Roulette winning systems
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A substantial amount has been written about systems at Roulette, including some very interesting books, a selection of which are given in the Bibliography. My advice to the reader is that it is an undeniable mathematical certainty no system gives the player any extra chance of winning and some are positively lethal. Some of the more popular systems over the years are examined here.
Martingale
The basis of this system is that the player bets on “even money” chances and doubles his previous bet after a loss, which is based on the theory that he must eventually win. If wins and losses roughly alternated this would work, but occasionally the Roulette wheel produces a long string of Reds or Blacks (or whatever “even money” chance the player selects). Besides the house edge on zero (where half the players bet is taken), of 1.39%, increases the likelihood of such a sequence occurring. For example, if the player is unlucky enough to encounter a sequence of 12 losses, he would need to stake $2,048 on the next number. A run of 20 losses would mean him staking $524,288 on the next spin of the wheel. In most casinos, the limit for a bet on an even money chance at Roulette is about $500, but even at a casino such as The Horseshoe, in Las Vegas, which will accept practically any amount, the player would need an enormous capital to cover the longest adverse sequence he might meet.
Reverse martingale
Essentially here the player makes the bank play Martingale by leaving a bet on an even money stake until either the house limit is reached or he decides to “take his winnings.” For example, if he gets 12 consecutive wins on an even money chance, he will have $2,048. If he loses he starts again at $1.
There is no great capital risk, but the player will have to wait a very long time before he expects to win $2,000, by which time he will have spent more than that amount in original $1 stakes.
Labouchere
This is sometimes known as the cancellation method. The player writes 1,2,3, and 4 vertically on a piece of paper and stakes the total of the first and last numbers 1, 2, 3, 4.
If the first bet wins, he crosses off the 1 and 4 and stakes the sum of the remaining numbers, again 5 chips. Let us say this bet loses, he then adds a 6 to the end of the line and stakes the sum of the first and last digits, in this case 2 + 6 = 8. If this bet loses again, he adds the first and last numbers and this is his new stake. Every time he wins he crosses off two numbers, and when the line has been completely crossed out he will have a profit of ten units.
The problem with this method is very similar to the Martingale. When the player has a long series in which losses outnumber wins by a ratio of more than 2-1, the stakes escalate astronomically. A computer simulation of the system shows how the player could fare. All went well for the first few “days.” It was assumed that the player would place 60 bets per hour for 5 hours, following the system rigidly. For the first seventeen “days” the simulation went well, with the player winning amounts between $31 and $89. Then on the eighteenth “day” disaster struck when an unlucky run of losses forced the stakes up to the casino limits (which was set at $500 for the exercise).
To continue the players system, his next bet needed to be the sum of the first and last digits, $429+$87, or $516, but the limit at the table was $500. At this stage his losses are $860 and they had wiped out all his winnings (and more) from the first 17 days! The example given was not that surprising a sequence (with W standing for WIN and L for LOSS):WLWLLLWLLWLLWLLLWLLLWLLWLLWL LLWLLLWL.
This represented only 11 wins out of 36 spins, but such sequences do happen, and this example should be a salutary warning to all “systems” players who can get deeper and deeper into the mire by believing that they can beat the odds.
Reverse labouchere
A thoroughly entertaining read entitled Thirteen Against the Bank traces the development of this system in which the bank is forced to play the dangerous Labouchere System against itself in a casino in Monte Carlo. This sounds good, but again there is no mathematical justification for the system. The author of the book, Norman Leigh, claimed sequences occur in which one even-money chance predominates over the other and by accepting small losses the player would sooner or later have a winning run when the casino would get into trouble and the bank would be broken. The built-in advantage which the bank has means that the adverse run experienced by our “player” on the score sheet given is less likely to be experienced by the casino. An identical simulation was run with a table limit of $500 to see how long it would take to reach the limit. This time the player made small losses of between $46 and $121 every “day” for a week, but then on the eighth day, a tremendous sequence of wins broke the table and the player won more than $2,000 as his bets mushroomed toward the limit. However, 31 more “days” went by on which the player lost all his winnings and a lot more before the next “progression” occurred and the player again broke the table. By day 100 the player was losing $39 per day on average.
A simple system
All of the above systems have an inherent drawback; if your stakes escalate then the casino take is larger because it is a fixed percentage of the total amount bet at the table. The advice to the gambler wishing to play Roulette for entertainment is as follows:
- Only bet on “even-money chances” which offer the least edge for the house.
- In an American casino, Craps offers a much better return and should be preferred over Roulette.
- If your aim is entertainment, then keep your stakes constant. If you place 100 $5 bets, then over the evening you will be on average about $8.50 down and may well come out ahead.
- If your aim is to win a substantial sum, while minimizing the risk of losing significantly, your best policy is to increase your bet by 50% after a win and decrease it by 50% after a loss. Set yourself a target amount to win and stop if your reach that target. If you are lucky and you have significantly more wins than losses you will win a sizable amount; if unlucky most of your bets will be at the minimum stake.
*/ House % calculated on assumption that even money bets lose on 0 or 00 as in Las Vegas; in Atlantic City half the bets are returned and this reduces the house percentage to 2.63% /