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What is Pabrai's Blackjack Secret?


Mephistopheles

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Exactly. Bunch of nonsense. Maybe he won but nor martingale nor reverse martingale work. If a single round of a game has a negative expected value and results are not correlated nothing you can do with bet sizes or house limits or whatever else you can think of will change that the end result still has a negative expected value. If only making money was that easy ..

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There's a roulette system called Reverse Labouchere that claims to have broken the banks in Europe and the strategy is replicable in blackjack - probably even more so because there's no "0" or "00" so your odds can be better.

 

There is a book called Thirteen Against the Bank that describes how they did it (pretty interesting read).  Roughly speaking the Labouchere method uses the premise of a near 50/50 bet (i.e. a blackjack hand) and if you win, you pocket the money and if you lose you double down over and over until you win (its more complicated than that but that's the general gist).  The problem was that if you went on a losing streak you would hit the bet limit before you could win back the original bet - and the combined bets would make you broke.  So they reversed it and if you won you would double down over and over again until you lost.  If you went on a run of doubling your bet each time you would hit the casino limit at which point you would start over at the minimum bet.

 

I read it like 20 years ago and I'm shocked given all the blackjack card counting books and movies this hasn't got more light shone on it.

 

I can assure you with 50/50 odds, mathematically your EV is 0. Blackjack without counting and perfect play is like 49.5 / 50.5, so you still have a negative EV, no matter how you "double down" or choose to take your profit.

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Yup. Thats why the casinos running 2 decks and playing them through was gold. If the deck was 70% played and loaded with high cards on the back end you knew you where good, and with the dealer showing a 5 doubling down with pretty much anything, including say an A/9 pays off. Or splitting 10s. Good luck doing that with 12 decks that get reshuffled halfway through.

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Card counting doesn't allow you to win more hands on average, only to win more money on average by being able to scale your bets when the odds become more attractive.

 

This is not purely true.  If the count is significant enough in either direction it can influence your hit/stand/split/double down decisions as well, increasing the % of hands you win.

 

But yes varying your bet size as the count changes is the main edge, by far.

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There's a roulette system called Reverse Labouchere that claims to have broken the banks in Europe and the strategy is replicable in blackjack - probably even more so because there's no "0" or "00" so your odds can be better.

 

There is a book called Thirteen Against the Bank that describes how they did it (pretty interesting read).  Roughly speaking the Labouchere method uses the premise of a near 50/50 bet (i.e. a blackjack hand) and if you win, you pocket the money and if you lose you double down over and over until you win (its more complicated than that but that's the general gist).  The problem was that if you went on a losing streak you would hit the bet limit before you could win back the original bet - and the combined bets would make you broke.  So they reversed it and if you won you would double down over and over again until you lost.  If you went on a run of doubling your bet each time you would hit the casino limit at which point you would start over at the minimum bet.

 

I read it like 20 years ago and I'm shocked given all the blackjack card counting books and movies this hasn't got more light shone on it.

 

I can assure you with 50/50 odds, mathematically your EV is 0. Blackjack without counting and perfect play is like 49.5 / 50.5, so you still have a negative EV, no matter how you "double down" or choose to take your profit.

 

Actually with 50/50 odds, the casino would go broke on roulette.  I've turned $50 into a couple thousand dollars numerous times in just a few hours without losing my bankroll in roulette...but you have to have high table limits and low minimum bets, and ideally either 0 or 00, but not both.  European roulette only has 0, while American roulette has both. If you can find European roulette tables...play them instead of American.

 

Why only a couple thousand dollars?  Because the table limit at the casinos I've played is $500 or $1000.  You start at $5 and double down on either red or black after a run of at least 5 reds or 5 blacks...so you have to be patient.  Every time you win, you start at $5 again.  Every time you lose, you make sure you double down on the subsequent bet.  You'll only be able to double-down 5 or 6 times before hitting the table limit, so you only bet once you see 5 reds or 5 blacks in a row.

 

Yes, yes, your probability of winning on any single spin is 50/50, but the probability of 7,8,9 in a row of the same color becomes less and less likely.  This takes time, because 5 blacks or 5 reds in a row only come up every 20-30 minutes or so.  I used to do this in my 20's and often it would take 5-10 hours of patiently playing.  But I never lost my bankroll, and I did it at least 25-30 times, usually turning a $50 bankroll into $900-$1500.  Often you would win small amounts until your bankroll increased in size, eventually allowing you to take slightly larger initial bets of $25-50.  But the number of times you double-down would decrease whenever you were wrong.  On the rare occasion 0 would show up and you start over at smaller bets...on rare occasions, you would have lost all that you gained that day and walk away with your $50 bankroll.

 

I've never played roulette in Vegas, but I hear the limits are around $10-15K per bet.  When I started investing after learning about Buffett and value investing, I promised myself that I would never gamble again, and I haven't.  I understand that there are online roulette games with very high limits.  I haven't tried them, nor have the urge to try them.  You have less than 50/50 odds playing roulette...American or European.  Going back to Mohnish's example, if you are right about your stocks even just 55-60% of the time, and you can choose your punches, why do anything else!  Cheers!

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Actually with 50/50 odds, the casino would go broke on roulette.  I've turned $50 into a couple thousand dollars numerous times in just a few hours without losing my bankroll in roulette...but you have to have high table limits and low minimum bets, and ideally either 0 or 00, but not both.  European roulette only has 0, while American roulette has both. If you can find European roulette tables...play them instead of American.

 

Why only a couple thousand dollars?  Because the table limit at the casinos I've played is $500 or $1000.  You start at $5 and double down on either red or black after a run of at least 5 reds or 5 blacks...so you have to be patient.  Every time you win, you start at $5 again.  Every time you lose, you make sure you double down on the subsequent bet.  You'll only be able to double-down 5 or 6 times before hitting the table limit, so you only bet once you see 5 reds or 5 blacks in a row.

 

Yes, yes, your probability of winning on any single spin is 50/50, but the probability of 7,8,9 in a row of the same color becomes less and less likely.  This takes time, because 5 blacks or 5 reds in a row only come up every 20-30 minutes or so.  I used to do this in my 20's and often it would take 5-10 hours of patiently playing.  But I never lost my bankroll, and I did it at least 25-30 times, usually turning a $50 bankroll into $900-$1500.  Often you would win small amounts until your bankroll increased in size, eventually allowing you to take slightly larger initial bets of $25-50.  But the number of times you double-down would decrease whenever you were wrong.  On the rare occasion 0 would show up and you start over at smaller bets...on rare occasions, you would have lost all that you gained that day and walk away with your $50 bankroll.

 

I've never played roulette in Vegas, but I hear the limits are around $10-15K per bet.  When I started investing after learning about Buffett and value investing, I promised myself that I would never gamble again, and I haven't.  I understand that there are online roulette games with very high limits.  I haven't tried them, nor have the urge to try them.  You have less than 50/50 odds playing roulette...American or European.  Going back to Mohnish's example, if you are right about your stocks even just 55-60% of the time, and you can choose your punches, why do anything else!  Cheers!

 

Parsad, I have a ton of respect for you. Both Casinos and Gamblers are subject to variance and gambler's ruin, no doubt there.

 

From a purely mathematical point of view, the strategy in the you outlined still has a negative EV since Roulette is designed with a house advantage. Each spin is memoryless, so even if the preceding 100 spins were red, the probability of the next spin being red/black is still 48.60% and green 2.70%, which is the error in your statement. Any winnings you have are due to variance (and I suspect, as we are human, due to a biased memory). I'm not doubting you made money, but as your number of bets increases, your winning % approaches the true probability, and you will lose money.

 

In real life however, there may be some tricks? In Thorpe's autobiography, he tried to create a machine to calculate final ball position based on starting position and velocity. There may be table defects as well. If you find such a table, I suggest you abandon the double down strategy, choose a consistent bet size to minimize risk of gamblers ruin, and ride out the winnings :)

 

Edit: I'll throw in a little more. Changing bet size works only if the odds are shifting. When counting cards, you have someone bet a low amount until the count in the deck is high (signalling a higher player edge), then you signal someone to come over to bet with a much higher amount. In roulette, the odds do not change, so there is no advantage to any type of double down strategy.

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I'm surprised and disappointed to see this quackery on this board. If the EV of an event is neutral and events are uncorrelated, when you bet a million your expected value is a million. Doesn't matter if you bet 1x 1m, 10x 100k or 100.000x 10 dollar. You can only change the distribution of possible outcomes, not the expected value of all possible outcomes. With Martingale you change the distribution in such a way that there's a probable profit but a tail risk of gigantic losses. With reverse Martingale it's the other way around. But both have the same expected outcome in the long run. If you made money using one of these strategies: congratulations, you were lucky! The same holds for the house limit: it can change the distribution of possible outcomes but not the expected value. It is simply ridiculous to think that a roulette wheel with a house limit of $100 is unexploitable but a roulette wheel with a house limit of $100.000 can be easily exploited.

 

This is such a fundamental and basic tenet of statistics that I personally am tempted to say you should not be managing money if you don't understand (or even worse: don't believe) this concept. At the very least you should follow some math courses :) .

 

https://en.wikipedia.org/wiki/Optional_stopping_theorem

 

The optional stopping theorem can be used to prove the impossibility of successful betting strategies for a gambler with a finite lifetime (which gives condition (a)) or a house limit on bets (condition (b)). Suppose that the gambler can wager up to c dollars on a fair coin flip at times 1, 2, 3, etc., winning his wager if the coin comes up heads and losing it if the coin comes up tails. Suppose further that he can quit whenever he likes, but cannot predict the outcome of gambles that haven't happened yet. Then the gambler's fortune over time is a martingale, and the time τ at which he decides to quit (or goes broke and is forced to quit) is a stopping time. So the theorem says that E[Xτ] = E[X0]. In other words, the gambler leaves with the same amount of money on average as when he started. (The same result holds if the gambler, instead of having a house limit on individual bets, has a finite limit on his line of credit or how far in debt he may go, though this is easier to show with another version of the theorem.)

 

 

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There's a roulette system called Reverse Labouchere that claims to have broken the banks in Europe and the strategy is replicable in blackjack - probably even more so because there's no "0" or "00" so your odds can be better.

 

There is a book called Thirteen Against the Bank that describes how they did it (pretty interesting read).  Roughly speaking the Labouchere method uses the premise of a near 50/50 bet (i.e. a blackjack hand) and if you win, you pocket the money and if you lose you double down over and over until you win (its more complicated than that but that's the general gist).  The problem was that if you went on a losing streak you would hit the bet limit before you could win back the original bet - and the combined bets would make you broke.  So they reversed it and if you won you would double down over and over again until you lost.  If you went on a run of doubling your bet each time you would hit the casino limit at which point you would start over at the minimum bet.

 

I read it like 20 years ago and I'm shocked given all the blackjack card counting books and movies this hasn't got more light shone on it.

 

I can assure you with 50/50 odds, mathematically your EV is 0. Blackjack without counting and perfect play is like 49.5 / 50.5, so you still have a negative EV, no matter how you "double down" or choose to take your profit.

 

Actually with 50/50 odds, the casino would go broke on roulette.  I've turned $50 into a couple thousand dollars numerous times in just a few hours without losing my bankroll in roulette...but you have to have high table limits and low minimum bets, and ideally either 0 or 00, but not both.  European roulette only has 0, while American roulette has both. If you can find European roulette tables...play them instead of American.

 

Why only a couple thousand dollars?  Because the table limit at the casinos I've played is $500 or $1000.  You start at $5 and double down on either red or black after a run of at least 5 reds or 5 blacks...so you have to be patient.  Every time you win, you start at $5 again.  Every time you lose, you make sure you double down on the subsequent bet.  You'll only be able to double-down 5 or 6 times before hitting the table limit, so you only bet once you see 5 reds or 5 blacks in a row.

 

Yes, yes, your probability of winning on any single spin is 50/50, but the probability of 7,8,9 in a row of the same color becomes less and less likely.  This takes time, because 5 blacks or 5 reds in a row only come up every 20-30 minutes or so.  I used to do this in my 20's and often it would take 5-10 hours of patiently playing.  But I never lost my bankroll, and I did it at least 25-30 times, usually turning a $50 bankroll into $900-$1500.  Often you would win small amounts until your bankroll increased in size, eventually allowing you to take slightly larger initial bets of $25-50.  But the number of times you double-down would decrease whenever you were wrong.  On the rare occasion 0 would show up and you start over at smaller bets...on rare occasions, you would have lost all that you gained that day and walk away with your $50 bankroll.

 

I've never played roulette in Vegas, but I hear the limits are around $10-15K per bet.  When I started investing after learning about Buffett and value investing, I promised myself that I would never gamble again, and I haven't.  I understand that there are online roulette games with very high limits.  I haven't tried them, nor have the urge to try them.  You have less than 50/50 odds playing roulette...American or European.  Going back to Mohnish's example, if you are right about your stocks even just 55-60% of the time, and you can choose your punches, why do anything else!  Cheers!

 

This is probably a fun way to do some mental exercise, practice discipline, and stretch your night at the casino rather than risk being done with your risk allotted capital in a few minutes, but you are basically just tricking yourself into mentally getting comfortable making the same wager you could make randomly walking up to the first table you see upon arrival. Mark Wahlberg basically does this(well, the opposite of it) in The Gambler(a mediocre film about a degenerate gambler) and outside of his uncanny ability to win 7 hands in a row on the regular without ever knowing he always loses the 8th....its the same concept. But not much different than any other way of gambling.

 

At least with investing, should your process generally be right, a short term loss is beneficial, and, well, a short term win is always fun. Win/win.

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Actually with 50/50 odds, the casino would go broke on roulette.  I've turned $50 into a couple thousand dollars numerous times in just a few hours without losing my bankroll in roulette...but you have to have high table limits and low minimum bets, and ideally either 0 or 00, but not both.  European roulette only has 0, while American roulette has both. If you can find European roulette tables...play them instead of American.

 

Why only a couple thousand dollars?  Because the table limit at the casinos I've played is $500 or $1000.  You start at $5 and double down on either red or black after a run of at least 5 reds or 5 blacks...so you have to be patient.  Every time you win, you start at $5 again.  Every time you lose, you make sure you double down on the subsequent bet.  You'll only be able to double-down 5 or 6 times before hitting the table limit, so you only bet once you see 5 reds or 5 blacks in a row.

 

Yes, yes, your probability of winning on any single spin is 50/50, but the probability of 7,8,9 in a row of the same color becomes less and less likely.  This takes time, because 5 blacks or 5 reds in a row only come up every 20-30 minutes or so.  I used to do this in my 20's and often it would take 5-10 hours of patiently playing.  But I never lost my bankroll, and I did it at least 25-30 times, usually turning a $50 bankroll into $900-$1500.  Often you would win small amounts until your bankroll increased in size, eventually allowing you to take slightly larger initial bets of $25-50.  But the number of times you double-down would decrease whenever you were wrong.  On the rare occasion 0 would show up and you start over at smaller bets...on rare occasions, you would have lost all that you gained that day and walk away with your $50 bankroll.

 

I've never played roulette in Vegas, but I hear the limits are around $10-15K per bet.  When I started investing after learning about Buffett and value investing, I promised myself that I would never gamble again, and I haven't.  I understand that there are online roulette games with very high limits.  I haven't tried them, nor have the urge to try them.  You have less than 50/50 odds playing roulette...American or European.  Going back to Mohnish's example, if you are right about your stocks even just 55-60% of the time, and you can choose your punches, why do anything else!  Cheers!

 

Parsad, I have a ton of respect for you. Both Casinos and Gamblers are subject to variance and gambler's ruin, no doubt there.

 

From a purely mathematical point of view, the strategy in the you outlined still has a negative EV since Roulette is designed with a house advantage. Each spin is memoryless, so even if the preceding 100 spins were red, the probability of the next spin being red/black is still 48.60% and green 2.70%, which is the error in your statement. Any winnings you have are due to variance (and I suspect, as we are human, due to a biased memory). I'm not doubting you made money, but as your number of bets increases, your winning % approaches the true probability, and you will lose money.

 

In real life however, there may be some tricks? In Thorpe's autobiography, he tried to create a machine to calculate final ball position based on starting position and velocity. There may be table defects as well. If you find such a table, I suggest you abandon the double down strategy, choose a consistent bet size to minimize risk of gamblers ruin, and ride out the winnings :)

 

Edit: I'll throw in a little more. Changing bet size works only if the odds are shifting. When counting cards, you have someone bet a low amount until the count in the deck is high (signalling a higher player edge), then you signal someone to come over to bet with a much higher amount. In roulette, the odds do not change, so there is no advantage to any type of double down strategy.

 

Each spin is memory less and your odds are 48.60% on the next spin, but the odds of red or black coming up consecutively is 0.4860 x 0.4860 x 0.4860....!  Cheers!

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I'm surprised and disappointed to see this quackery on this board. If the EV of an event is neutral and events are uncorrelated, when you bet a million your expected value is a million. Doesn't matter if you bet 1x 1m, 10x 100k or 100.000x 10 dollar. You can only change the distribution of possible outcomes, not the expected value of all possible outcomes. With Martingale you change the distribution in such a way that there's a probable profit but a tail risk of gigantic losses. With reverse Martingale it's the other way around. But both have the same expected outcome in the long run. If you made money using one of these strategies: congratulations, you were lucky! The same holds for the house limit: it can change the distribution of possible outcomes but not the expected value. It is simply ridiculous to think that a roulette wheel with a house limit of $100 is unexploitable but a roulette wheel with a house limit of $100.000 can be easily exploited.

 

This is such a fundamental and basic tenet of statistics that I personally am tempted to say you should not be managing money if you don't understand (or even worse: don't believe) this concept. At the very least you should follow some math courses :) .

 

https://en.wikipedia.org/wiki/Optional_stopping_theorem

 

The optional stopping theorem can be used to prove the impossibility of successful betting strategies for a gambler with a finite lifetime (which gives condition (a)) or a house limit on bets (condition (b)). Suppose that the gambler can wager up to c dollars on a fair coin flip at times 1, 2, 3, etc., winning his wager if the coin comes up heads and losing it if the coin comes up tails. Suppose further that he can quit whenever he likes, but cannot predict the outcome of gambles that haven't happened yet. Then the gambler's fortune over time is a martingale, and the time τ at which he decides to quit (or goes broke and is forced to quit) is a stopping time. So the theorem says that E[Xτ] = E[X0]. In other words, the gambler leaves with the same amount of money on average as when he started. (The same result holds if the gambler, instead of having a house limit on individual bets, has a finite limit on his line of credit or how far in debt he may go, though this is easier to show with another version of the theorem.)

 

Writser, that's kind of an asshole comment!  The Martingale strategy works for small amounts and durations.  If EV is 50/50, and you have very high table limits and a large bankroll, a gambler on a run could easily take down a casino.  That's all I'm saying.  I didn't say that the Martingale strategy is foolproof, but that a conservative, patient gambler, can make money from it without wiping out their bankroll...in particular on a European table.  I also said that even with 50/50 odds, why would anyone take the risk when they can invest in stocks and have a 55/45 advantage or better.  Cheers!

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Let me here just say:

 

Geez, I'm really tired of this topic, because I do not [basically] consider it investment related. [However just about everything allowed for discussion in the "General Discussion" forum].

 

Edit :

 

Perhaps "the issue at hand" is that I haven't been "attacked" by anyone one here on CoBF for some time now? [To keep me sharp!][ ; - D ]

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Let me here just say:

 

Geez, I'm really tired of this topic, because I do not [basically] consider it investment related. [However just about everything allowed for discussion in the "General Discussion" forum].

 

Edit :

 

Perhaps "the issue at hand" is that I haven't been "attacked" by anyone one here on CoBF for some time now? [To keep me sharp!][ ; - D ]

 

John, stop being a twat!  ;D  Cheers!

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I can't help making asshole comments every now and then. Don't take it personal.

 

I didn't say that the Martingale strategy is foolproof, but that a conservative, patient gambler, can make money from it without wiping out their bankroll.

If you are lucky you can make some money in the short run. However, you cannot EXPECT to make sustainable profits with Martingale or any other strategy in a game that is neutral or minus EV. That has nothing to do with being conservative or patient, with table limits, with whatever, it's just math. Whatever your betting strategy, if you flip a fair coin X times your expected value is zero. You can change your bet size strategy in such a way that you, for example, win 1 dollar 999 times out of a thousand. That's basically Martingale and if you practice it it might seem like a solid strategy. But it isn't, if you are ahead after a few months in the casino you are just lucky you haven't encountered the tail event yet, which is that you lose 999 dollar every once in a while (on average once every thousand hands, so it evens out exactly in the long run). Table limits or your personal net worth do not change that equation at all. I just linked to the math, which you don't have to understand but I think you should, as an investor, at least understand the concept.

 

Geez, I'm really tired of this topic, because I do not [basically] consider it investment related. [However just about everything allowed for discussion in the "General Discussion" forum.

In some ways the casino is a simplified version of the stock market. You can make bets without annoying distractions like security analysis or other wordly events. It's a good place to learn the fundamentals about position sizing, variance, risk taking, expected value, etc and it's easier to spot and fix weaknesses and mistakes in a (theoretical) casino that it is in the stock market. Why? Because in the casino the nerds among us have actually proven that certain things are stupid. That's pretty valuable feedback. In the stock market you don't have that: you can always bail out by blaming the FED, unforesee macro events, the market being irrational, management not executing well, etc. Very hard to know if you make mistakes and very easy to fool yourself, which all of us do some of the time. Which is why I think it is useful to point out flawed reasoning in the casino: it looks like the stock market but you can figure out for sure whether you are wrong or not. It's math, it's not up for discussion. Unfortunately, it often still is ..

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I'm also surprised to see someone om this board saying that Martingale works, let alone a professional money manager. More reasons to believe that buying s&p 500 index is the better choice than trusting some (irrational) human to beat the index...

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I'm also surprised to see someone om this board saying that Martingale works, let alone a professional money manager. More reasons to believe that buying s&p 500 index is the better choice than trusting some (irrational) human to beat the index...

Seriously. The only way to win at any casino game is to cheat. Otherwise they would be out of business.

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I'm also surprised to see someone om this board saying that Martingale works, let alone a professional money manager. More reasons to believe that buying s&p 500 index is the better choice than trusting some (irrational) human to beat the index...

 

What the f**k!  You're a frickin' engineer and you've made investments in cryptocurrencies!  Pot calling the kettle black.  Cheers!

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Each spin is memory less and your odds are 48.60% on the next spin, but the odds of red or black coming up consecutively is 0.4860 x 0.4860 x 0.4860....!  Cheers!

 

Each spin is 48.6% black or 48.6% red, no matter what the preceding spins were.

 

The odds of red 4x in a row is .486 x .486 x .486 x .486.

 

The odds of red 3x in a row and then getting black is also .486 x .486 x .486 x .486.

 

Thus, after the 3rd spin, it's equally likely you will get black or red. The odds of RRRB in that order are exactly the same as the odds of RRRR.

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The thing about Martingale is that many people confuse p(6 reds in a row) with p(next spin is red). The memoryless aspect/fact that each spin is independent is crucial to understand...and you are not betting on p(7 reds in a row), you are only betting on each spin which is independent from the last...

 

For example, if you pick up a coin that has been flipped by someone else before you without you knowing it, does what that person flipped before you affect what result you will achieve? The answer is an obvious no, even if they happened to flip 8 heads in a row (the chances that the next flip is heads by you is still an unchanged 50%).

 

Now if there is some situation where what happens in the past affects future outcomes (like playing with limited number of decks and counting cards), then you may be able to extract some sort of advantage.

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Sanjeev & Writser,

 

I'm not even searching - desperately - for DooDiligence's hurt feelings report once uploaded here on CoBF! [ : - ) ]

 

I've always found Writser's investment style fascinating. I suppose you guys are much more transactional in your investment style than me, which I think is perhaps somewhat related to taxes [i'm taxed on everything I do - no four letter abbreviation tax free account type available for poor me!].

 

I also consider Writser's comment "non-a$$hole", because it's actually a good explanation of Writser's modus operandi.

 

Have a nice weekend to you both! [ : - ) ]

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Sanjeev & Writser,

 

I'm not even searching - desperately - for DooDiligence's hurt feelings report once uploaded here on CoBF! [ : - ) ]

 

I've always found Writser's investment style fascinating. I suppose you guys are much more transactional in your investment style than me, which I think is perhaps somewhat related to taxes [i'm taxed on everything I do - no four letter abbreviation tax free account type available for poor me!].

 

I also consider Writser's comment "non-a$$hole", because it's actually a good explanation of Writser's modus operandi.

 

Have a nice weekend to you both! [ : - ) ]

 

I'm touched that you remembered  ;)

and glad to be able to contribute to the forum.

Hurt_Feelings_Report.pdf

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I'm also surprised to see someone om this board saying that Martingale works, let alone a professional money manager. More reasons to believe that buying s&p 500 index is the better choice than trusting some (irrational) human to beat the index...

 

What the f**k!  You're a frickin' engineer and you've made investments in cryptocurrencies!  Pot calling the kettle black.  Cheers!

 

Think of it as Isaac Newton buying the South Sea stock... althought this time it hasn't crashed yet.  ;)

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I must admit I don't understand how the Martingale system purports to work since it seems to imply that spins are not independent of the previous spin.

 

But the argument on Labouchere is actually the opposite. That spins are independent.  The logic is simply to take your win off the table and double down every time you lose.  By simple math, as long as a winning spin eventually comes up you will ultimately win back that original $1.  Yes you could be betting hundreds of thousands of $ to win back $1 if enough spins go against you in a row but the math is sound.

 

Labouchere method spreads it out so you don't double every time but its the same logic and math.

 

The problem is when a long series goes against you, the table limit comes into play quickly and you lose a ton.  Reverse Labouchere therefore switched it around to use that table limit in your favor.  Instead of doubling down when you lose, you double down when you win.  In a normal sequence you will continue to lose $1 each series but eventually a long run will put you at table limit where you stop, pocket the money and start over at $1.  The risk you take is that the small losing bets while waiting for a long run of wins could exceed the amount you win over the long streak. 

 

Whether you buy into it or not, I'd suggest the book. It's a fun read and goes into a ton more detail and reasoning than we are talking here.

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