reunite to gamble.
This machine has a big roulette wheel, where four big dice roll to form the usual combinations. There are two green dice, a black die and a white die, all of them marked from one to six; the green dice are in charge of zero (both showing ones) and double zero (both showing sixes) while the black one is in charge of each of the six zones on the board, and the white one is in charge of each individual position within a zone. Thus, if the black die shows a two, the valid numbers will be from seven to twelve, and if the white die shows a five, the winning bet will be eleven.
The idea is that each roll will be totally random; however, with dice there are certain posibilities that are more probable than the rest. To calculate our odds, we first need to know what our chances are to obtain a certain value. Because we have two dice and there is no way we can obtain a zero or a one, those numbers aren’t calculated.
The lowest number is two, when you roll one and one. The highest number is twelve, when you roll six and six. Because we have two dice, each die with six faces, we have 36 combinations (six times six). The combinations are as follows:
| Two: 1 combination | 1+1 | 2.78% |
| Three: 2 combinations | 2+1, 1+2 | 5.56% |
| Four: 3 combinations | 2+2, 3+1, 1+3 | 8.33% |
| Five: 4 combinations | 4+1, 3+2, 2+3, 1+4 | 11.11% |
| Six: 5 combinations | 5+1, 4+2, 3+3, 2+4, 5+1 | 13.89% |
| Seven: 6 combinations | 6+1, 5+2, 4+3, 3+4, 2+5, 1+6 | 16.67% |
| Eight: 5 combinations | 6+2, 5+3, 4+4, 3+5, 2+6 | 13.89% |
| Nine: 4 combinations | 6+3, 5+4, 4+5, 3+6 | 11.11% |
| Ten: 3 combinations | 6+4, 5+5, 4+6 | 8.33% |
| Eleven: 2 combinations | 6+5, 5+6 | 5.56% |
| Twelve: 1 combination | 6+6 | 2.78% |
As you can see there is a bigger chance to get a seven in any given roll than any other number. Therefore, unlike a common roulette, there will be a better chance to get a seven, eleven, sixteen, twenty one, twenty six and thirty one. Given these odds, it seems obvious to bet to those numbers more often. But the obvious and common sense does not apply to gambling. It has been said, and often attributed to Albert Einstein, that the only way to win in roulette is to steal money from the table while the croupier isn’t looking. Let’s check the bets:
The biggest bet is a single. You choose a number, any number, and if the ball lands on that square (or the dice roll that combination) you win 36 to one. The next bet is a split, where you place your bet between two numbers, say 17 & 21 or 16 & 17. In this bet you win 17 to one. Then you can bet on a street, three numbers in any given row, as 16, 17 & 18 or 4, 5, & 6, paying 11 to one. Then you can bet a corner, four adjacent numbers like 32, 33, 35 & 36 or 16, 17, 19 & 20, paying 8 to one. Most games I’ve seen skip the first five and go directly to sixline, a full section, say 1 to 6 or 31 to 36, paying 5 to one. Then you bet to a third of the board (1 to 12, 13 to 14 or 25 to 36), paying 2 to one; and half the board (1 to 18 and 19 to 36), evens, odds, blacks and reds, each one paying one to one. Some casinos allows betting on zero and double zero.
The best bet being the hardest to achieve, you’re supposed to bet on the best numbers available. While on a common roulette the numbers are authentically random, we’ve seen that on dice roulettes there are better chances to roll sevens. So let’s simulate a little bit what happens in a casino. We will bet a buck in each number, and we will randomly roll the dice. On any random roll we have one chance in 38 (counting zero and double zero) or 37 (just counting zero) to win with our number. Because the bet is 36 to one, it does not matter what we do, in the long term we will lose at least one dollar for each 38 turns. The only way to win is to score each and every time the best bet, which is almost impossible. The story is a little bit different while playing with dice: zeroes and double zeroes makes you lose your money, while in a normal roulette your bet would be imprisoned and the roulette would be rolled a second time, or you may lose half your bet and change the number. With dice, you have a chance of 5.56% of losing the bet each hundred bets. Everything being equal,and betting to the sevens, you’re expected to win 11 times for each 100 rolls. You will risk 6 bucks, and you can expect a return of 30 bucks. Therefore, for each hundred rounds you bet 600 hundred bucks and win at least eleven times, so you’ll get 333 bucks back. Even if the game would not count 0 and 00, you can only hope to win 500 bucks for each 600 hundred bucks bet you wager. You can’t even fill your board with coins: that will automagically lose, because even if you win your losses will be bigger than your return.
Those ain’t good odds for you: casinos will always win. So what is your winning strategy in roulette? Just enjoy your game, place a limit on your losses and enjoy the buffet. There is no chance for you to win, but you’ll always have fun. And don’t fall for the gambler’s fallacy and don’t even, ever try the Martingale. We’ll have a nice chat about it next week.
See you next week, guise.
Dijo.
An atheist, a freethinker, an engineer, and a good man. He loves to write, but sucks at it. And, of course, English is not his mother tongue, but was learned as a second language.
