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Betting systems, progressions and “trends”

• The “streak-seaker
• The “formal progressionist
• The Wong test
• Words of wisdom from gambling luminaries
• Related progression articles

One of the many endemic gamblers' beliefs is that the pattern of your betting can turn you from a loser into a winner. This is based, I believe, on two assumptions:

1) Since gambling games are inherently “streaky”, successful identification of these so-called streaks will lead you to betting low during runs of bad cards and high during the good cards.

2) Since luck evens out over time (the “Law Of Averages”), if you progressively increase your bets during The Bad Times, you'll be betting bigger when The Good Times come a-rollin' - and so recoup your losses and finish ahead.

Both these assumptions are flawed.

The “streak-seeker”

Nobody can deny that streaks - extended runs of predominantly winning and losing hands - exist in gambling games. They have to. In order for streaks to not exist, it would be necessary that all games follow the format of win / loss / win / loss /win / loss / win / loss ad infinitum, never deviating from the pattern of single wins and losses - because as soon as we have just two consecutive wins or losses, we have a “streak”. Since you will rarely play even six hands without at least two back-to-back wins or losses, it's apparent that streaks exist.

So what is incorrect? If streaks exist, and I identify a winning one and raise my bets accordingly, I'll be betting big during a winning streak. If I identify a losing one, and lower my bets accordingly, I'll be betting small during those bad cards. As long as I can capitalise on these patterns, I'll be betting more when I'm winning than I bet when I'm losing. Correct?


It's not that you have incorrectly identified the streak - you haven't. It was there - but do you know it will continue into the future? Unfortunately, you don't. To say “I'm on a winning streak” is to make the apparently superficial mistake of referring to the event in the present, whereas its actual temporal location is the past. There is no way of knowing that the winning streak will continue into the next bet or the one after that, but it's our human nature to confuse this emotionally-charged past event with the “now”. It's not that a conscious decision is taken to believe that the past will continue into the future, it's that the current position in the life of the lucky run in question gets misidentified as a result of the general excitement of the event - it's taken to be still happening, whereas in fact it's finished.

We can ONLY ever be at the end of any series of happenings, because to be somehow “in” them would require of us knowledge of future events - which we clearly don't have.

To say “I'm on a streak!”, though a common and natural exclamation, is strictly speaking incorrect.

All this may seem ridiculously dogmatic: I can't say “I'm on a streak”? I have to say “I've been on a streak but I am no longer”?? Unfortunately, if you do make this fundamental misidentification of your position in the current run of cards, if you do start thinking along the lines of “well, it's going really well so I'm going to push my luck and up the ante a bit”, you run the risk of upping your bets based on a false premise.

The “formal progressionist”

There's another kind of player who, rather than actively looking for winning runs and then raising or lowering his bet, simply structures his wagering based on a pre-determined betting system.

For example, he might bet $10, then if that bet wins increase to $15, then $20, then $25. At this point he might stop and flat-bet $25 until a loss, at which point he'd return to his $10 base-bet; there's an infinite variety of possibilities, and this kind of player is doing nothing in essence different to the "streak-seeker", other than being more systematic in his approach, using a pre-determined pattern to take away the decision making on the spur of the moment that his streak-seeking counterpart is faced with; his increased bets have no better a chance of winning than the other.

An argument put forward in support of this apparently systematic approach is that, since a cluster of consecutive wins will inevitably contain larger bets than a cluster of losses, the progressionist will inevitably come out ahead of somebody flat-betting; to give an example of the thinking: the above scenario of four consecutive wins following the $10 / $15 / $20 / $25 formula would net $70, whereas four consecutive losses at $10 minimum bets would lose only $40.

That may seem an attractive proposition, and there's only one little problem with it. Unfortunately, the one little problem is what invalidates the entire exercise, and that is: although a series of uninterrupted successes wins you more money than the same number of failures loses, the occasions when you increase your bet and LOSE bring things back into balance. In other words, the gains you make during those four consecutive win patterns are cancelled out by the much more frequent two-wins-followed-by-loss scenarios, or one-followed-by-loss, or whatever else.

To give a specific example: you win two then lose; using the 10/15/20/25 format you win $25 and lose $20, for an overall win of $5. However, simply flat-betting $10 a go would have won $20 and lost $10, for an overall win of $10.

All progressions have certain patterns they respond best to and others they respond worst to. It all comes to the same conclusion: they don't work.

The Wong test

In an attempt to give the lie to the streak argument once and for all, blackjack player and author Stanford Wong made a “streak study”, recording the results in his book Professional Blackjack (see “Search For Streakiness”, pages 239 - 244).

A computer simulation of 20 million hands recorded wins, losses and pushes as a function of the previous two hands, for the purpose of highlighting possible changes in the win/lose/push statistics based on preceding combinations. The results are recorded in the table below (reproduction courtesy of Stanford Wong); the left hand column lists the eight possible two-card combinations of win/lose/push, and the three columns to the right show the results for the hand following. For example, row one (win, win) shows the percentages recorded for all the hands following two wins.

two hands
Outcome of this hand
Win %Lose %Push %
win, win43.247.88.9
win, lose43.247.88.9
win, push43.247.88.9
lose, win43.347.88.9
lose, lose43.247.98.9
lose, push43.347.88.9
push, win43.347.88.9
push, lose43.247.88.9
push, push43.247.98.9

Clearly, there is no difference - no two-card combination results in any significant change in the win/lose/push rate of the subsequent hand. The tiny discrepancies, 43.2 / 43.3 and 47.8 / 47.9, result from the relative shortness of the simulation: in order to eradicate ANY differences it would need to have been substantially longer.

(There's a review of Professional Blackjack on the resources page. It's main focus is card counting, but there's of a lot that's of interest and value to all blackjack players, and I highly recommend it.)

Don't raise - or lower - your bets on false pretexts. There is nothing inherently wrong with so doing; if you've been betting $5 a hand, a sudden bet of $50 a hand doesn't have any less a chance of winning. The chances remain equal, the odds remain the same. What DOES change is the volatility of your bankroll. If you always bet $5 a hand, then suddenly change your playing style and throw in regular bets of $50, you will see much greater bankroll fluctuations. If that's what you want, fair enough, but don't make the mistake of thinking that trying to take advantage of the streaks will turn a losing gambler into a winner. It will not. Other things will do this - and a lot of the content of this site is directly geared to that end - but believing in streaks won't.

Words of wisdom from gambling luminaries

I'll conclude with quotes from a couple of leading authorities on gambling theory:

The expectation for a series of bets is the total of the expectations for the individual bets. For instance, if you bet $1 on Red, then $2, then $4, your expectations are -$2/38, -$4/38, and -$8/38. Your total expectation is -$14/38, or (a loss of) about -$.37. Thus, if your expectation on each of a series of bets is -5.26% of the amount bet, then the expectation on the whole series if -5.26% of the total of all bets. This is one of the fundamental reasons why "staking systems" don't work: a series of negative expectation bets must have negative expectation.

(Excerpt from “The Mathematics of Gambling” by Dr E. O. Thorp.)

The number of “guaranteed” betting systems, the proliferation of myths and fallacies concerning such systems, and the countless people believing, propagating, venerating, protecting, and swearing by such systems are legion. Betting systems constitute one of the oldest delusions of gambling history. Betting systems votaries are spiritually akin to the proponents of perpetual motion machines, butting their heads against the second law of thermodynamcs.

(Excerpt from “The Theory of Gambling and Statistical Logic” by Richard A. Epstein.)

Related progression articles

Here is a smattering of articles from around the 'net which describe progressions and analyse their value...or lack thereof.

• BJ 21

The myth of the long run

• BJ Info

The most common myth in blackjack

• BJ Insider

Betting systems and the house edge

• Vegas Click

Betting systems

• Wizard Of Odds

Betting systems are all equally worthless

Frequently asked questions about the gambler's fallacy

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