The probability of a 6-loss streak in fair coin flip is 1/64 (or 1/45 in blackjack), and a streak can begin on any hand. So, it will take only 50 fair coin flips or 36 hands of blackjack to provide a 50% risk of ruin with 6-step martingale. A 10% risk of ruin is reached in a mere 10 hands. So theoretically, your risk of ruin is always zero.' Risks in Kaplan's other ventures are less clear-cut. 'It's not like blackjack, where you can program the whole game into a computer,' he says.

Learn how to beat the house with card counting from the pros who've won millions. The best resource for card counting training, community, and info. Risk given no goal and no time constraint - This is the Simple Risk of Ruin formula on Blackjack Attack page 112. The result is the risk of ruin with no limit on the number of hands and no quit point. Simply set the bankroll. Risk given no goal but a time constraint - This.

OK, I'll answer your question strictly in terms of math.

Betting style:
(martingale)
...
In addition...I would play 'never bust' - always force the dealer to make a hand AND beat mine.
...
First, what are the odds of losing 9 straight hands where you never bust.

The odds of winning with the 'never bust' strategy are approximately equal to the odds of being dealt either a 19-21 or 2-11 and upgrading to 19-21, plus the odds of dealer busting. You will win approximately 40% of hands and lose about 50%. Pushes not counting, you will lose about 55% of hands and win 45%.
The odds of losing 9 hands in a row are 0.55^9=1/217. The probability of a 9-hand losing streak can then be found as 1-(1-1/217)^(N-8)...
edit: Nevermind the formula. I've been told this calculation for the risk of a losing streak is oversimplified, and seems to double-count longer streaks. An accurate calculator can be found here: http://www.pulcinientertainment.com/info/Streak-Calculator-enter.html
The correct probabilities are 10.6% in 60 hands, 21% in 120, 39% in 240, 65% in 500 and 88% in 1,000 hands.
---
However, this should be put into context for comparing with other betting patterns. Here is a post I recently wrote elsewhere about martingale, I'll repost it here, tweaked a bit for context.
---
While most betting systems are mathematically neutral, martingale stands out as being mathematically damaging to the player in all long-term performance metrics, such as risk of ruin, SCORE, time to double the bankroll, and, critically, chance to double the bankroll.
For instance, the risk of ruin in typical blackjack with a 64-bet bankroll is 10% in 1,000 hands, 1.8% in 500 hands, or 0.01% in 200 hands. A 6-step martingaler will run out of his 64 bets the first 6-loss streak he gets. The probability of a 6-loss streak in fair coin flip is 1/64 (or 1/45 in blackjack), and a streak can begin on any hand.
So, it will take only 50 fair coin flips or 36 hands of blackjack to provide a 50% risk of ruin with 6-step martingale. A 10% risk of ruin is reached in a mere 10 hands. A 1.8% chance will be exceeded in just 6 hands, since your first 6-hand sequence entails a 2.2% risk of ruin. That is for a bankroll that will last flat-bettors through thousands of hands.
All this while, martingale limits the winnings to a single unit at a time, slowing down the winnings. Even under ideal conditions, perfect 1-0-1 (just what martingale is designed for), a 6-step martingaler needs 128 bets to double his bankroll, a 86% risk or ruin in coin flip or 94% in blackjack.
So while per-bet house edge is unchanged, with a martingale the chance to double a 64-bet bankroll is a mere 14% in fair coin flip, as opposed to 50% for a flat-bettor. This is a mathematical disadvantage, voluntarily creating house edge even in a game that doesn't have any. All martingale provides in the long run is just massively increased risk of ruin, without a corresponding increase in gain.
---I agree that a lot of people have seen the Martingale and variations before. However, not everyone has, and I think it's on the regulars to be able to explain gently why it's a non-working strategy, based on the questions the player asked.
Or keep schtum.
Your ire can be reserved for the point when the poster has revealed themselves to be willfilly ignorant/selling snake oil/unable to follow a logical train of thought.
Both questions could have been answered with some math, and it might just have been that the math would have been enough to convince the OP why it's a bad idea (TM).
As with all forum, what's old too one person is brand new to another, and repeated questions and themes will always appear. Or the forum disappears up its own backside into a insular community of anti-social jackarsery.

Well, you did offer some pretty ridiculous advice--'wait until the table gets hot.' Anyone offering such advice might very well have to be reminded that there is no such thing as a 'hot table', in the meaning of 'the players have recently won, so the players are more likely to win in the immediate future.'

Yeah - I didn't say 'wait until the table gets hot' or anything of the sort. I said that I've never seen a person make 12 passes in a row. I also said that while it is possible, in my 40 plus years of playing craps I've never seen it. Of course the dice don't remember but craps is a very simple, binary game. It is biased to the dark side. Even the house edge shows that. (And although people scoff at small biases I do not. Small errors accumulate into large errors, small advantages accumulate into large advantages. And even if that advantage is on the losing side I will lose less if I play the don't. That is just a cold, hard mathematical fact).
I also said that I have never seen more than 8 field numbers rolled in a row and while I am certain that it has happened I am also certain that it doesn't happen very often. I am also certain that for every set containing 8 field numbers rolled in a row there has been at least one set of 7.n non-field numbers rolled in a row (there being fewer non-field numbers than field numbers). I am also certain that craps is a closed system and that it contains a small number of events and that it regresses to the mean a lot more often than many people credit it with doing.
So if you are going to quote me try actually reading what I say and quoting me accurately. I think I have had the EV Knighthood up to my ass and beyond and I should be doing better things with my life. So if you will pardon me I will leave you now - for good.

Both questions could have been answered with some math, and it might just have been that the math would have been enough to convince the OP why it's a bad idea (TM).

But why should anyone bother to do the math? It's like resorting to a detailed explication of physics and chemistry to show someone why their scheme to turn cotton balls into plutonium won't work.
It's a far better service to simply say to such a person, 'It won't work.' If you explain the math, and by some miracle that person understands that math and agrees with the conclusion, they'll just go back to their basement and cook up some different system in the forlorn hope that the math will validate that new one.
I think the odds of the math convincing the OP that Martingales don't work were about 40,000,000 to one. I respect the various quixotic tries to do so, though.

OK, I'll answer your question strictly in terms of math.
The odds of winning with the 'never bust' strategy are approximately equal to the odds of being dealt either a 19-21 or 2-11 and upgrading to 19-21, plus the odds of dealer busting. You will win approximately 40% of hands and lose about 50%. Pushes not counting, you will lose about 55% of hands and win 45%.
The odds of losing 9 hands in a row are 0.55^9=1/217. The probability of a 9-hand losing streak is 21% in 60 hands, 40% in 120 hands, 54% in 180 hands, 65% in 240 hands, 90% in 500 hands, 99% in 1,000 hands. The formula is 1-(1-1/217)^(N-8), where N is the number of hands played.
---
However, this should be put into context for comparing with other betting patterns. Here is a post I recently wrote elsewhere about martingale, I'll repost it here, tweaked a bit for context.
---
While most betting systems are mathematically neutral, martingale stands out as being mathematically damaging to the player in all long-term performance metrics, such as risk of ruin, SCORE, time to double the bankroll, and, critically, chance to double the bankroll.
For instance, the risk of ruin in typical blackjack with a 64-bet bankroll is 10% in 1,000 hands, 1.8% in 500 hands, or 0.01% in 200 hands. A 6-step martingaler will run out of his 64 bets the first 6-loss streak he gets. The probability of a 6-loss streak in fair coin flip is 1/64 (or 1/45 in blackjack), and a streak can begin on any hand.
So, it will take only 50 fair coin flips or 36 hands of blackjack to provide a 50% risk of ruin with 6-step martingale. A 10% risk of ruin is reached in a mere 10 hands. A 1.8% chance will be exceeded in just 6 hands, since your first 6-hand sequence entails a 2.2% risk of ruin. That is for a bankroll that will last flat-bettors through thousands of hands.
All this while, martingale limits the winnings to a single unit at a time, slowing down the winnings. Even under ideal conditions, perfect 1-0-1 (just what martingale is designed for), a 6-step martingaler needs 128 bets to double his bankroll, a 86% risk or ruin in coin flip or 94% in blackjack.
So while per-bet house edge is unchanged, with a martingale the chance to double a 64-bet bankroll is a mere 14% in fair coin flip, as opposed to 50% for a flat-bettor. This is a mathematical disadvantage, voluntarily creating house edge even in a game that doesn't have any. All martingale provides in the long run is just massively increased risk of ruin, without a corresponding increase in gain.
---

Blackjack Apprenticeship Risk Of Ruin The Following

nice post

Of course - how ignorant of me to forget that single, most important aspect. Oh thank you wise one for setting me on the path to enlightenment.

What did I do?

But why should anyone bother to do the math?
It's a far better service to simply say to such a person, 'It won't work.' If you explain the math, and by some miracle that person understands that math and agrees with the conclusion, they'll just go back to their basement and cook up some different system in the forlorn hope that the math will validate that new one.

I disagree with your comments for two reasons. I think that the reason this website exists is to educate and inform people. By just telling someone something won't work in answer to their question...

So what I can't get my mind around basically is...
First, what are the odds of losing 9 straight hands where you never bust.
Second, since extra profit will be made whenever I get a blackjack (and obviously, the farther into the sequence I am, the higher the profit), how significant is that to the overall final edge?
Any input would be greatly appreciated! I tested this method out on a free game online for around 3 hours (I know, small sample size for sure) and profited $435.

... you are in effect telling them that their question is not valid and is not worth answering. I assume that you have decided that the question is not worth answering mathematically mkl but please don't presume that others on this site feel the same way. I know you like to respond to every post on the site (or at least the overwhelming evidence points to that conclusion) but perhaps you might look at a post such as this one and simply decide not to post anything instead of jumping on it and insulting the poster.
I know (as does anyone who has read your posts) that you don't believe any kind of Martingale system can possibly create an advantage for a player. I agree with you as do most here. If you feel you've explained this to death and have no inclination to take the time to explain it again, you could just ignore the question.
My second point is that having read your posts in the past it seems to me that you are not sufficiently capable of actually performing the math to answer many of these math oriented questions. It's not that you can't add and subtract and multiply and divide; I'm sure you can. It just seems that the breaking down of the questions to be able to create a workable formula is a bit over your head from time to time. Rather than leave the question for someone better suited to provide an answer, you prefer to give some half-hearted quasi-mathematical answer and then deride the person who has asked the question.
I'd say that's what's happened here.
To the OP (Bruski), I'm working on an answer.OK, I'll answer your question strictly in terms of math.

Betting style:
(martingale)
...
In addition...I would play 'never bust' - always force the dealer to make a hand AND beat mine.
...
First, what are the odds of losing 9 straight hands where you never bust.

The odds of winning with the 'never bust' strategy are approximately equal to the odds of being dealt either a 19-21 or 2-11 and upgrading to 19-21, plus the odds of dealer busting. You will win approximately 40% of hands and lose about 50%. Pushes not counting, you will lose about 55% of hands and win 45%.
The odds of losing 9 hands in a row are 0.55^9=1/217. The probability of a 9-hand losing streak can then be found as 1-(1-1/217)^(N-8)...
edit: Nevermind the formula. I've been told this calculation for the risk of a losing streak is oversimplified, and seems to double-count longer streaks. An accurate calculator can be found here: http://www.pulcinientertainment.com/info/Streak-Calculator-enter.html
The correct probabilities are 10.6% in 60 hands, 21% in 120, 39% in 240, 65% in 500 and 88% in 1,000 hands.
---
However, this should be put into context for comparing with other betting patterns. Here is a post I recently wrote elsewhere about martingale, I'll repost it here, tweaked a bit for context.
---
While most betting systems are mathematically neutral, martingale stands out as being mathematically damaging to the player in all long-term performance metrics, such as risk of ruin, SCORE, time to double the bankroll, and, critically, chance to double the bankroll.
For instance, the risk of ruin in typical blackjack with a 64-bet bankroll is 10% in 1,000 hands, 1.8% in 500 hands, or 0.01% in 200 hands. A 6-step martingaler will run out of his 64 bets the first 6-loss streak he gets. The probability of a 6-loss streak in fair coin flip is 1/64 (or 1/45 in blackjack), and a streak can begin on any hand.
So, it will take only 50 fair coin flips or 36 hands of blackjack to provide a 50% risk of ruin with 6-step martingale. A 10% risk of ruin is reached in a mere 10 hands. A 1.8% chance will be exceeded in just 6 hands, since your first 6-hand sequence entails a 2.2% risk of ruin. That is for a bankroll that will last flat-bettors through thousands of hands.
All this while, martingale limits the winnings to a single unit at a time, slowing down the winnings. Even under ideal conditions, perfect 1-0-1 (just what martingale is designed for), a 6-step martingaler needs 128 bets to double his bankroll, a 86% risk or ruin in coin flip or 94% in blackjack.
So while per-bet house edge is unchanged, with a martingale the chance to double a 64-bet bankroll is a mere 14% in fair coin flip, as opposed to 50% for a flat-bettor. This is a mathematical disadvantage, voluntarily creating house edge even in a game that doesn't have any. All martingale provides in the long run is just massively increased risk of ruin, without a corresponding increase in gain.
---I agree that a lot of people have seen the Martingale and variations before. However, not everyone has, and I think it's on the regulars to be able to explain gently why it's a non-working strategy, based on the questions the player asked.
Or keep schtum.
Your ire can be reserved for the point when the poster has revealed themselves to be willfilly ignorant/selling snake oil/unable to follow a logical train of thought.
Both questions could have been answered with some math, and it might just have been that the math would have been enough to convince the OP why it's a bad idea (TM).
As with all forum, what's old too one person is brand new to another, and repeated questions and themes will always appear. Or the forum disappears up its own backside into a insular community of anti-social jackarsery.

Well, you did offer some pretty ridiculous advice--'wait until the table gets hot.' Anyone offering such advice might very well have to be reminded that there is no such thing as a 'hot table', in the meaning of 'the players have recently won, so the players are more likely to win in the immediate future.'

Yeah - I didn't say 'wait until the table gets hot' or anything of the sort. I said that I've never seen a person make 12 passes in a row. I also said that while it is possible, in my 40 plus years of playing craps I've never seen it. Of course the dice don't remember but craps is a very simple, binary game. It is biased to the dark side. Even the house edge shows that. (And although people scoff at small biases I do not. Small errors accumulate into large errors, small advantages accumulate into large advantages. And even if that advantage is on the losing side I will lose less if I play the don't. That is just a cold, hard mathematical fact).
I also said that I have never seen more than 8 field numbers rolled in a row and while I am certain that it has happened I am also certain that it doesn't happen very often. I am also certain that for every set containing 8 field numbers rolled in a row there has been at least one set of 7.n non-field numbers rolled in a row (there being fewer non-field numbers than field numbers). I am also certain that craps is a closed system and that it contains a small number of events and that it regresses to the mean a lot more often than many people credit it with doing.
So if you are going to quote me try actually reading what I say and quoting me accurately. I think I have had the EV Knighthood up to my ass and beyond and I should be doing better things with my life. So if you will pardon me I will leave you now - for good.

Both questions could have been answered with some math, and it might just have been that the math would have been enough to convince the OP why it's a bad idea (TM).

But why should anyone bother to do the math? It's like resorting to a detailed explication of physics and chemistry to show someone why their scheme to turn cotton balls into plutonium won't work.
It's a far better service to simply say to such a person, 'It won't work.' If you explain the math, and by some miracle that person understands that math and agrees with the conclusion, they'll just go back to their basement and cook up some different system in the forlorn hope that the math will validate that new one.
I think the odds of the math convincing the OP that Martingales don't work were about 40,000,000 to one. I respect the various quixotic tries to do so, though.

Blackjack Apprenticeship App

OK, I'll answer your question strictly in terms of math.
The odds of winning with the 'never bust' strategy are approximately equal to the odds of being dealt either a 19-21 or 2-11 and upgrading to 19-21, plus the odds of dealer busting. You will win approximately 40% of hands and lose about 50%. Pushes not counting, you will lose about 55% of hands and win 45%.
The odds of losing 9 hands in a row are 0.55^9=1/217. The probability of a 9-hand losing streak is 21% in 60 hands, 40% in 120 hands, 54% in 180 hands, 65% in 240 hands, 90% in 500 hands, 99% in 1,000 hands. The formula is 1-(1-1/217)^(N-8), where N is the number of hands played.
---
However, this should be put into context for comparing with other betting patterns. Here is a post I recently wrote elsewhere about martingale, I'll repost it here, tweaked a bit for context.
---
While most betting systems are mathematically neutral, martingale stands out as being mathematically damaging to the player in all long-term performance metrics, such as risk of ruin, SCORE, time to double the bankroll, and, critically, chance to double the bankroll.
For instance, the risk of ruin in typical blackjack with a 64-bet bankroll is 10% in 1,000 hands, 1.8% in 500 hands, or 0.01% in 200 hands. A 6-step martingaler will run out of his 64 bets the first 6-loss streak he gets. The probability of a 6-loss streak in fair coin flip is 1/64 (or 1/45 in blackjack), and a streak can begin on any hand.
So, it will take only 50 fair coin flips or 36 hands of blackjack to provide a 50% risk of ruin with 6-step martingale. A 10% risk of ruin is reached in a mere 10 hands. A 1.8% chance will be exceeded in just 6 hands, since your first 6-hand sequence entails a 2.2% risk of ruin. That is for a bankroll that will last flat-bettors through thousands of hands.
All this while, martingale limits the winnings to a single unit at a time, slowing down the winnings. Even under ideal conditions, perfect 1-0-1 (just what martingale is designed for), a 6-step martingaler needs 128 bets to double his bankroll, a 86% risk or ruin in coin flip or 94% in blackjack.
So while per-bet house edge is unchanged, with a martingale the chance to double a 64-bet bankroll is a mere 14% in fair coin flip, as opposed to 50% for a flat-bettor. This is a mathematical disadvantage, voluntarily creating house edge even in a game that doesn't have any. All martingale provides in the long run is just massively increased risk of ruin, without a corresponding increase in gain.
---

nice post

Of course - how ignorant of me to forget that single, most important aspect. Oh thank you wise one for setting me on the path to enlightenment.

What did I do?

But why should anyone bother to do the math?
It's a far better service to simply say to such a person, 'It won't work.' If you explain the math, and by some miracle that person understands that math and agrees with the conclusion, they'll just go back to their basement and cook up some different system in the forlorn hope that the math will validate that new one.

I disagree with your comments for two reasons. I think that the reason this website exists is to educate and inform people. By just telling someone something won't work in answer to their question...

So what I can't get my mind around basically is...
First, what are the odds of losing 9 straight hands where you never bust.
Second, since extra profit will be made whenever I get a blackjack (and obviously, the farther into the sequence I am, the higher the profit), how significant is that to the overall final edge?
Any input would be greatly appreciated! I tested this method out on a free game online for around 3 hours (I know, small sample size for sure) and profited $435.

... you are in effect telling them that their question is not valid and is not worth answering. I assume that you have decided that the question is not worth answering mathematically mkl but please don't presume that others on this site feel the same way. I know you like to respond to every post on the site (or at least the overwhelming evidence points to that conclusion) but perhaps you might look at a post such as this one and simply decide not to post anything instead of jumping on it and insulting the poster.
I know (as does anyone who has read your posts) that you don't believe any kind of Martingale system can possibly create an advantage for a player. I agree with you as do most here. If you feel you've explained this to death and have no inclination to take the time to explain it again, you could just ignore the question.
My second point is that having read your posts in the past it seems to me that you are not sufficiently capable of actually performing the math to answer many of these math oriented questions. It's not that you can't add and subtract and multiply and divide; I'm sure you can. It just seems that the breaking down of the questions to be able to create a workable formula is a bit over your head from time to time. Rather than leave the question for someone better suited to provide an answer, you prefer to give some half-hearted quasi-mathematical answer and then deride the person who has asked the question.
I'd say that's what's happened here.
To the OP (Bruski), I'm working on an answer.