This is my first post at this website, but I was hoping that someone would be willing to comment if any holes can be found in a betting system which I believe to be viable for on-line Blackjack.
Please keep in mind that it is unlikely for one to be able to employ this system in live casino Blackjack as the memory requirements would be incredible (and you can not have a paper/pen at the table) however, nobody can stop you from having such implements in your own home.
I believe everyone here should be familiar with the cancellation system of betting, (I prefer Labouchere) so please keep in mind that this post takes such familiarity for granted. The system, as you well know, is typically applied to even payout propositions such as Even/Odd in Roulette.
In any event, for the Cancellation System to successfully complete a line requires that a winning percentage of 33.3333334+% be achieved. For example, if a line starts out with five values such as:
2, 2, 2, 2, 2
You will add one value (the first plus the last, which is the amount bet) for every loss and cross out two values for every win. I'm going to steal from the Wikipedia article (which I largely wrote) for a paragraph. I will cite Wikipedia all the same:
Theoretically, because the player is cancelling out two numbers on the list for every win, and adding only one number for every loss, the player needs to have his proposition come at least 33.34% to eventually complete the list. For example, if the list starts with seven numbers and the player wins five times and loses three (62.5% winning percentage) the list is completed and the player wins the desired amount, if the list starts with seven numbers and the player wins 43,600 times and loses 87,193 times (33.34% winning percentage) the list completes and the player wins.
It is theoretically impossible for this system to fail to complete, given infinite time, because it requires a winning percentage less than the probabilistic expected winning percentage. For this reason, it is equally theoretically impossible for the Martingale system to fail to return the original amount bet.
In actuality, however, we are confronted with Table Limits, and most importantly, our own bankrolls.
Table Limits can prevent the Martingale System from completing because it is possible to reach a point where the next bet, as demanded by the system, is not possible to make. The fortunate aspect of Labouchere is that it takes much longer for this to happen.
Let's imagine a theoretical table where the Table Minimum is $2.00 and the Table Maximum is $200. You will see that the Martingale also fails to make the next necessary bet as demanded by the system, given a string of consecutive losses, far quicker than the Labouchere.
With Martingale, you would start with $2 and bet as follows:
2, 4, 8, 16, 32, 64, 128
In short, seven consecutive losses wipes you out.
However, if you start with a Labouchere line of:
2, 2, 2, 2, 2
Your bets will go 4, 6, 8, 10,......
You would not fail to make the next required bet ($202) until after 99 consecutive losses. Please keep in mind that these results are NOT typical, and you will usually find yourself making larger individual bets after a series of wins and losses. For example, if all of your 2's are crossed out (and the line has still not completed) the small end of your bet will be, by necessity, a 4 and so on...
Bankroll will often be more of a factor causing failure than Table Limits.
In any event, the Labouchere can be modified for on-line Blackjack in a fashion that enables two possibilities:
1.) A winning percentage of 33.34%+ will not necessarily be needed to complete the line. The less you HAVE to win, the more often you WILL win.
2.) You can complete the line in a fashion that results in an amount won greater than the sum of the individual line numbers.
The way the system works is that you play the standard Labouchere line, and you apply basic Blackjack Strategy as recommended on this site. (Disclaimer 1) The only difference is that any winnings in EXCESS of the base bet will also be applied to your line. For example, let's say you have a starting line of:
2, 2, 2, 2, 2
The base bet is four units.
Imagine I am dealt a pair of eights and the dealer is showing me a five. I am going to split the eights. The first eight gets a ten-value added to it while the second eight gets a deuce. I'm going to stand on eighteen and double on my ten. The ten that I have doubled gets another ten-card. The dealer flips a ten card for fifteen and draws a nine. The dealer busts.
Your base bet was four, but you split and won on a double. The result is a profit of 12 units.
In this case, the line has completed with one hand and instead of the sum of units (10) the player profit is (12)
That's obviously a best case scenario. Just for the sake of providing an example that may be more common, let's say you have a line of:
6, 8, 10, 16, 20
Your bet is going to be 26 units. You play the same hand, except you split and draw two ten values. The dealer busts, in whatever fashion.
You have achieved 52 units won. You would cross out the 20 and 6 anyway, however, the 16 and 10 also results in 26, so you will cross them out as well.
Your new line is:
There are going to be events where no two (or more) numbers on the line add up to the amount won in excess of the base bet. In such an event, there are two ways you can handle that:
1.) You can use the excess to cross out as many numbers as possible on the low end.
2.) You can subtract the remainder from your highest number and replace it with the result.
The advantage to the first way is that it reduces the necessary winning percentage for the line to complete to a greater extent. However, you are crossing out your smallest numbers which can be used to keep your bets reasonably low in the event of losses.
The advantage to the second way is that, by reducing your highest number, you will also reduce your highest theoretical bet (and future bets) given the current line. I believe this is a more worthy endeavor because it will enable you to avoid hitting the table limit for a longer period of time.
One other way to reduce your line with only one win is the fact that a Natural pays 3:2. The same reduction rules apply.
The advantage to this system compared to the straight Labouchere is that it will enable the player to complete a line faster (and with fewer wins) than the standard Labouchere line would be completed merely by crossing out the front and back numbers for every win. Furthermore, you are also getting more money out there when the dealer is at his weakest.
Keep in mind, that in the event of an overall loss (even with Splits/Doubles) the amount added to the end of the line will ALWAYS be the amount lost. For instance, if you play a line of:
2, 2, 2, 2, 2
That resulted in:
2, 4, 8, 16, 24
If you double and lose and only add 26 at the back end of the line, then instead of playing the line for a goal of $10 profit, you would be playing the line for a, "Goal," of losing only $16. ($10 (amount desired to win) -$26 (Money over base bet lost) = -$16)
The disadvantages of this system are the same as with Standard Labouchere. Bankroll, Table Limits, and mostly the fact that you will be down amounts greater than $10 with the goal of winning $10 on that line.
I will post more detailed results after I have played 1,000 hands using the Practice Game on this website and basic strategy.
The amount of a single bet may NOT exceed $200. The player's bankroll is $1,000.
I have played 177 hands over 1:45 and am presently ahead $279. I have completed about eighteen lines (Sorry, I don't have my notebook with me at the moment). I have not yet attempted to complete a line and failed by busting my bankroll or the system demanding a bet of $200+. I eventually WILL fail to complete a line. The law of probability says that I must, but after 1,000 hands (if everything is looking good) I will expand my trial to 10,000 hands.
If everything is looking good after that, I may accept the $1,000/$10,000 challenge. I'm not sure. What I am really interested in is obtaining code for this system that way it can be ran for 1,000,000 lines to test its effectiveness.
Disclaimer 1: I do not always surrender when the Basic Strategy advises a surrender. If you do surrender, as with anything else, the amount lost should be added to the end of the line. I have not developed a hard-and-fast surrender rule yet, but mathematically, I am only hurting myself by not surrendering when it tells me to, so if anything, not surrendering will make my findings even more valid because I am not playing in the best possible manner.
Quote: Wizard of Odds, Commandment #6
Thou shalt not believe in betting systems.
For every one legitimate gambling writer there are a hundred charlatans trying to sell worthless betting systems promising an easy way to beat the casinos. I know it sounds like a cliché, but if it sounds too good to be true it probably is.
Also, please read this page... The Truth About Betting Systems
And this page The Ten Commandments
Welcome to the Forum.
I am not the world's fastest typist.
Thank you for the welcome.
It is not possible to use a card-counting system because this system applies only to on-line Blackjack and the deck is re-shuffled after every hand, at least, it is reshuffled in the Practice Game available here after every hand. I also play with six decks.
With all due respect, I have already read both of the pages to which you have kindly linked me.
The question is simply a mathematical one. I'm looking for mathematical problems in my system. I have not run nearly enough trial hands to claim that this system even works. I can claim that it is better, by necessity, than playing Blackjack with Standard Labouchere. That system, by the way, has been demonstrated by the Wizard to essentially be no worse than straight betting.
My system is also not entirely new, I make no such claim. I'm looking to improve upon an existant system and apply it to a casino game (which is darn near 50/50) to begin with and to which, in my observations, it has not been previously applied.
I hope that eventually the Wizard may read my post and see what he thinks about the system. It is difficult to say whether or not he will do that.
I am also not promising anything, nor would I attempt to sell my system, even if it turns out that it works.
In the meantime, I am open to accounting for and attempting to discuss any potential problem that exists within my system. I know that eventually it WILL fail to complete a line. It MUST fail to complete a line. The real question is: How often?
Consider a martingale for example:-
Bets of 10, 20, 40, 80 and 160. (You will win $10 as with 2 2 2 2 2 in the cancellation system)
Now you only need to win 1 out of 5 hands in order to make a $10 profit - so just a 20% win ratio!!!
In fact, depending on the starting bet and maximum limit you could fix that to be a much smaller win % than 20%.
The bottom line is that you will still be making large bets with both systems at some point ... the house edge still kicks in even if the win ratio looks appealing at first.
Welcome to the forum!
I appreciate both your post and your welcoming me to this Forum.
I agree with your statements concerning winning percentages. I would counter, however, that for your Martingale example to reach the $200 Limit (and be unable to complete the next bet) requires only five consecutive losses at any time. This will not happen with the Labouchere, at least, not if you start off with five consecutive losses. My argument would be that the reduced liklihood of exceeding the $200 limit offsets the 13.34% difference in necessary winning percentage.
Further, Doubles, Splits and Naturals also offset the 33.34% winning percentage necessary to complete the line to an extent. I don't believe the exact extent can be calculated (except through intensive trial) as the necessary winning percentage will be continuously variable given the number of such hands that come to pass.
In any event, the necessary winning percentage will never EXCEED 33.34%, but it is also rare to complete a line with an actual winning percentage that low. Simply stated, it would be a very long line.
In Blackjack, you may have the same advantages with Naturals because they pay 3:2. Thus, if your Martingale Line is:
10, 20, 40, 80 (loss)
And you get a Natural betting $160, the profit is $240 (on that bet) resulting in an overall Martingale profit $90 as opposed to $10.
However, if you were to Split on $80 and lose both hands, you'd be done.
I think the Modified Labouchere would be found to lose at a lesser frequency.
I should also like to add that your 20% figure assumes a win on every fifth hand, where my 33.34% figure is a long-run figure.
If you only won 20% of the time, you'd be finished either way, don't get me wrong, but:
if the list starts with seven numbers and the player wins 43,600 times and loses 87,193 times (33.34% winning percentage) the list completes and the player wins.
That's long run. If you were playing Martingale and only won 33.34% in the long run, you'd be finished in a big-time hurry.
These betting systems are like having a big closed box with 9999 white balls and 1 red ball inside. You select one at random and as long as its white you win £1 for your £10000 bet. As you win £1 again and again you think you have found the holy grail of betting. But eventually you WILL select that one red ball and go bankrupt.