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THE TARGET MESSAGE
That’s not just my opinion—the gambling industry believes it too, which is why there are table and house limits, all of them in place solely to make effective progressive betting difficult, if not impossible.
The argument that I have with the so-called, self-appointed “experts” challenges their insistence that exactly the same method of progressive betting must be used in every game and in every circumstance.
That’s as dumb as saying that if you can’t drive off-road over rocks or snow and ice the same way as you drive on a wide open road in warm sunshine, then you shouldn’t drive at all (hence my analogy that the safest car in the world is a death trap if the steering, brakes and gas pedal are all disabled!).
We all have to deal with two harsh realities: a limit on the amount that we are willing or able to risk in a casino game, and restrictions on the amount the house is prepared to let us bet in order to recover our past losses.
When I started out on this project more than 30 years ago, I too believed that it might be possible to discover a single method that could mathematically overcome the long-term house advantage in casino games of chance.
Now, I know better, which is why I recommend a flexible application of progressive betting.
You may have seen that the Target Betting objective is to “win more when you win than you lose when you lose” and while that motto might seem to be stating the obvious, few gamblers seem to realize that since we’re all certain to lose more often than we win over the long haul, we have no winning option but to ensure that our average win is worth more than our average loss.
That objective cannot be achieved long-term without progressive betting. Period. Luck can make it happen in the short term, but over time, luck becomes totally irrelevant (as well as being unreliable!).
For example, let’s say you place 100 bets and encounter a house edge of 2.0% which results in you winning 49 bets and losing 51 bets. If your average overall bet value was $100, you will have won $4,900 and lost $5,100 and in 100 bets, you will have lost $200 or 2.0% of total action of $10,000.
Now let’s say your average win value is $120 and your average loss value is $100, a 20% win/loss surplus which is consistently achieved with the Target method.
The picture changes: 49 wins @ $120 = $5,880 and 51 losses @ $100 = $5,100, giving you an overall win of $780/$10,980 = +7.1% against a -2.0% house edge that gave you (according to those “experts”) an expected LOSS of -2.0% x $10,980 = -$218.
I have often been accused of attempting to deny or change the house advantage, and of course that’s impossible.
But it’s only impossible when we’re talking about the overall number of losses vs. the overall number of wins. The loss total (number of losses, if you like) will always exceed the win total (number of wins) over time, but that does not mean that the total amount of money lost must exceed the total amount of money won.
I do not recommend use of the standard Martingale, which is the best-known method of progressive betting (-1, -2, -4, -8, -16, -32, +64). It is the simplest approach, but it is also the most dangerous—and an added problem is that casinos routinely interfere with its use because when it works, it can be very bad for the house’s bottom line.
In the sequence above, the average win was 64 units and the average loss was just over 10 units. We don’t need a win/loss surplus to be that dramatic (600%!) to achieve steady profits long-term. An average win value that exceeds our average loss value by 20-30% will do the job just fine.
It is relatively simple to create a random number generator simulation which will demonstrate conclusively that the conventional wisdom about the house advantage is just plain wrong.
What such a simulation will repeatedly confirm is that while the house has a slight mathematical or statistical edge in every bet, the house wins two bets in succession only about half as often as a house win is followed by a player win (-1, +1 from the player’s viewpoint) and three consecutive house wins occur about half as frequently as two house wins followed by a player win (-1, -1, +1 for the player).
The problem with the Martingale is that while, say, 10 successive house wins is an extremely rare phenomenon, it is a “black swan” event that does occur from time to time, however infinitesimal the odds, and when it does, it can be very expensive for the player.
So when talking about progressive betting, we should be thinking in terms of imposing our own limits on bet values and on the number of times we are willing to re-double our bet before applying damage control by either freezing or reducing the sum of money in play.
One rule must always be applied: When we win a bet after a losing sequence of any duration, we must follow that win with a bet that, if permissible, recovers all of our prior losses—our loss to date or LTD—plus an overall win target, or profit.
A Martingale makes a profit of just one unit after a losing streak, whether it’s an isolated loss (-1, +1) or a prolonged downturn (-1, -2, -4, -8, -16, -32, +64) and that’s not enough—unless you’re playing blackjack or betting the field at craps, which occasionally provide paybacks that are multiples of the original bet value.
I just set my “sim” to bet 5,000 rounds using a very conservative method of progressive betting that applied the following rules:
· If the first bet in a new series or sequence of bets is a loser, double the bet
· If the first bet in a new series is a winner, add 1 unit to the bet
· After any isolated loss in a recovery series, doublethe bet
· After a second or subsequent loss occurs in a recovery series, halve the bet
· After a mid-series win, double the bet. If the bet wins and all prior losses for the series are recovered, fall back to a minimum (1 unit) bet. If the bet loses, double it once, then halve it if another loss occurs, and continue halving the bet until the minimum is reached.
· The maximum permitted bet is 5,000 units
The opening few hands in my sim looked like this (the first column shows the bet value, the next the outcome, the third tallies the total win or loss for the current series, and right-hand column tracks streaks and indicates when a turnaround bet is called for or a recovery has been achieved):
1 | -1 | -1 | -1 |
2 | 2 | 1 | OK |
1 | -1 | -1 | -1 |
2 | 2 | 1 | OK |
1 | 1 | 1 | + |
2 | -2 | -2 | -1 |
4 | 4 | 2 | OK |
1 | 1 | 1 | + |
2 | 2 | 2 | + |
3 | -3 | -3 | -1 |
6 | -6 | -9 | -2 |
3 | -3 | -12 | -3 |
2 | -2 | -14 | -4 |
1 | 1 | -13 | ta |
2 | 2 | -11 | ta |
4 | 4 | -7 | ta |
8 | 8 | 1 | OK |
1 | -1 | -1 | -1 |
2 | 2 | 1 | OK |
1 | 1 | 1 | + |
2 | -2 | -2 | -1 |
4 | 4 | 2 | OK |
1 | 1 | 1 | + |
2 | -2 | -2 | -1 |
4 | -4 | -6 | -2 |
2 | -2 | -8 | -3 |
1 | 1 | -7 | ta |
2 | 2 | -5 | ta |
4 | -4 | -9 | -1 |
8 | 8 | -1 | ta |
16 | 16 | 15 | OK |
1 | -1 | -1 | -1 |
2 | 2 | 1 | OK |
In Target betting, a “recovery series” is a sequence of bets in which the player is in the hole and looking to win enough to achieve turnaround (“ta” in the example above).
Wherever you see “OK” above, prior losses have been recovered in the indicated series, and the bet reverts to the minimum so we can start all over again.
Here are the results for just one iteration of the simulation:
Maximum bet permitted | 5,000 | units | ||||
Actual maximum risked | 5,000 | 11 | max bets | 0.22% | ||
Final outcome | 20,073 | 12.64% | ||||
Overall action | 158,851 | |||||
Flat bet final outcome | -60 | |||||
House advantage | -1.20% | |||||
Expected outcome | -1,906 | units lost | ||||
Won | 2470 | 36 | average | 132% | ||
Lost | 2530 | -27 | ||||
You can see that the house won more bets than we did, giving it an overall edge of 1.2% which is about right for blackjack or baccarat.
We won 20,073 units after placing 5,000 bets that were collectively worth a total of 158,851 units in action/handle/churn (all terms that describe the combined aggregate of winning and losing bets).
We had to “bet the max” 11 times in 5,000 rounds—once in every 454 bets, on average. Overall, our average bet was worth 32 units. But what matters the most is that although we lost more often than we won, progressive betting enable us to win more when we won than we lost when we lost to the tune of 36/27 = 132%.
The house edge of 1.20% indicated an expected loss (edge x action) of 1,906 units—but progressive betting in this sample gave us a “player’s edge” of 12.6%.
Of course, I am not suggesting that a win like this will happen every time, using this same set of rules, and all those “experts” out there will dismiss these data as being anecdotal, which is just a fancy way of saying that they are unique and therefore irrelevant to the big picture.
But the experts can’t have it both ways.
It’s hard to argue that 5,000 rounds is “not a representative sample” because that many bets would take most players at least 50 hours to play out (far longer playing baccarat!) and that’s a lot of time by anyone’s standards.
The conventional wisdom is absolutely clear: Bet 5,000 rounds against a house advantage of 1.20% and you will lose at least 1.20% of your total action.
What the experts never tell you is that the relentlessly-repeated axiom that any amount bet against a negative expectation must have a negative result only applies if bet values are fixed or randomly selected.
And that’s really what this whole argument is all about.
If you bet the same amount every time, or if you vary your bets randomly according to hunches, whims, gut feelings or the careful study of runes and/or chicken entrails, and if you lose more often than you win, then at the end of the day you will have “made a contribution” to the casino’s bulging coffers.
Bet progressively using discipline, confidence and consistency (the Target method being the smartest way to go!) and when you go to the cashier’s cage, you will be making a withdrawal in cold hard cash instead of counting your losses.
As I said, accurate simulations that mathematically demonstrate the inherent weakness in the house edge at casino games of chance are easy to write and just as easy to validate.
But for some reason, all the vocal champions of the status quo choose to ignore the truth.
It may well be that the same simulation will show multiple losses over hundreds or thousands of iterations—I don’t deny that.
What I do say is that all simulations, mine included, ignore what I call the inertia factor by assuming two things:
- A player must be willing to keep on betting through a prolonged losing streak without taking any defensive action by, for example, dropping back to minimum bets or walking away from an anomalous downturn, and
- The house must be willing to permit bets from 1 to 5,000 units (or any other very large amount) at the same layout.
Neither of the above conditions exist in the real world, so any “proof” that the same betting strategy applied the same way for a bazillion rounds must eventually crash and burn is...worthless.
I have watched countless Martingale bettors escaping the notice of eagle-eyed pit personnel (at least for a while) by placing no more than two or three losing bets (-1, -2, -4) at any one layout before moving on to another table or a different game in search of the single win that will recover all their prior losses plus a profit.
I mentioned blackjack and craps as the best Martingale prospects because of 3-2 (these days, more likely 6-5) paybacks on naturals, “extra” profits from successful splits or double-downs, and the allure of 2x or 3x field payouts on 2 or 12 at craps.
The same potential benefits apply to Target betting, obviously, and the level of aggressiveness applied is entirely a matter of player choice.
I find it tiresome when yet another Target critic whines on about rule changes and “cheating” and the best I can do on that score is provide a link to a web pagewhere I address the charge.
The crux is that there’s only one immutable rule, and that’s the one that kicks in when a win finally comes along in the middle of a recovery series.
Your chances of winning a second consecutive bet are no better or worse after a first mid-series win than they are at any other time—you don’t need to be a gambling “expert” to figure that out.
But it’s your job to see that IF that second or “twin” win occurs, you derive maximum benefit from it.
Table limits have nothing to do with Target’s prospects of long-term profits, but of course house limits do.
You’ll read anti-progression rants that point out that if you’re betting from a $5 start at a table with a $300 maximum, it will take “only” six successive losses before you hit the table limit and then what...?
The What? is easy: You either bet the table limit, then bet it again (or just enough to recover the balance of your prior losses)—or move to another layout with higher limits and bet what’s needed.
You can, if you wish, bet just once at each layout, switching from baccarat to blackjack to craps to roulette or whatever with each successive loss, and your win and loss prospects are mathematically unaffected.
You are only “in trouble” (and it’s not much trouble at that) if you are stuck in a casino where ALL the tables and games have a low house limit.
And even then, you can simply walk away with a losing series unresolved, and resume betting at the same level when you next have access to a casino that permits you to spread wider than at the tin-pot locale where you initially got into trouble.
The numbers—“The Math”—stay the same no matter what.
It’s true that the size of bets Target sometimes requires can be intimidating to someone who’s just starting out on a winning path.
But the strategy builds profits at a steady pace, making it possible to increase your minimum little by little as your burgeoning bankroll allows.
My rule after any winning session is to add half the session profit to my bankroll, putting the other half in my pocket to cover expenses plus wine, women and song or whatever else takes my fancy.
It’s why I haven’t had a losing year since 1989. Tough days, weeks and even months, for sure—but never a losing year.
Seth Theobeau
Nevada
©1978-2013
An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you. One more piece of friendly advice: If you are inclined to use target betting with real money against online "casinos" such as Bodog, spend a few minutes and save a lot of money by reading this._
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