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Mission146

For the past month I've been testing a 7 step Martingale system over 100 hand-dealt shoes.
The Wizard states all betting systems are worthless (including Martingale), but it seems like this one works pretty well in the short run.
To my amazement, I managed to win 3471 units of profit over the 100 shoes and I got hit with only one unlucky streak of 7 straight losses in shoe #53. By shoe #57, I was able to completely recoup all losses from that streak.
For all the math people here, what is the probability of reproducing similar results in the casino if my bankroll is large enough for 8 separate sessions (1024 units)?
What is the probability of doubling my bankroll to 2048 units before going broke?
Assume I play EZ baccarat with no banker commission and bet on both banker and player. If I lose 7 hands in a row, I restart my system and bet 1 unit.

1.) The Martingale can, not does work well in the short run. The Martingale is a sytem based on probabilities rather than odds, you're essentially risking $635 to win $5 on a 99%+ probability. The necessary result of this is that the Martingale will rarely fail, but when it does, it will be catastrophic.
The thing about a 99%+ probability is that (and for the sake of simplicity, we'll assume 99%, that and I don'y know the loss rate of Baccarat off the top of my head) 99 wins at $5 bet is $495 and you should be expected to lose once for every 99 wins. If you win $5 99 times and lose $635 once per, you're down. The math on that really is that simple.
2.) 100 shoes is a small sample size. It seems like a lot, because it takes time to play those, but that is a small sample size.
3.) You did perform better than expected, but that should come as no surprise. If nobody ever performed better than expected (the expectation being a loss) then there would be no casinos because nobody would go.
I will answer the other few questions more specifically at a later time unless someone beats me to it.

The thing about a 99%+ probability is that (and for the sake of simplicity, we'll assume 99%, that and I don'y know the loss rate of Baccarat off the top of my head) 99 wins at $5 bet is $495 and you should be expected to lose once for every 99 wins. If you win $5 99 times and lose $635 once per, you're down. The math on that really is that simple.

I'm pretty sure the probability of losing 7 EZ baccarat hands is roughly 1/128 if you bet on banker and player and ignore ties.
If I win a unit 127 times and then get hit by a losing streak, I'll be even.
In the 100 shoes I tested, I was up 1901 units in shoe #53 before a losing streak hit!

but it seems like this one works pretty well in the short run.

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Incorrect tense. This one 'worked' pretty well in the short run. Someone else can do the math, but your odds of doubling your bankroll before going broke is less than 50%. Excatly how low will be up to the more well versed at math, but I'll guess 25%. For whatever its worth, are baccarat minimums and maximiums that far apart that you can even bet 1024 units on one hand?These questions do not deserve careful analysis, so I will just use some quick math to estimate some answers.

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For simplicity, assume the probability of losing 7 in a row is 1 in 128. (It's actually more likely).
It doesn't work exactly like this, but if you assume each hand has an equal an independent chance of starting a 7-hand losing streak, then each hand you have a 1/128 chance of losing those 127 units. The probability of not losing is 127/128, and the probability of not hitting a streak in n hands is (127/128)^n. I'll repeat that this math is a gross oversimplification, but will give an ok estimate.
With around 80 hands in a 8-deck baccarat shoe, you claim you went 53 shoes before hitting a losing streak. This is n = 4240, with an estimated probability of 1 in 277 trillion. Your odds of doing that again (if ever) are astronomical.
On average, you should hit one of these losing streaks every 1.5 shoes. Your martingale system will not work in a casino environment for long.
Remember: the second worst thing that can happen to a new gambler is losing.

With around 80 hands in a 8-deck baccarat shoe, you claim you went 53 shoes before hitting a losing streak. This is n = 4240, with an estimated probability of 1 in 277 trillion. Your odds of doing that again (if ever) are astronomical.
On average, you should hit one of these losing streaks every 1.5 shoes. Your martingale system will not work in a casino environment for long.

Shouldn't n = 1901 since that is how many times the system worked before the losing streak hit?
How did you come up with 1 in 277 trillion?
Also, shouldn't I theoretically hit a losing streak every 4 shoes since on average I'm implementing my system 34 times per shoe?
By the way, I've played hundreds of shoes in the casino over the past decade and I've lost 7 in a row only once or twice the entire time.

For whatever its worth, are baccarat minimums and maximiums that far apart that you can even bet 1024 units on one hand?

There's a casino near me that has a $25 min and $100,000 max bet.
Also, if I lose my 7th bet (64 units), I restart with 1 unit since I should be able to recoup my losses within the next 4 shoes.Here's a random calculator I found, I cannot vouch for its accuracy, but it seems reasonable.
http://www.sbrforum.com/betting-tools/streak-calculator/
Input a series length of 80 (1 shoe), a streak length of 7, and a prob of loss of 51% to see the chance of hitting a 7 loss martingale in 1 shoe is over 28%. Stretch to 160 to see a probability of over 50%.

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By 20 shoes, or 1600 hands, the probability of seeing a losing streak is over 99.9%

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It is inconceivable that you could play 50 shoes (n = 4000) and not see a streak of 7.

Here's a random calculator I found, I cannot vouch for its accuracy, but it seems reasonable.
http://www.sbrforum.com/betting-tools/streak-calculator/
Input a series length of 80 (1 shoe), a streak length of 7, and a prob of loss of 51% to see the chance of hitting a 7 loss martingale in 1 shoe is over 28%. Stretch to 160 to see a probability of over 50%.
By 20 shoes, or 1600 hands, the probability of seeing a losing streak is over 99.9%
It is inconceivable that you could play 50 shoes (n = 4000) and not see a streak of 7.

That calculator, It is not that accurate.
This one is.
http://www.pulcinientertainment.com/info/Streak-Calculator-enter.html
BruceZ at 2+2 repaired the JavaScript
That page has good links to do the math
http://wizardofvegas.com/forum/questions-and-answers/math/4855-ask-the-wizard-correction/
The OP claims to have a better bet selection method than other Bac players.
Always possible to choose more winners than the averages show in a finite number of trials.
It is possible for him to win overall but not for 1 million others that want to play his method.
IMO, very poor instructions on how he plays his method BTW.. in other words
one can not have a computer play 1 billion shoes with his betting instructions. Way to vague.
Even a few blind gorillas can pick winning sports bets at a 60% rate.
Way better than most human cappers.
I am sure one could do the same at playing Baccarat (not equating that the OP is a blind gorilla)
They are still in the large minority.

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It is inconceivable that you could play 50 shoes (n = 4000) and not see a streak of 7.

One of the keys to my system is that I bet with streaks and chops, never against them.
I encountered a banker streak of 9 in the very first shoe.

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In the 4th shoe I encountered a banker streak of 13 and in the 74th & 80th shoes I encountered banker streaks of 12.

How To Deal Blackjack From The Shoes

I've seen 2 separate streaks in the casino that exceeded 20 and after many years of getting wiped out by betting against them, I finally realized it's much wiser to bet with them.

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