Tuesday, April 26, 2016

Bottom line: If you bet randomly, you will probably lose; If you bet progressively, using a consistent strategy that includes rational self defense, you probably won't. The casinos know this, and you should too.

The bad news, of course, is that if you take on any house game with inadequate funds, the best strategy in the world won't save your bankroll.

I don't spend as much time as I used to bouncing around the web looking for useful insights into gambling because I know that most of the information out there is disinformation.

I'm tackling a couple of common examples of what I call "mythematics" this time because they illustrate how far some people will go to mislead gamblers.

The first holds that anyone promoting any form of betting strategy is foolishly challenging the great wisdom of a long line of mathematical geniuses who, for centuries, have demonstrated that if you lose more often than you win then in the long run you must also lose more money than you win.

The other is a more modern interpretation of the conventional wisdom which says that since every bet in a game of negative expectation is subject to the same negative probability (-1.32% for baccarat, for example), then every bet of any value is subject to the same loss percentage.

So, if in 10,000 rounds you bet $100 500 times for a total of $50,000 four centuries of mathematical geniuses will spin in their graves if you don't lose $50,000 x -1.32% = -$660.

Logically, the same applies to all other bets, regardless of their value, and if in 10,000 rounds you see $500,000 worth of action against a house edge of 1.32%, you'll leave $6,600 behind in the casino's coffers.

It all sounds so sensible and logical.

And if you bet randomly, it's also TRUE.

Progressive betting throws a spanner in the works, as they say in England, because it's not random.

Bets increase in value in response to an anomalous prolonged negative trend, and fall back to the minimum value once prior losses in given sequence of rounds have been recovered, plus whatever modest profit the strategy requires.

So for example, -1, -2, -4, -8, +16 delivers a profit of +1/31 = +3.2% against a house edge of -3/5 = -60.0%.

Expectation (meaning the probable outcome) for the sequence was -60.0% x 31 = -19 units.  And as usual, expectation was WRONG.

What happens with progressive betting (and I don't recommend a simple double-up or Martingale like the one above) is that the next bet value is adjusted after each successive loss in the demonstrably reasonable belief that a run in the house's favour cannot last forever.

Simply put, the objective is to recover prior losses in fewer bets than it took to fall into a deep red hole. 

In the simplistic example above, we lost four bets and won just one, but the win recovered the losses from the four wrong bets that preceded it.

This is all old territory for regular readers of this blog, so I'm simply going to put up some screen shots that demonstrate that the conventional wisdom (and the wisdom of the ages) is right on the money if bet values are random...but is just plain wrong against a progressive strategy.

In the model that supplied the snaps below, Target 3-Play was deployed against 10,000 random outcomes from a RNG set at -1.4%.

Random betting from 1 to 5,000 units per round was applied to the same data set, and wins and losses from both methods were separated into bets above/equal to and below the 2,500-unit mid value.

Logic required that given progressive betting, bets of 2,500 units and above would see a loss/win differential that was lower than either the overall negative expectation, or the loss expected from bets below the mid value.

The fact is that casino games of chance are designed so that extended swings in the house's favour will be relatively rare, but in the long run, the house will win more bets than the player.

There's nothing altruistic or generous about this design.  It simply responds to the plain truth that if casino games were impossible to beat, no one would play them.

And obviously, no punters means no profits.

So, $10,000 of action against a game with a (negative) expectation of 1.32% will probably result in a player loss of at least $132 as long as bet values are randomly selected.

The house percentage is almost always boosted by such factors as player greed, stupidity, insobriety (hence those "free" cocktails) and inadequate funding.

I put a time and date stamp on the model so you can see that these are successive outcomes: 50,000 randomly-generated rounds in all.

AV indicates the actual value of a given data set expressed in percentage terms.

So in the 5th snap above, 5048 losses vs. 4952 wins gave an AV of -96/10000 = -0.96%.

Random bets between 1 and 5,000 units saw a loss of -1.15% which is in the flat AV ballpark.

Target 3-Play, meanwhile, squashed negative expectation by achieving a win against the same data set equal to more than +11.0% of total action.

More importantly, high bets (above 2,500 units) saw an overall positive expectation above +50.0% while low bets (below 2,500 units) recorded a -2.0% AV.

There is nothing uncommon about these results.  And nothing illogical either.

The whole point of progressive betting is to first accept that you are going to lose more often than you win in the long run, and then bet in such a way that when you win, you win more on average than you lose when you lose.

In Sample #1 above, Target's average win value was 122% greater than its average loss value, followed by 109%, 111%, 117% and 128% for a five-session (50,000 rounds) average of +115%.

Apply that average percentage to a notional block of 50,000 outcomes in which the AV proved to be -1.06% with 25,290 losses and 24,710 wins.

Now assume that the average losing bet was $100 and the average winning bet was $115.

Crunch those numbers, and you get losses of $2,520,900 offset by wins worth $2,841,650 giving you a win of $320,750 (+6.0%) and more money than you started with in spite of the fact that, as expected, you lost more bets than you won.

There's no cheating here, no fiddling or faking, just plain and reliable old arithmetic rather than the mythematics so vigorously promoted by the casinos.

Of course, you would be right in surmising that if I pulled up my model and kept pressing the recalc key, eventually I'd see a horrendous flood of red numbers showing that Target 3-Play had crashed and burned, wiping out all its past profits as if by divine ordination.

But here's the thing: Wipeout can only come if a player does nothing whatever in response to a succession of punishing losses, the most appropriate tactic being a suspension of betting and a move to a different game or layout, or even a different casino.

The fact is that streaks lasting longer than three decisions in either direction (LLL or WWW) occur less than 15% of the time in an honest game.

That's not to say that they don't occur often enough to hurt us, but it does tell us that if bad runs keep coming up in the same recovery series or sequence of bets, we need to pay attention.

Sims that "prove" that no betting strategy can beat negative expectation rely entirely on what I call the Inertia Fallacy, and inertia can be interpreted as an acronym for I Never Ever Respond To Insane Anomalies.

Insane anomalies are a fact of life in any game with a house advantage.

A less dramatic name for them is standard deviation.

And casinos depend on unschooled players to respond to punishing downturns emotionally and erratically, throwing good money after bad.

You must at some point increase your bet values in a downturn to have any hope of recovering prior losses.

But you can't do it haphazardly or randomly if you want to bet your way out of a slump.

Money management is the key, and the key depends on discipline and consistency.

It's not always easy.  Often, it's bloody hard work.  But is anything achieved without effort ever worth a damn in the end?

As for the huge bets that Target sometimes requires, think of the risk that the house routinely accepts  because it has faith in long-term factors that are always in its favour.

First is the house edge: 1.0% for blackjack, 1.32% for baccarat, 2.63% for single-zero roulette and so on.

Just as important are the things players can be counted upon to do to cripple their own chances.

These include going to the table with too little money, betting too narrow a spread, drinking "free" cocktails and losing focus and/or their minds, ignoring the arithmetic, and giving up too soon.

And then of course there's greed and ignorance, assisted by erratic, random betting.

All around you in any casino, you'll find rules that gently nudge you towards betting the way the house needs you to.

That includes a narrow ratio between the minimum and the maximum bet permitted at any one layout, 1 to 100 being the most common.

Don't believe the guff you'll read about limits existing for "player comfort" or to ensure that high rollers don't have to rub shoulders with penny-ante Peter Punters.

Limits exist for the house's sake and no one else's, because the house knows that allowing any player to bet a 1 to 5,000 spread at the same game will more often than not prove problematic.

The upside for the casino is that most players faced with a prolonged downturn won't get up and walk away, they'll sit tight in the belief that a bad run will end soon.

Conversely, winners will starting thinking they are invincible and will keep pumping their bets until at last they over-reach and push all their profits into the dealer's tray, plus a hefty penalty for getting uppity.
The best reason for taking big bets in stride and even welcoming them when the strategy requires them is that (surprise!) they're where the money's at.

You will bounce up and down at low bet levels, but a winning strategy really comes into its own when the going gets tough and the hole gets temporarily deep.

In the last summary above, you will see that there were just six max bets, and five of them won

And if in real-time play you could somehow track every bet and get a summary of win percentages above and below the median value, you would see a set of numbers that look something like this:

Blind luck! say the skeptics, when the truth is that by the time a max bet is called for under a very patient and restrained set of rules, the house must be so far ahead in flat bet terms with losses exceeding wins by a double-digit percentage, that a partial offset is mathematically inevitable.

It won't always come as fast as we'd like, but come it will.

Then as soon as a recovery finally arrives, it's time to quietly chalk up another success to discipline and consistency, and start all over again with a minimum bet.

That, of course, is the moment when most punters will lose their heads and decide to press their luck, keeping the chips piled high until they all disappear, never to be seen again.

Strategic betting tells you when you've won enough, and it's time to drop back to a minimum bet.

Strategic betting also makes you follow a strict set of rules, so that you don't have to keep track of the long-term numbers.

Winning any one bet is no more probable when you respond to a break in a losing streak by pumping your bet 4x or more from the previous bet.

But the good news is that it's no less probable either.

And because Target keeps on adjusting bet values in line with the loss to date (LTD) in a recovery series, if you miss one turnaround try, another opportunity will come along soon enough, and you know you will derive maximum benefit from a two win (or twin) mini-streak.

Random betting, which can be defined as any approach which fails to tie bet values to a win target, is what the house needs and expects from you, and most of you will do your duty and blow your chances of getting ahead in the long run.

You have to know at all times how far you are behind and what it's going to take in order for you to win more when you win than you lose when you lose.

Without discipline, confidence and commitment, you are almost certain to go home broke.

I say "almost" because the big draw for all casino games are the winners who get rich in spite of themselves, thanks to blind luck.

If you count on blind luck, you're a fool.  And while fools can win once in a while, like a blind squirrel tripping over a nut, their long-term prospects are very poor indeed.

Here's one last screen shot, until next time.

One of my models permits the random selection of 1,000-round blocks from almost 60,000 rounds of real play submitted to me or logged by me in recent years.

It also offers the option of 1,000 randomly-generated outcomes, along with tests against Zumma Publishing's 1,000-shoe and 600-shoe real baccarat samples.

It is very hard indeed to pull up 1,000 rounds that the Target 3-Play rules fail to beat in spite of a substantial house edge.

And every time the strategy delivers a profit, it thumbs its nose at the mythematical lie that casino games of chance cannot be beaten.

There's a lot of information in the above screen snap which shows why the conventional wisdom about progressive betting and house games is a crock of crap.

Especially worth a look is the line referring to the number of times Target 3-Play delivers a turnaround or recovery from prior losses in just ONE win.

In the summary above, there were 416 recovery/turnaround attempts in 1,000 rounds, and 173 of those (42%) succeeded, raking back all prior losses, plus a modest profit.

Of those recoveries, 129 came with a single win following one or more losses. That's 75% of all recoveries that did not need "twins" to get out of the hole.

And it's not all uncommon for 1-win turnarounds to occur 85% or 90% of the time.

It is fair to say that after pressing the recalc button several dozen times, each of them confirming T3P wins against 1,000 random outcomes with a negative AV, you will see a huge red number at the top of the model...a catastrophic crash 'n burn that could be interpreted as "proof" that God is always on the house's side in the end.

But horror stories like that depend on killer sets of losing streaks such as (and this is a real example) EIGHT consecutive losses, a single win, NINE losses in a row, one win, then -3, +1, -7, +1 and -4, +1.

That amounts to 31 house wins and 5 player wins, for an overall house edge of -26/36 = -72%.

Ask yourself if you would still be pushing out chips and watching them disappear after a downturn like that!

If yes, then you should stay home and set fire to your money and save yourself the expense of going to a casino to give it all away.

Sims (mine included) depend on the total elimination of common sense and good judgment.

Casinos depend on the same formula, and are very rarely disappointed.

And that takes us back to the first lesson: Bet randomly, and you'll lose in the end; bet progressively, with a viable strategy such as T3P, and you'll make steady money.

You will also be harassed, cheated and occasionally banned.

But that's just part of the game...

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 Bovada, spend a few minutes and save a lot of money by reading this.