• Blackjack Apprenticeship Risk Of Ruin Death
• Blackjack Apprenticeship Risk Of Ruin The Following
• Blackjack Apprenticeship Risk Of Ruin Wisdom

I was explaining the basics of card counting to a stats guy I know, and he pointed something that really stumped me. I don’t get what risk of ruin means, I don’t think. If you have any non-zero risk of ruin, and you play long enough, won’t you always eventually hit a streak bad enough to wipe you out? In which case, what does it mean to have a 5% risk vs. A 2% risk, if everyone busts. For more information Risk of Ruin click here. Round: In Blackjack, a Round starts with no cards on the table, and the player’s bets being placed. A hand is dealt to every player, and the dealer, and the Round ends when those hands have been played through, and the player’s bets have been paid out. 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.

I'm an amateur interested in recreational blackjack. Just like to find out the risk of ruin probability based on these conditions: 1. Dealer stands on S17 2. Double allowed after splits 3. Early surrender 4. Deploying basic strategy but not card counting (am a newbie after all) 5. Goal of increasing bankroll from 40 to 50-60.

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.
---

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.

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It’s wise to know the risks of losing set amounts of money when playing Blackjack games. The more you know about the risks you are taking at the table, the easier it is to control the amount you can potentially lose (or hopefully win) from one session to the next. This article will cover the basics of the “risk of ruin” in Blackjack to help you understand how you can minimize, or increase, the risk involved the next time you sit down at the Blackjack table.

What is risk of ruin?

Risk of ruin is the percentage likelihood of losing a set amount of money over a specific number of hands at the Blackjack table. Ruin is just a way of saying “going broke”. For example, if you decided to take a $100 bankroll and bet $1 on each hand for 100 hands, your risk of ruin would be 0.5% (or a 1 in 200 chance of going broke).

I’ll show you how I worked this out in a moment.

Why learn about the risk of ruin?

Risk of ruin is perfect if:

• You want to stay in control of risk as much as possible.
• You want to know the varying risk for different bet sizes and number of hands.
• You want to clear bonus play-through requirements as quickly but as safely as possible.

Almost every gambler takes risk of ruin in to account when they place their bets, providing that they are sober of course. This article is simply going to help you put some numbers to that intuition.

The Blackjack risk of ruin table.

• The risk of ruin column is on the left.
• The number of hands row goes along the top.
• The centre numbers show the number of betting units. (Don’t worry; I’ll explain all of this very soon.)

Risk of Ruin Blackjack Charts

Risk of Ruin	Number of Hands to Play
	100	200	300	400	500	600	700	800	900
50%	7	11	14	16	18	20	22	24	25
40%	9	14	17	20	23	25	27	29	31
30%	12	17	21	25	28	31	33	36	38
20%	15	21	26	31	34	38	41	44	47
10%	19	27	34	39	44	48	53	57	60
5%	22	32	40	46	52	58	62	67	71
4%	23	34	42	49	55	60	65	70	75
3%	25	36	44	51	58	64	69	74	79
2%	27	38	47	55	62	68	74	79	84
1%	29	42	52	61	68	75	82	88	93
0.5%	32	46	57	66	74	82	89	95	101
0.25%	35	50	61	71	80	88	96	102	109
0.1%	38	54	67	77	87	95	104	111	118
0.01%	45	64	79	91	102	112	122	131	139

Risk of Ruin	Number of Hands to Play
	1000	1200	1400	1600	1800	2000	2500	3000
50%	27	30	32	35	37	40	45	50
40%	33	37	40	43	46	49	56	62
30%	41	45	49	53	56	60	68	75
20%	50	55	60	65	69	73	83	92
10%	64	70	76	82	88	93	105	116
5%	76	83	90	97	104	110	124	137
4%	79	87	95	102	108	114	129	143
3%	83	92	100	107	114	121	136	151
2%	89	98	107	114	122	129	145	161
1%	99	108	118	126	134	142	160	177
0.5%	107	118	128	137	146	154	174	192
0.25%	115	126	137	147	156	166	187	206
0.1%	125	138	149	160	170	180	202	223
0.01%	148	162	175	188	198	212	236	261

Both risk of ruin tables were originally published on the Wizard of Odds blackjack risk of ruin article.

The 3 variables involved with risk of ruin in Blackjack.

Whenever you work out risk of ruin in Blackjack, there are 3 variables you need to consider.

1. The number of betting units (this is just your bankroll divided by bet size).
2. The set number of hands to be played.
3. The risk of ruin.

As long as you know at least 2, any 1 of the 3 remaining variables can be worked out using the table above.

Example 1: Working out your risk of ruin.

Let’s say that you have a $200 bankroll and you want to play 300 hands whilst betting $5 on each hand. You now decide that you want to work out your risk of ruin for this session.

By betting $5 on each hand with our $200 bankroll, we have 40 betting units in total ($200 / $5). Now we have 2 our variables, we can figure out our risk of ruin from the table.

Firstly we look across the top row to find the number of hands we wish to play (300, remember?). We then look down this column to find the betting units closest to 40. Luckily 40 is perfectly set in the table there already, so we can look across to the left to the risk of ruin column and see that our risk of ruin for this session will be 5%.

Easy stuff really. All you need to know is 2 variables/numbers from the table and you can work out your risk of ruin, the number of hands you should play or the number of betting units required.

Example 2: Working out your ideal betting units.

A more probable situation is where you want to control your risk of ruin before you play. So for example, let’s say you have a $1000 bankroll and you want your risk of ruin to be 1% over 500 hands. How big should your bets be?

If we look at 500 hands and the 1% risk of ruin on the table, it tells us that we should have 68 betting units behind us to achieve these figures. So what’s 68 betting units from $1000?

Blackjack Apprenticeship Risk Of Ruin Death

Easy, just divide $1000 by 68 and we get $14 (or $14.7 to be precise). Therefore to play 500 hands with just a 1% risk of ruin, we should only bet $14 on each hand we play.

Evaluation of risk of ruin in Blackjack.

Risk of ruin applies to all forms of gambling, whether it’s; Sports Betting, Texas Hold’em Poker, Bingo or Casino games like Blackjack (of course).

Even though we all subconsciously work out rough ideas of the risk of ruin in our heads, it’s far better to have solid numbers to work with so that we can be more precise with the money we are putting at risk. The last thing any of us want is to be surprised by losses that we never could have expected.

I realise that I’ve left out an example for working out how many hands you should play if you have a risk of ruin in mind and have already worked out your ideal betting units, but it should be fairly easy to figure out if you understood the first two examples.

The mathematics involved with risk of ruin may look a little intimidating at first, but trust me when I say that it’s so much easier than it looks if you spend a little time working with it.

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