The quote above is from Christopher Hitchens, an author and philosopher who has the temerity to suggest that evidence is an important prerequisite for belief.
Those who doubt the existence of the house advantage at casino games of chance need only venture money and time to gather their own evidence that, barring blind luck, winning does not come easy.
It is also mathematically demonstrable (a pencil stub and the back of an envelope will do) that if you lose more bets than you win, you will most likely lose more money than you win.
But credulity begins to strain past breaking point when the mathematicians who bolster the gambling industry's disinformation machine insist that the numbers that support the house edge can under no circumstances be used to render it ineffectual.
A pencil and a scrap of paper confirms that if you can consistently win more when you win than you lose when you lose by a percentage significantly greater than the prevailing house bias, losing more bets than you win will not cost you money.
If in 100 bets against a 2% house edge your 49 winning bets bring add more chips to your stash than your 51 losing bets take away, you will end up ahead of the game in spite of negative expectation.
And if you can keep doing that again and again, you will soon become your local casino's worst nightmare.
Academic mathematicians (most of whom are way too smart to gamble), insist on a series of gambling axioms that beggar belief.
One is that blocks of outcomes from casino house games (blackjack, baccarat, craps and roulette among them) are uniquely random and therefore have no patterns or cycles that can be studied, and then relied upon to predict future results.
Another is that computer simulations based on random number generators (RNGs) very rapidly produce outcomes that closely match those that will be encountered in a real-time game of chance.
A third is that because of Rule #1 above, any sample of past outcomes, however large or objective - verifiable and unpolluted might be another way of putting it - is anecdotal and therefore totally irrelevant to any study of gambling, which is in itself a fatuous undertaking.
There is no evidence to support any of those contentions, but the position the "experts" take is much like a firm parent wagging a finger at an errant child: "It's so because I said so."
First, patterns.
Here are screenshots from two iterations of an Excel file that uses the Windows RNG to supply 5,000 outcomes in objective order with the house edge set at (-)1.5%.
SS#1 ended up with an actual house bias of more than 3.7% overall, which happens. Often.
Target betting relies on paired or "twin" wins to achieve turnaround for a recovery series, and you will see that in spite of the house bias, there were almost as many paired wins (339) as there were paired losses (343).
The simulation does not "double dip" meaning that three wins in a row do not count as both a double and a triple. This confirmed by the "streaks total" numbers on each side, which closely approximate the total number of wins and losses, each pair consisting of two bets, each triple, three bets, and so on.
Given 5,000 rounds, there were more of each category of losing streaks (pairs, triples, quads and so on) than there were matching winning ones, which we would expect in a sample with a high house edge overall.
In the second SS, there was a negligible house edge, which also happens. Not often enough.
There, twins, triple wins, quads and so on matched or exceeded the frequency of their "opposite numbers" but all in all, the difference was not worth much.
The file generates a new set of 5,000 rounds with each tap of the F9 recalc key, and anyone who would like to study it more closely is more than welcome to e-mail me for a copy.
I know I am safe in using a low-grade, less than perfect RNG because mathematicians everywhere love them to PCs (sorry) and will bravely stand up for them as accurate simulations of a real game.
So now to that second preposterous claim: the one about RNGs being reliable indicators of how an actual casino table game will apply its known pro-house percentage.
For anyone betting randomly or wagering flat or fixed sums, a prolonged negative trend or pattern is very likely to prove fatal, and it is possible that any attempts at damage control will ultimately fail.
"Damage control" in this context means either reducing bet values to ride out a negative trend of unknown duration, or walking away from a beating in progress hoping for a friendlier pattern at a different layout or game.
The same does not apply to a target player who has full confidence that as long as he has not yet reached his maximum bet value, two consecutive wins will get him out of trouble.
What makes the use of RNG output against a betting strategy both disingenuous and reprehensible is the knowledge that human beings have an essential role to play in the gambling process.
Any RNG-reliant sim, mine included, demands the assumption that a player would make no attempt to defend himself against a prolonged negative trend, either by varying his betting policy or walking away from the game and resuming play elsewhere.
Add this to the fact that sims also exclude cards, shoes, dice, wheels, dealers, money and real time, and the mathematicians who depend on them as indicators of actual play do not seem so smart after all.
I am much more comfortable with actual output from real games, so here is a streak analysis of a block of 5,000 bets taken at random from the BST blackjack trial that is still ongoing. (OK, not wholly random, because I took today's date, 0517, and extracted outcomes 517 through 5016 from BST blocks #5 and #6).
As you can see, there's not a whole lot of difference between the blackjack analysis and those for two RNG samples set at a 1.5% house edge. I would have preferred a clear negative expectation, but this is what happens when you select data at random: 4,884 rounds from BST05 and 16 from BST06.
Repeating patterns are everywhere in the course of any game of chance. But unless you know how to be ready for them so that you can use them to your advantage, that knowledge will be of no help to you.
You will not be able to see them coming, so you must bet in such a way that whenever favorable patterns occur, you will derive maximum benefit from them.
Successful betting, like so much in life, depends on good timing. But "good" does not have to mean "accidental" if you have a plan.
Skeptics often point to the size of the recommended bets for target play, usually because they do not understand that a narrow spread and a low maximum will invariably result in more action - and therefore more risk - than the levels I call for.
Here are some more patterns, tracking maximum wagering in two very large samples of baccarat outcomes, plus 80,000 or so rounds of "real" blackjack against Ken Smith's Blackjack Strategy Trainer.
Once again, any one set of data looks pretty much like any other...
The summaries at the bottom of each of these panels probably provide enough information for most readers.
Those of you who are more detail oriented might want to know the following:-
- The numbers in the second column refer to lines in each separate sample with the overall actual value (AV) to the right, indicating how many bets the "house" was ahead at the moment when the bet level hit the max.
- The AV for the series can be deduced from the next two columns to the right, which show first the series starting line, then the AV at that point.
- Skeptical mathematicians will often claim that there is no reason to hope that once the bet limit has been reached, robbing target betting of its "wiggle room", an egregious negative trend will abate sufficiently to permit recovery. This is invariably not the case, as columns 6 (ending line #) and 7 (AV at that point) confirm.
- The reason for predictable offsets to a very unusual house spike is shown in column 8, in bright red numerals: the series-to-date house edge at the moment when the first "max" bet was required. The average is around -50% and since generally it requires at least 25 bets to dig that deep a hole, numbers that large do not happen often.
- The next column to the right shows how much deeper the "hole" became before recovery was achieved. Usually not much, but once the max has been reached, the bankroll must be large enough to withstand an occasional ongoing slump before turnaround.
- Next comes the number of bets in the whole series, followed by the number of rounds it took to get into trouble in the first place.
The three separate summaries are very similar in many ways, confirming that outside of our inability to predict the outcome of the very next wager are options that enable us to win consistently in spite of the house advantage.
I have gone to great lengths here to refute the idiocy of some mythematical assertions with evidence, rather than without it, as Mr. Hitchens suggests in the quote at the top of this post.
Mr. Hitchens specializes in skewering traditions and attitudes that he believes have no basis in reality and no place in modern times.
The standard academic prohibition of the study and use of past outcomes is perhaps the most idiotic gambling axiom of them all, worthy of his attention if he were ever to turn it to earthly matters.
We cannot predict the outcome of the very next bet, or any one bet at any one point in the future.
We all understand that, with many of us falling back on the old cliche, "that's why they call it gambling..."
But when bets in quantity are studied collectively rather than one by one, distinctive patterns always emerge, as they must.
Denying the validity of analysis and its potential for prediction in "big picture" terms is both illogical and unscientific.
What on earth could make gambling's math distinct from any other kind of math? Nothing, that's what.
Perhaps there is one very good reason why house-trained mathematicians seeking to support the "you can't win" conventional wisdom refuse to accept the relevance of prior outcomes.
The study of what's past will invariably prove them wrong.
And wrong is something an academic (especially one with an agenda) hates to be.
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.
_ttern
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