Blackjack Streaks, Gambling Formula, Probability, Odds:Software to Analyze Blackjack Streaks: Wins (W+), Losses (L-), Busts, Pushes

By Ion Saliu, Founder of Blackjack Mathematics

• Streaks: The probability software calculates the number of like-streaks in a number of trials. For example: how many streaks of exactly 5 consecutive heads in 1000 coin tosses?
• Blackjack, probability and statistical analyzers of thousands of blackjack hands from the perspective of a strict blackjack basic strategy player.

True formulas are always simplicity itself. Simple is the most powerful demonstrative element of Truth. "It is so simple, it is undeniable," good people say.

Let's calculate the number of streaks of losing exactly four consecutive blackjack hands (from the Player's perspective). We symbolize a Dealer's win by L and a player's win by W. We can calculate the number of the streaks consisting of exactly four consecutive losses for the Player.

That is, calculate the number of the streaks in the format WLLLLW. If probability for W = .41 and the probability for L = 50% (give to Caesar what belongs to Caesar, although this is too much... and the Kasino denies it), then the combined probability is: .41 * (.50 * .50 * .50 * .50) * .41 = .01050625 or 1 in 95 hands. Let's not forget there are pushes as well (9%), not only WL. Yes, it is possible, albeit more rarely, that the blackjack player can experience 2-3 such streaks in 100 hands. Equivalently, however (casino fat-cats hate the equivalent thing!), the blackjack player could experience 100-hand sessions with ALL his losing streaks shorter than four! Those are likely sessions with longer player's wins, usually with more frequent dealer's busts, and more pushes too!

Let's change the perspective, axiomatic one. There are 9 pushes (no-decisions) in 100 hands; therefore, 91 hands reach a decision: Win or Lose (from Player's perspective). Dealer wins 50, Player wins 41 of the 91 decision-hands. Thusly, probability for Player's win is now 41 / 91 = 0.45; Player's loss probability is 50 / 91 = 55%.

The calculations for the number of streaks in the format WLLLLW becomes now: .45 x (.55 x .55 x .55 x .55) x .45 = 0.01853 = 1 in 54 BJ hands. WLLLLW is 43% more frequent in 100-hand blackjack sessions than the previous perspective. This new figure is much closer to real-life casino gambling (NOT counting those completely fraudulent online gambling outlets!)

Unfortunately, the bin always contains a few bad apples. Creatures of smallness equivocate simple to insignificant. Or, they say, it is so simple that even average kids knew it! In truth, nobody knew simple before. Not before one individual discovers simple after an elaborate thought process, painstaking at times.

Pascal discovered the simplest formula of probability theory: p = n / N (probability equals number of favorable cases over total number of possibilities). "Simple stuff… I knew it all the way," say bad humans now, the mooks and kooks and lowlifes of the world. Their absurdity becomes evident when you remind them that the simple formula was discovered some two hundred and a few score years ago! When you discovered something, you express it before anybody else. Or, say, that somebody else discovered a Truth before you; you might have been able to deepen the discovery. Be prepared to defend yourself from the heated anger of the sour-grape lowlifes!

That's exactly what my recent writings on gambling streaks triggered (beginning late September of the year of grace 2008). I attracted more anger and hatred, especially from casino guys and competing gambling authors. "You should have kept all that stuff to yourself and WIN big!" they mouthfoamed in intense anger.
"Yeah," I sez, "but you did NOT allow me to play anymore! If you had let me play, I would have been more secretive for longer! For, in the end, Truth must always come to life!"

Just look attentively at this report created by Blackjack. It is for 1000 uninterrupted blackjack hands. You should run the program first for some-million hands. You will get most precise figures for percentages and, especially, the FFG medians. Write them down for future reference. You will memorize them soon. You will no longer need to run the software for a very large number of blackjack hands (number of trials in the Fundamental Formula of Gambling FFG).

The FFG median is an essential element in gambling mathematics. After that, you should run Blackjack for fewer hands. I suggest 200 or even 100 hands at a time. You will notice on a consistent basis that playing fewer hands is the best requirement when gambling at blackjack. Key: The losing streaks for the Player are shorter. The Player can be more aggressive at the blackjack table. Drawback: The winning streaks for Player are also shorter. But, hey, it is not too bad to expect winning streaks of only three or four consecutive hands!

``` Copyright Ion Saliu. All rights reserved SALIU.COM/blackjack.html

Blackjack Analysis ~ IGNORE Pushes
Data File: BJ-NO-Push1000.REP
Total Hands: 1000
Probability p = 45 %

* WIN (W+) Hits: 454  times in 1000 BJ decision hands, or 45.4 %

* The most recent 20 Win (W+) skips:
0  9  8  2  1  2  3  0  0  3  4  2  4  2  0  2  0  0  1  1

* 0 (zero) means Win in two consecutive hands (no skip between wins).

* MEDIAN W+ skip in 1000 hands = 1

* Number of Win W+ skips of 0 = 207 or 20.7 % of 1000 hands
* Number of Win W+ skips of 1 = 115 or 11.5 % of 1000 hands
* Number of Win W+ skips of 2 and over = 132 or 13.2 % of 1000 hands

* The 10 longest Win (W+) skips in 1000 hands:
11  9  8  8  8  7  7  7  7  7

******

* LOSS (L-) Hits: 546  times in 1000 hands BJ decision hands, or 54.6 %

* The most recent 20 Loss (L-) skips:
1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  1  0  1

* 0 (zero) means Lose in two consecutive hands (no skip between losses).

* MEDIAN L- Skip For 1000 Hands = 0

* Number of Loss L- skips of 0 = 298 or 29.8 % of 1000 hands
* Number of Loss L- skips of 1 and over = 248 or 24.8 % of 1000 hands

* The 10 longest Loss (L-) skips in 1000 hands:
8  7  6  5  5  5  5  5  5  5

******

* Dealer BUST (B+) Hits ->  321  times in 1000 hands BJ decision hands, or 32.1 %

* The most recent 20 Bust (B+) skips:
32  0  3  4  2  4  3  2  0  0  1  2  4  2  3  0  3  1  3  0

* 0 (zero) means Bust in two consecutive hands (no skip between busts).

* MEDIAN B+ Skip For 1000 Hands = 1

* Number of Bust B+ skips of 0 = 101 or 10.1 % of 1000 hands
* Number of Bust B+ skips of 1 = 74 or 7.4 % of 1000 hands
* Number of Bust B+ skips of 2 and over = 146 or 14.6 % of 1000 hands

* The 10 longest Bust (B+) skips in 1000 hands:
32  13  13  11  10  9  8  8  8  8

```

In this run, the statistics are close to theoretical calculations (although Player won 1% less than the norm). The theoretical values are based on a 9% hand-advantage for Dealer (see the figures in the 2nd screenshot). These values are very different than what most pundits and casino agents believe in. The results in my reports, however, are much closer to the reality in real-life casinos. Read also:

• Blackjack Dealer Bust: New Software to Calculate Odds, House Edge.

That great probability software, known to the entire world as Streaks, creates this illustrative report for the 0.45 / 0.55 blackjack parameters —

``` Copyright Ion Saliu. All rights reserved SALIU.COM/theory-of-probability.html

Streaks Report 'Calculate Probability p'
Probability p = 41 / 91 = .451
Number of Trials N = 1000

=============================================================================
Streak Lengths       1     2    3    4    5    6    7    8    9   10  TOTAL
=============================================================================
Winning Streaks W   136   61   28   12    6    3    1    1    0    0   453
-----------------------------------------------------------------------------
Losing Streaks  L   112   61   34   19    10   6    3    2    1    1   554
=============================================================================

Uncounted Elements:-7; Distributed as: Win =-3.15 / Loss =-3.85
* If negative, it means the rounding added extra streaks;
e.g. 33.678... became 34 *

The 41 winning hands for Player in 91 blackjack hands (9 hands are pushes)
represents the closest-to-reality blackjack probability.

The theory of streaks can be applied, in incomplete form, by following the
Blackjack Mental System presented in great detail on this Web page:

SALIU.COM/occult-science-gambling.html
```

As you can see, mathematics calculates 2 WLLLLW patterns (exactly 4 consecutive losses) in 100 blackjack hands. Again worth underlining, the Player is strongly advised to play shorter sessions (up to 200 blackjack hands). It is possible for the Player to win a higher percentage of the hands. But, the most important advantage of short blackjack sessions is the lengths of the losing streaks. The losing streaks are shorter for the blackjack Player. A more aggressive martingale can bring the house down!

The following is an application of gambling streaks — My Mental Blackjack System:

• Gambling Mathematics Is Science of Winning / Losing Streaks.

"For you shall forever carry your notebook of streaks on the rugged path of your life! For you shall, at every falling step, get up from that negative streak and emphatically make it positive! And thusly you shall win with a big W."
(From "The Art of Casino War" by The Dawai Lama of Gambling.)

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