Analysis of Blackjack Streaks: Wins (W+), Losses (L-), Busts

- Streaks.EXE: 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.exe, 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 = .48 and the probability for L = 52% (give to Caesar's what belongs to Caesar), then the combined probability is: .48 * (.52 * .52 * .52 * .52) * .48 = .016845963 or '1 in 59 or 60' hands. Mathematics of gambling expects such a streak once every 60 hands, or twice in 120 blackjack hands. Yes, it is possible, albeit rarely, that the blackjack player can experience 3 such streaks in 100 hands. Equivalently, however (casino fat-cats hate the equivalent thing!), the blackjack player could experience 100-hand sessions with losing streaks shorter than four! Those are likely sessions with longer player's wins, usually with more frequent dealer's busts!

Unfortunately, the bin always contains a few bad apples. Bad people equivocate Simple for 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. 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!

Exactly what my recent writings on gambling streaks triggered (beginning late September of the year of grace 2008). 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 no more! If you had had let me play, I might 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.exe. It is for one hundred consecutive 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).

The FFG median is an essential element in gambling mathematics. After that, you should run Blackjack.exe for fewer hands. I suggest 100 or even 50 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 shorter. But, hey, it is not too bad to expect winning streaks of only three or four consecutive hands!

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Data File: Blackjack.REP Total Hands: 100 * WIN (W+) Hits: 48 times in 100 hands or 48 % * The most recent 20 Win (W+) skips: 0 0 5 3 0 1 0 0 1 2 0 2 0 0 2 1 7 1 0 0 * 0 (zero) means Win in two consecutive hands (no skip between wins). * MEDIAN W+ skip in 100 hands = 0 * Number of Win W+ skips of 0 = 26 or 26 % of 100 hands * Number of Win W+ skips of 1 and over = 22 or 22 % of 100 hands * The 10 longest Win (W+) skips in 100 hands: 7 5 5 3 3 3 3 3 2 2 * LOSS (L-) Hits: 44 times in 100 hands or 44 % * The most recent 20 Loss (L-) skips: 2 0 0 0 0 1 0 0 2 3 1 3 4 0 1 1 0 0 0 0 * 0 (zero) means Lose in two consecutive hands (no skip between losses). * MEDIAN L- Skip For 100 Hands = 0 * Number of Loss L- skips of 0 = 22 or 22 % of 100 hands * Number of Loss L- skips of 1 and over = 22 or 22 % of 100 hands * The 10 longest Loss (L-) skips in 100 hands: 13 4 4 3 3 3 3 3 2 2 *** Number of ties (pushes) P: 8 times in 100 hands or 8 % * Dealer BUST (B+) Hits: 25 times in 100 hands or 25 % * The most recent 20 Bust (B+) skips: 11 2 0 0 1 7 0 2 1 9 0 0 2 2 4 3 11 4 3 0 * 0 (zero) means Bust in two consecutive hands (no skip between busts). * MEDIAN B+ Skip For 100 Hands = 2 * Number of Bust B+ skips of 0 = 7 or 7 % of 100 hands * Number of Bust B+ skips of 1 = 4 or 4 % of 100 hands * Number of Bust B+ skips of 2 = 4 or 4 % of 100 hands * Number of Bust B+ skips of 3 and over = 10 or 10 % of 100 hands * The 10 longest Bust (B+) skips in 100 hands: 11 11 9 8 7 4 4 3 3 3 * BlackJack Winning Pattern For Player* W+ = Win; L- = Loss; P = Push B+ = Dealer Bust; N- = Dealer No-Bust Hand Result Dealer # W/L/P Bust(B/N) 1 W+ N- 2 W+ N- 3 L- N- 4 L- N- 5 L- N- 6 L- N- 7 L- N- 8 W+ N- ... 15 W+ B+ 16 W+ B+ 17 W+ B+ 18 L- N- 19 W+ B+ 20 L- N- 21 P N- ... 45 W+ B+ 46 L- N- 47 L- N- 48 W+ B+ 49 L- N- 50 W+ N- 51 W+ B+ 52 W+ N- 53 P N- 54 W+ N- 55 W+ N- 56 W+ B+ 57 W+ N- 58 W+ N- 59 W+ N- ... 85 W+ N- 86 W+ B+ 87 L- N- 88 L- N- 89 W+ N- 90 W+ N- 91 W+ N- 92 P N- 93 L- N- 94 L- N- 95 W+ B+ 96 L- N- 97 W+ B+ 98 W+ B+ 99 L- N- 100 W+ B+

In this run, the dealer busted less than the norm: 25%, instead of 28%. On the other hand, the Player won a higher percentage than the norm. This emphasizes the advise to play shorter hands. It is possible for the Player to win a higher percentage of the hands. But, the most important element of short blackjack sessions is the lengths of the losing streaks. The losing streaks are shorter for the blackjack Player.

*"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".)

Parpaluck,

Kasino Pluck At-Large