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The Cancellation Betting System
Introduction
I make an effort to communicate effectively that all of these systems, including the cancellation technique, are largely deceptive; however, my audience persistently requests recommendations for one. Any betting strategy can influence the likelihood of a successful gaming session, but it invariably comes at the expense of potential losses in an unsuccessful session. Ultimately, there is a fundamental reality that the ratio of funds lost in relation to funds wagered will consistently head toward a specific constant. This ratio is game-dependent, yet it invariably equals the betting systems While not endorsing gambling techniques, but rather aiming to protect individuals from fraudulent schemes that sell dubious systems, I would like to explain what is referred to as the cancellation system. Also known as the Labouchere, this approach bears similarities to most gambling strategies by exchanging a few significant losses for numerous minor wins. Some players enjoy a spontaneous approach at the gaming table, while others favor a more structured method. This explanation addresses the latter group. house advantage .
A viewer of this web page introduced me to the 'cancellation system' after expressing strong faith in it and seeking my perspective. Later, I encountered a discussion about it in the book The Winner's Guide to Casino Gambling by Edwin Silberstang. The principle behind this strategy posits that, over time, two events with similar probabilities will occur approximately the same number of times. However, this system relies on this assumption holding true in the short term. The more capital you wager, the longer you can extend into the long run, thereby improving your chances of a winning session, albeit with the risk of incurring greater losses.
How to Play
The primary objective of this strategy is to achieve a predetermined target of units in a fair game, such as betting on red or black in roulette, or the pass and don't pass options in craps. Players must determine the value of a single unit and how many units they are willing to risk. The total amount at stake for a given session will be referred to as the 'bankroll.' For illustration, let's assume the target is to win ten units. Below are detailed instructions on how to apply this system:
Begin by writing down ten 1s sequentially (1 1 1 1 1 1 1 1 1 1) on a sheet of paper. Each figure represents one unit for betting. When all the figures have been crossed off, you will have achieved a win of 10 units.
For each wager, place a bet equal to the sum of the number on the left and the number on the right, unless only a single numeral remains, in which case you wager that one.
In the event of a loss, append the sum to the end of the right side.
If you win cross off both numbers.
If the bankroll you established at the start is insufficient to cover the combined total of the left and right numbers, then:
If your bankroll can afford the left number, proceed to wager that. Winning means you cross off the left number; losing requires you to add the loss to the left number.
If your bankroll cannot accommodate the left number, bet all that remains in your bankroll. If you win, reduce the left number by your winnings. A loss results in depleting your bankroll, necessitating your exit from the table.
Continue following these procedures until either all numbers have been crossed off or your initially designated bankroll is exhausted.
- You then place a bet of two units and win, crossing off the 1s on both the left and right, resulting in 1 1 1 1 1 1 1 1.
Here is an example:
- You start with 1 1 1 1 1 1 1 1 1 1.
- You then make another two-unit wager but lose, adding a 2 to the right, resulting in 1 1 1 1 1 1 1 1 2.
- You then bet three units (1+2) and lose once more, appending a 3 on the right, culminating in 1 1 1 1 1 1 1 1 2 3.
- You then risk four units (1+3) and achieve a win, crossing off the 1 on the left and the 3 on the right, leaving you with 1 1 1 1 1 1 1 2.
- Here is a scenario outlining what to do if you're nearing your bankroll limit:
You have the numbers 10 11 12 13 14 15. Your bankroll only holds 20 units.
- Since you don’t possess the necessary 25 units (10+15), you can only wager the leftmost number, which is 10, and succeed, resulting in 11 12 13 14 15.
- Your bankroll now has 30 units, adequate to cover 26 (11+15), but you lose, resulting in 11 12 13 14 15 26.
- Your bankroll now has dwindled to just 4, which isn't sufficient to cover the left number, so you wager all 4 and win, deducting 4 from the 11, leading to 7 12 13 14 15 26.
- With your bankroll now at 8, you bet the leftmost number, 7, and unfortunately lose, adding the loss to the left number, yielding 14 12 13 14 15 26.
- Now your bankroll stands at just 1. You bet that and lose, resulting in 15 12 13 14 16 26.
- At this point, your bankroll is depleted, and you must exit the game. The total of all remaining numbers will equal your initial sum of 10 plus the amount of your exhausted bankroll.
- The theory suggests that by removing two numbers for each win while only adding one for every loss, you will ultimately cross off all numbers. However, during a stretch of losses, those numbers can accumulate rapidly, potentially draining your bankroll more swiftly than expected. The greater the amount you risk, the higher the likelihood of eliminating all numbers. Nevertheless, the final outcome will essentially be either winning ten units or losing your entire bankroll. You have the flexibility to adapt your strategy at any time, starting with more or fewer numbers if desired. The higher the initial numbers, the greater the potential reward, but also the increased risk of your bankroll's depletion. The individual who shared this system with me mentioned that when approaching the limits of his bankroll, he would often opt to divide the numbers in half and play each set separately. While most gambling systems insist on strict adherence to their methods, modifying your approach won’t significantly alter your long-term results. The book The Winner’s Guide to Casino Gambling discusses that any numbers can be employed, yet the most frequently used format is sequential numbers, such as 1 2 3 4 5. Gambling systems should enhance the enjoyment of the experience rather than influence the long-term outcomes, so feel free to make any adjustments you wish.
The bankroll consists of units, and it is up to you to determine the value of a single unit. For instance, if you're willing to risk $100, you might decide that each unit is worth $2, creating a bankroll of 50 units. If you utilize this system in craps, your chances of winning 10 units (or $20) sit at 81.4%, with an 18.6% chance of losing your full bankroll of 50 units (or $100).Numerous systems draw from the principles contained within this strategy. Rather than squandering your money purchasing a system, you can take advantage of this one and redirect the funds saved into enjoying entertainment. Should you engage with this system or any other, I wish you the best of luck, but do not expect to consistently profit over time.It's important to recognize that this system can be adjusted for any number of initial figures, and they need not all be ones. However, at the end of the day, regardless of how a player chooses to operate within this system, they cannot surmount the house edge nor even minimally affect it.
Probability of Losing
To test this strategy I wrote a computer program to perform ten million sessions at various bankrolls on both roulette and craps. When applied to craps the bet was on the pass line which pays even money and has a probability of winning any given trial of 244/495 = 49.29%. In roulette the basic bet is any even money bet, which has a probability of winning of 47.37%. Naturally it is to the players advantage to apply this strategy, as well as any other, to craps as opposed to roulette. As with any betting system the ratio of the total amount lost to total amount bet was always very close to 1.41% in craps and 5.26% in roulette over the entire ten million sessions. Below are the results:
Results Against Roulette
Bankroll | Probability of Session Loss |
Average Trials per Session |
Average Total Bet per Session |
---|---|---|---|
5 | 72.9% | 7.6 | 17.8 |
10 | 58.2% | 11.7 | 31.1 |
20 | 42.2% | 15.1 | 50.7 |
50 | 21.5% | 19.3 | 90.0 |
100 | 15.3% | 21.4 | 129.7 |
200 | 9.2% | 22.8 | 177.2 |
300 | 6.8% | 23.3 | 208.6 |
500 | 4.6% | 23.8 | 252.8 |
750 | 3.3% | 24.0 | 291.0 |
1000 | 2.7% | 24.1 | 321.1 |
Results Against Craps
Bankroll | Probability of Session Loss |
Average Trials per Session |
Average Total Bet per Session |
---|---|---|---|
5 | 68.4% | 7.8 | 18.3 |
10 | 52.2% | 11.8 | 31.2 |
20 | 35.7% | 14.8 | 49.1 |
50 | 18.6% | 18.3 | 82.3 |
100 | 10.6% | 19.9 | 112.6 |
200 | 5.7% | 20.7 | 144.9 |
300 | 4.0% | 21.0 | 164.8 |
500 | 2.5% | 21.3 | 190.4 |
750 | 1.7% | 21.4 | 211.6 |
1000 | 1.3% | 21.5 | 227.0 |
The computer program used for testing this system can be accessed, and if you possess a C++ compiler, you’re welcome to download it and customize it as you like. If you wish to run it but lack a compiler, just ask, and I may be able to share it with you via email.
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