In the article “Betting Systems Basics,” I debunked the idea that systems can alter the long-term odds or “house advantage.
” You might therefore think that there can be no such a thing as a “the best betting systems.” Betting systems do not change the ultimate picture, just as a bicycle does not make you stronger.
However just as a bicycle can “change gears” to modify your energy, betting systems can deliver smaller and more frequent wins-or if you prefer, greater risk in the hope of some bigger wins.
Also according to the Big Bet Theory (see below) the right system just might convert some lucky players from losers into winners.
This article will help you to understand how systems work and thus to find and master those most suitable to you.
1. Loss Progressions vs. Win Progressions
2. Making the Best of the Popular Systems
3. The Big Bet Theory
Loss Progressions VS Win Progressions
There are two types of betting systems. These are “loss progressions” or “up-as-you-lose” systems, and “win progressions” that ask you to go “up-as-you-win.”
What is the difference? As explained in “Betting Systems Basics”, gambling is composed of “independent events.” “When” you bet high does not matter in the long run. Therefore in the long run, win progressions and loss progressions can achieve the same goal: to minimize the frequency of larger bets, and to bet high only so long as you are winning.
However, you personally will not necessarily experience “the long run.” If your lifetime performance is slightly better than average-a loss progression is more likely to change you from being a slight loser into a big winner.
For example, using the classic Martingale system, you can simply “double the bet” every time you lose: $1-$2-$4-$8-$16-$32. (You could go higher, but had better not.)
With this system you will win $1 frequently, although this does not alter the odds. After a million plays, you can be certain that for each time you bet $32, there would be more losses than wins-for each time you bet $16, there would be more losses than wins-etc.
This is the law of “independent events.” However, you personally will not live long enough to see five losses in a row a million times! It is possible this will happen to you a bit less than average, in which case a loser has been made into a winner.
If this happens to you more than average-nothing happens except a loser quits earlier, if you do not go above $32 and if you maintain the discipline to stop at the same loss limit.
A win progression may well do the opposite. Let us say you are so lucky, that in your lifetime, your individual wins actually outnumber your losses. If you play a reverse-Martingale, and “double-as-you-win”-this might convert you into a big loser.
Nonetheless, this is an extreme example. Win progressions probably are more popular and can be modified. Each time you win at a loss progression like Martingale, you only win $1-there is little chance to “win big.”
Meanwhile each time you lose, there goes your bankroll. Loss progressions are especially hazardous for Blackjack, where you must prepare for long streaks of losing as well as of winning.
In summary, a loss progression is “mathematically better.” A win progression is less efficient, it can seriously reduce your number of winning sessions, and it requires winning streaks to pay off.
However if those winning streaks do come, a win progression gives you the biggest jackpot. Also if you hit long losing streaks and do not want to “quit early,” a win progression requires less discipline.
Most systems’ players advise that you just have to experiment to find what is right for you. Ideally, have several systems up your sleeve and be ready to switch whenever one is not working.
Making the Best of the Popular Systems
Please note that in each example, for higher play you can replace $1 with $5 or $10, and multiply all other steps by 5 or 10, or by whatever you like.Martingale. 1-2-4-8-16-32. Each time you lose, you bet double. Do this again until you win, or until you play the highest bet. Then return to the lowest bet.
1. Bet $1 and win. Keep betting $1 until you lose, then bet $2.
2. If you win the $2, return to $1. If you lose, then bet $4.
3. If you win the $4, return to $1. If you lose, then bet $8.
4. If you win the $8, return to $1. If you lose, then bet $16.
5. If you win the $32, return to $1. If you lose, then also return to $1.
If someone puts a gun to your head and says, “I just lost $1, you must win it back!”-Martingale is your best shot. (No pun intended.) Also in theory, if you could double forever you need never lose.
However in practice, the frequent player will experience 10-20 or even more losses in a row someday. Once you get to such high levels, you are trapped into betting more than you otherwise might lose in your entire life. So you had better give up after 6 losses-and this is not so uncommon-and so, most players agree, Martingale is not recommended.
Variant: there are numerous “Parlay,” “Paroli,” and “Pyramid” systems that basically reverse the Martingale, making larger bets as you win up to a fixed goal. These were originally developed for horse racing.
For casino play, many people swear by these systems and claim that they never lose. This may be so-but in my personal experience and also in my simulations, the story is quite different. All “reverse Martingale” variations somewhat contradict the Big Bet Theory (see below) and thus I do not list them here.
Fibonacci series. 1-2-3-5-8-13-21-34. Go up one step with each loss, down 2 steps with each win. Note that every win pays for the two losses before it.
1. Bet $1 until you lose. Then bet $2.
2. If you win at $2, then return to step 1. If you lose, then bet $3.
3. If you win at $3, then return to step 1. If you lose, then bet $5.
4. If you win at $5, then return to step 2. If you lose, then bet $8.
5. If you win at $8, then return to step 3. If you lose, then bet $13.
6. If you win at $13, then return to step 4. If you lose, then bet $21.
7. If you win at $21, then return to step 5. If you lose, then bet $34.
8. If you win at $34, then return to step 6. If you lose, return to step 1.
Recommended variant for the high roller: instead of going down 2 steps with each win, go down 1 step with each win, until you win 2 in a row-then go down 2 steps.
According to the Big Bet Theory (see below) this variant may be as likely as any system to help you in the long run, and meanwhile you get some tremendous wins and excitement. There are numerous other variants.
However the usual Fibonacci is extremely unsatisfactory for the high roller-you lose often and never win big. Whereas for the player who prefers not to play 34 times his minimum bet if possible, it is debatable whether any Fibonacci is any better than Martingale, or just gives you 2 extra steps and then helps you fall off the cliff more often. Therefore, no Fibonacci is recommended for the cautious player.
Labouchere or “cancellation”. Write down any series of numbers such as 1-1-1-1-1-1. Play the sum of the first and the last in the series. If you win, cancel those two numbers from the series.
If you lose, add that sum to the series. For example, let us assume you start out losing three times, then winning three times:
Write down the most sensible series: 1-1-1-1-1-1.
Bet the sum of the first plus the last: $1 + $1 = $2. You lose the $2, and so you add it to the series giving: 1-1-1-1-1-1-2.
Then you bet the first plus the last: $1 + $2 = $3. You lose the $3, so add this to the series giving: 1-1-1-1-1-1-2-3.
Then bet the first plus the last: $1 + $3 = $4. You lose, so you add $4 giving: 1-1-1-1-1-1-2-3-4.
Then bet the first plus the last: $1 + $4 = $5. You win, and so you cancel the first and the last numbers giving: 1-1-1-1-1-2-3.
Next play $1 + $3 = $4 and win. Cancel again giving: 1-1-1-1-2.
Next play $1 + $2 = $3 and win giving: 1-1-1
My advice: as soon as there is nothing in the series except 1’s, might as well restart with 6 of them at step 1: 1-1-1-1-1-1.
Cancellation is similar to Fibonacci, and better. One win cancels 2 losses, and yet there are quite a few steps before you lose large amounts, and so it can work quite often. Here you almost have completed the series.
However, also please note even as you win, you are running out of $1 bets to cross off. If your luck turns, soon you must add $2 to the highest bet with each loss-and immediately after that, if you lose more you must add $3, $4, $5 and etc. As soon as you run out of 1’s, you are asking for trouble.
Therefore as with Fibonacci, an appropriate place to “give up” would be on any loss at $34-and unlike Fibonacci, the more conservative player also can stop as low as $10.
Possible variant: “reverse cancellation.” After losing all the way to the house limits, some cancellation players have decided to try the reverse and some have won.
However, usually using reverse cancellation, you must set the “ultimate bet” at a reasonable goal such as 10 times the minimum. Otherwise you might play all your life and do nothing but lose.
In any case reverse cancellation is costly, somewhat contradicts the Big Bet Theory (see below) and has performed poorly in my simulation studies. The premise that “if the casino can beat the cancellation system, so can we”-also blithely ignores the fact that the casino has the advantage.
Other variants. It is common to suggest another series of numbers, such as 1-2-3-4-5-6 or 1-1-1-2-2-2. However this is rather nonsensical. If you want to bet higher, just make it 2-2-2-2-2-2 or 10-10-10-10-10-10 or whatever.
Technically there is no difference, and by starting with all the same numbers, it is just that much clearer how the heck you are doing.
D’Alenbert. 1-2-3-4-5-6-7-8-9-etc. Each loss go up one unit, each win go down one unit. Thus “hopefully” you get back where you started, meanwhile in the end making $1 from each and every win.
1. First bet $1. If you win, bet $1. If you lose, bet $2.
2. If you win $2, next bet $1. If you lose, bet $3.
3. If you win $3, next bet $2. If you lose, bet $4.
4. If you win $4, next bet $3. If you lose, bet $5.
5. If you win $5, next bet $4. If you lose, bet $6.
6. If you win $6, next bet $5. If you lose, bet $8.
You’d better set limits or will find yourself in outer space some day-but usually, D’Alenbert is the most efficient system. For example if you start at $1 and “return to base” every 100 plays, whether winning or losing-this is definitely better than flat betting at $50.
The Ten Percent Solution. With each loss, go up 10% rounded to the nearest non-zero bet unit, with each win go down 10%. After you break even, then with each extra win, return halfway back to the lowest bet.
This is identical to D’Alenbert except that if you hit $20, you then go up and down $2. If you hit $30, you then go up and down $3. Etc. Be sure to keep track of your total since the last time you saw $1, and reduce bets by 50% after each win that causes a total net win or that breaks even.
Invented by me and named after a Sherlock Holmes story, the Ten Percent Solution is for D’Alenbert players who never want to give up, or for “cancellation” players who want to go the limit with slightly less insanity.
With the Ten Percent Solution, the higher you play the more you might win-instead of being doomed to play higher and higher with less and less hope or reason.
Also there are significant safeguards against playing higher. Therefore if you are daring, the Ten Percent Solution even can be used for Blackjack and for Pass line bets at Craps with double odds.
This will not place a win higher than a loss in every instance. In Blackjack for example, sometimes you will “double down” and lose much more than you might win back on the next bet. However in the long run, the times that you will win even bigger sums will greatly outweigh these instances.
The Ten Percent Solution can be efficient. Be warned however that this is not a low risk strategy-it is only “lower-risk play for high risk players.” The Ten Percent Solution is not for the faint of heart or for those who lack discipline.
These systems are directly based on the Big Bet Theory (see below) so that in the long run they might encourage the wins to be at higher levels.
They also are poised to exploit long winning streaks, or even the extremely remote possibility of some glitch in an online system, such that wins might tend to clump together.
Sometimes these systems do not work at all-but then I just stop quickly. Whereas if I am winning, generally I win quite a lot.
Pacing the table. Bet very low when the table seems “cold”-bet high when the table seems “hot.” That’s it! This old-fashioned idea is so un-systematic that it is seldom mentioned as a “system” these days-but it has made fortunes for some, and still is all-pervasive at casinos.
“Pacing” can be ideal if you prefer to “feel your way” rather than to follow a lot of arithmetic. The trick is to know the Big Bet Theory (see below) and to keep your powder dry-you must not bet high too often.
Also when your big bets fail-or if you prefer, when they succeed-you might want to bet slightly higher next time. Thus you might feel your way into the same leveraged progression as any other system-perhaps better.
The Big Bet Theory
I developed this theory myself so I cannot say it is supported by any leading mathematicians. However this primarily is a way to enable players and mathematicians alike to visualize better what formally is called “standard deviation.”
Suppose you could afford to buy a small casino for a million dollars. Instead, you walk in and lay it on the Pass line. If they accept this bet, they would be as crazy as you, because there is no telling the outcome.
If you win this bet, and you never bet again, the retrospective advantage was yours +100%. If you lose, you are -100% and might as well have lit a bonfire.
Even mathematicians sometimes can forget that, because of the law of independent events: After you have won or lost, it makes no difference what the odds were. If the odds were greatly against you and you won-the money is yours.
Whereas if the odds were greatly in your favor and you lost-you might as well have been mugged. That loss is not any more likely to “come back to you later.” Now if you play very little, the fact that “most people” who try this may be losers or winners, has no relevance to you personally. If however you
make 10,000 bets of $100, that is different. Then it is almost impossible for you to win-the “law of averages” must predominate.
Now consider instead a 14-step Martingale progression: $100-$200-$400-$800-$1,600-$3,200-$6,400-$12,800-$25,600-$51,200-$102,400-$204,800-$409,600-$819,200.
To win $1,000,000, you would need to do this successfully 10,000 times. However, out of 10,000 times that you bet $100, then according to the law of averages, there would only be about 1 occurrence of a bet at $819,200.
This is insane but with a little luck, this bet might not even happen. You definitely are more likely to win than if you flat bet at $100-and perhaps even more likely to win than from a single bet of $1,000,000.
The Big Bet Theory states that in any progressive betting system, two good things might happen.
Firstly, the higher the bet, the less often it occurs, therefore greatly reducing any need to obey the law of averages. Secondly, if well designed, the progression may create a tendency for wins to be at a higher level.
For example, in an ideal loss progression, for every loss at a low level, there is a win at a higher level. Even if not ideal, there is a clear tendency for wins to predominate at a higher level-because each time you win, you go to a lower level.
A win progression cannot be as efficient. However even with a win progression, if you “quit as soon as you lose” at any higher level, then there also is some possibility of reducing relative losses at the higher levels.
However with either a win progression or a loss progression, you “must not go too high,” because then, just a few losses can cause you either to win or to lose far more than otherwise.
If the Big Bet Theory is correct, then with a well designed system, there is no need to go to extreme levels. Whereas if the Big Bet Theory is incorrect…there is even less point in going to extreme levels.
What is “theoretical” about this is whether or not it might reduce the total profits of casinos if everyone followed the best systems.
What is not theoretical are the facts that (a) there always must be a significant group of players whose luck is slightly better than average, and that (b) with the right system, these players can be changed from slight losers into big winners.
Therefore if you are going to gamble at all, I suggest to keep in mind the Big Bet Theory.
If you were looking for bragging about an “infallible” system, you have come to the wrong page. Using these techniques, I have converted twenty dollars into hundreds of dollars a number of times.
I hope and I rather expect this will happen to you, if you understand these systems and keep experimenting.
However, please be prepared that according to the law of independent events, you also might just lose…and lose…and lose… Also when you are a winner, to keep this money, please remember to stop using any system, however “ideal,” as soon as it stops winning.
Also see the companion article: “Betting Systems Basics”.