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The first thing that we want to emphasize is that there is no betting system that can yield a winning expectation when one plays a game of Blackjack with a negative expectation either live or online. When it comes to betting systems, the only thing that they really serve to accomplish is changing the distribution of results, but with respect to the final outcome, the expectation will always be the total amount bet (in dollars) multiplied by the House Edge expressed as a decimal.

While the game of Blackjack at various online casinos may have different variants as well as changes to rules that may either be player-favorable or player-unfavorable, the average House Edge that a player is bucking will usually range from 0.4%-0.5% and the ultimate result of a player’s betting, over the long-run, will be that the player expects to lose the sum of his bets multiplied by the house edge expressed as a decimal.

In other words, if a player makes $1,000 in total bets at a game that has a House Edge of one-half of one percent (0.5%), then:

$1000 * .005 = $5

The expected loss on the sum of those bets that the player will incur is $5. The fundamental flaw of ALL betting systems is that, without exception, the betting system cannot do anything to change this immutable expected loss for either better or worse. Many players will fall into the trap of believing that a betting system works simply because it changes the distribution of outcomes. However, one can change the distribution of outcomes without employing a betting system at all.

For example, ignoring the potential for splits, doubles and surrender, the expected loss of $1,000 played at the Blackjack table is going to be $5 based on the House Edge of 0.5% that we are assuming for these purposes. However, in the event that a player chooses to make one bet of $1,000 (again, ignoring splits, doubles and surrenders just for this paragraph) the player will either get a Natural without the dealer having one and win $1,500, the player will win the hand some other way and win $1,000, the player will push and neither win nor lose, or the dealer will win and the player will lose $1,000.

In effect, the player either profits $1,000, $1,500, $0 or loses $1,000.

Alternatively, the player could decide to bet $5 every single hand until the player has bet a total of $1,000, which would likely happen in no more than 200 hands, but probably fewer than that as the player is extremely likely to either double, split or surrender prior to playing 200 hands. In the event that the player bets this way, it would be very close to impossible for the player to lose all $1,000 having only made $1,000 in total bets.

What some betting system advocates believe (some play them just for fun or because they want to change the distribution of results) is that, by changing the amounts that are going to be bet, the outcome will also be changed somehow. However, what the two extremes (betting $1,000 all at once or flat betting $5 until $1,000 in total bets has been made) have in common is the fact that the expected loss is unchanged at $5.

One might ask: How can that be the case, if the player bets $1,000 all at once, then he cannot possibly finish down only $5, right?

The answer to that question is that is absolutely right. However, that doesn’t change the fact that the expectations are based on the probabilities of the game combined with a player who is assumed to make optimal playing decisions relative to the rules of a particular Blackjack game. In other words, for our assumed House Edge of exactly 0.5%, if we take all of the amounts that a player can win based on a single bet of $1,000, multiply each of those results by the probability of them happening, and then subtract that result by the probability of all of the ways that a player could manage to lose the $1,000 bet, the final result is -$5. Therefore, losing five dollars would be the expectation of a single bet of $1,000 or some number of bets that total $1,000

## The Martingale System

Perhaps the oldest betting system and certainly one of the most popular, the Martingale System is a simple system by which a player will double his/her bet any time that the player incurs a loss until the player does one of the following things:

- Wins a hand
- Hits the Table Maximum
- Runs Out of Money

The way that the Martingale system works is that a player will place a bet that is commonly known as the, *‘Base Bet,’* and in the event that the player wins, he will place the base bet again. If the player loses, the player will then double his/her bet by the amount that was lost until the player eventually wins and reverts to the base bet.

While the Martingale is typically used on strictly Even-Money propositions, such as Red/Black at Roulette, or Pass/Don’t Pass at Craps, the Martingale can be modified slightly to accomodate the game of Blackjack. Because the most common win in Blackjack is one in which a player will be paid even money (though other wins are, indeed, both possible and frequent with correct strategy) the player will usually make a bet of the total amount that has been lost on all previous wins until a win takes place.

For example, if a player starts off with a $5 bet and loses without splitting/doubling, then the next bet that the player would make would be a $10 bet. Imagine that the player ends up doubling down on that $10 bet and losing, then the player will have incurred a loss of $20 on the second hand, and would then want to make a bet of $30 which is one base bet more than the total amount that has been lost of $25.

The goal is that, when the player eventually does win a hand, (and with a long enough negative progression- number of hands that could be played -the player becomes increasingly likely to win a hand before reaching the end of the progression) the player will finish ahead at least one unit, or alternatively, one base bet.

Once again, the fact that Blackjack has several pays that do not result in Even Money makes the system slightly more complicated than it otherwise would be, however, it is still not an overly difficult system to maintain. Quite frankly, the player only needs to remember to return to the Base Bet after any hand in which the player has added at least one unit to his/her bankroll. Secondly, the player needs to remember to simply add one unit to the total amount lost on an individual progression to know what the next bet should be. For example, if a player has lost a total of $85 after three hands, then the next bet should be $90 which is the total amount lost plus one base bet.

Proponents of the Martingale System in Blackjack will sometimes maintain that the Martingale is better for Blackjack than it is for other games due to the fact that the player can win in excess of even money on certain outcomes, such as being dealt a natural when the dealer is not. This claim, of course, could not possibly be further from the truth. An individual could utilize the Martingale to play the Field Bet at Craps, for example, but just because either the Two or the Twelve is usually tripled while the other is doubled does not mean that the Martingale player is somehow overcoming the House Edge.

The House Edge of every game is completely immutable and includes every possible result of a given trial (hand) of that game and what that result, if it occurs, will pay. Therefore, if an individual is interested in using some form of the Martingale System, then Blackjack is not a bad game upon which to do that, but that is only because Blackjack has a lower house edge than most other games. Ignoring doubles, splits and surrenders, the player is no better off playing the Martingale, flat-betting a single unit or making a single bet of everything that the player is willing to lose all at once. In terms of the House Edge, the total amount that is bet is what determines the expected loss, not the manner in which it is bet.

With that said, it is easy to see why the Martingale System might be attractive to some players who wish to enjoy sessions of small wins at the risk of a devastating loss, as the distribution of results is thoroughly changed by the Martingale in the short-run. For example, let’s look at a game that would have a House Edge of 0%, a simple coin toss:

Given a fair coin, a player would have a 50/50 chance of winning a coin toss, so if the player is getting even money every time the result desired by the player comes up, then the player has an expected loss of $0 regardless of the amount being bet. If there are six coin tosses in what we will call a, *‘Session,’* then the expected result is three heads, three tails, nobody wins and nobody loses. Of course, all six of the tosses can come up heads, zero of the tosses could result in heads, or anything in between.

For these purposes, we are going to assume that a player either intends to win on one toss, or will otherwise lose six tosses in a row and quit. The probability of losing six tosses in a row is simple to determine:

(.5)^6 = 0.015625

Which means that the probability that the player will win at least one of the six tosses is .984375, or 98.4375%.

If the player is committed to the Martingale, then the player will either lose $5 on the first toss, $10 more on the second, $20 more on the third, $40 more on the fourth, $80 more on the fifth and $160 more on the sixth for a total loss of $315. If the player stops playing as soon as the first toss is won, then the player shall win $5. We can see how that works out as such:

($5 * .984375) - ($315 * .015625) = $0.00

In other words, the player stands to win $0, and this is so because the Expected Value of a coin toss game that pays even money, and assuming a fair coin, is $0 regardless of the number of times the coin is tossed. The game of Blackjack, and any other game to which the Martingale System could be applied, works the same way just with a different distribution of possible outcomes. To wit, not every win in Blackjack is going to pay even money.

In our coin toss example, if the player only does it once, the player has a 98.4375% chance to come out ahead $5. However, over the long run, the player will eventually lose six tosses so many times in a row that the result will be that the player has neither won nor lost anything, at least, in terms of expectations.

Imagine that we have a coin toss in which the player has an advantage, for example, the player is getting paid 2:1 (or $10 for a $5 bet) on a win. On each coin toss, the player has an expected profit of:

(10 * .5) - (5 * .5) = 2.5

However, the player will enjoy that expected profit of 50% of the amount bet regardless of whether or not the player employs the Martingale System, or any other system for that matter.

The only thing that the Martingale System accomplishes is that it gives a player committed to it a greater probability of incurring a small win at the risk of incurring a devastating loss. In terms of the Expected Value of a particular proposition, nothing can change the fact that such expected value is merely the result of the total amount being bet multiplied by the house edge or the player edge expressed as a decimal. In the long-term, the Martingale changes nothing.

## The Reverse Martingale

The Reverse Martingale does exactly what it says on the box, it is a system by which the player will double his bet on a win, *‘Let it Ride,’* while reverting to the Base Bet on a loss. The player will generally employ this strategy until the player has either reached the table limit and cannot increase his bet, or alternatively, has reached some sort of arbitrary win goal.

The Reverse Martingale, in the short-term, also does the precise opposite of what the Martingale System sets out to accomplish. With the Reverse Martingale, the player will sustain several small losses all in the hopes of scoring a big win.

Interestingly enough, it can fairly be stated, at least with respect to the Martingale and the Reverse Martingale, that when an individual employs such a system, he is, *‘Forcing,’* the casino to employ the opposite system. In essence, if a player is playing the Martingale System, then the casino, albeit unwittingly, is playing the Reverse Martingale against the player. In the event that the player is playing the Reverse Martingale, the player is forcing the casino to play the Martingale System against him.

The casino, of course, could not possibly be less concerned with this arrangement. The fact of the matter is that the casino has the advantage in any Blackjack bet that the player is making in the absence of card-counting, edge-sorting, shuffle-tracking, hole-carding or some other method of advantage play. The result of that, of course, is that as long as you are playing within the table limits, the casino is dispassionate about the way you place your bets or how much you bet.

Simply put, the casino knows that it will win in the end.

## The Labouchere

The Labouchere System, which some call the Cancellation System, is my personal favorite system to employ when playing for fun, which is to say, **not for real money!** The way that the Labouchere System works is that a player will make a line of base bets, or other amounts, and will cross out numbers on that line for each bet that is completed. Here is an example of a Labouchere Line that calls for five base bets:

5, 5, 5, 5, 5

The way this would work is that the player will add the first number in the line to the last number, and upon winning the bet, the player will cross out both numbers on that line. In the event that the player loses the bet, in this case the first bet would be $10, the player will then place $10 at the end of the line in the event of a loss and the next bet would be $15.

There are some that believe this system would be difficult to apply to Blackjack, but I tend to disagree. When it comes to properly employing Splits, Doubles and Surrenders, the player would simply need to put the total amount lost at the end of the line. In the event that more than the total amount originally bet is won, then the player would have the option to either cross out (or change) additional numbers on the line to reflect the total amount won. The way that the Labouchere works is that, when the line completes, the player will have profited the original sum of the total bets on the line. In the example above, that would be $25.

Anyway, as with all other systems past, present or future the Labouchere can do nothing to change the fact that the expected loss on a Blackjack game for a player is simply the sum of the total amount that the player bets at that game multiplied by the House Edge expressed as a decimal. This is true whether using the Martingale, Reverse Martingale, Labouchere, Flat Betting, or anything else. Normally, I would also say that it is true of betting everything all at once, but in Blackjack, that’s a terrible decision because the player can then no longer split or double, and as a result, bucks an even greater house edge than actually intended by way of Optimal play.

## Online Applications of Betting Systems

Many online casino bonuses do not allow Blackjack to be played with respect to meeting the playthrough requirements to satisfy the bonus. When this happens, the player may be allowed to play Blackjack, or alternatively, the casino may say that the player may not play Blackjack at all while playing the bonus. Either way, if you are playing a bonus, there is no reason to play Blackjack if it does not contribute to the playthrough requirements.

For those casinos in which Blackjack can be played on a bonus and in which it does contribute to the playthrough requirements, it is absolutely essential that the player read through the terms and conditions of the casino in question prior to deciding to play Blackjack, and particularly, before playing Blackjack with a betting system. While betting systems cannot change the expected value of a game, unfortunately, there are many online casinos that still choose to state in their terms and conditions that, *‘System Play,’ ‘Structured Wagering,’* or some other thing can result in forfeiture of the bonus. In those cases, even if you would normally employ a betting system with respect to online Blackjack, that is definitely something to be avoided.

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