Martingale Craps
2021年7月21日Register here: http://gg.gg/vgxat
As previously explained, this is the best game to play when it comes to the Martingale system. The only downside is that you need a massive bankroll, but you are also in need of a large win in a short-time period. Did you know that you have the lowest house edge with this game? The martingale style only allows you to establish pass/come bets while grinding out a profit without the risk of losing short of a run of craps rolls(the achilles heal). The thing that differentiates craps bets from all the other casino bets is the line bets hang unresolved for awhile. The Martingale betting system increases your chances of winning in the short term. The catch is that when you do lose, you lose big. For example, starting with $1000 and a starting bet of $5, you’ve got about an 80% chance of turning a profit after one hour at craps or roulette, with an average win of about $100. The Martingale system is one of the oldest and currently most-used betting strategies by players all over the world. The origin of the strategy is yet unknown, but it is named after Mr. Henry Martingale, who was an owner of one of the most famous gambling houses in Britain in the 18th century. In most cases, the system is applied to games of chance that have a near 50/50 win to loss outcomes, such as the Roulette black and red bets or the pass and don’t pass lines at the craps tables. An uncommon but definitely applicable game that the Martingale system can be applied to is Baccarat.MartinAlthough as an frequent visitor to this forum I know that martingales never work I also know that they frequently work but not enough to overcome a loss. The problem is if you lose the 9 hands in a row then you are out 1960. Then you would have to win 49 martingales on the 9th hand (profit of each being 40) or, win a one or two-hand martingale (profit 5) at least 392 times (without a loss) just to break even on the one you lost. Seems like a lot of effort for nothing much. Because of the slowness of the game blackjack might not a good venue for such a play. One of the critical problems with the method suggested is that 66% of the time you get a break even as an outcome. Consequently you are going to spend a lot of time just spinning wheels.
I would suggest a change to your strategy. Go to a craps table and wait until three pass numbers have been made in a row. Then start your martingale on the don’t pass line. It will take some time because very few shooters make three passes in a row. However most craps venues don’t mind you standing there doing nothing as people ’track’ tables all the time.
While it is possible for someone to make 12 passes in a row I’ve never seen it. Of course I’m ignoring the ’pesky odds’ again and have only been playing craps for 40 some odd years so let’s just say the likelihood of this happening is really, really small even though there is a mathematical possibility that it could happen.
Another way to do this and one I’ve seen people actually use is on the field (confession - I’ve even used it). Wait for several non-field numbers to come in a row and then start your martingale. Can’t possibly work but once again I’ve never seen twelve non-field numbers come in a row (I have seen eight) but just because I haven’t seen it doesn’t make the math change.
Another way would be using one of the outside bets at roulette. Again wait for a predetermined period of reds/blacks, highs/lows, even/odds to pass by and then start the martingale.
The Wizard has some free games where you could test these things out and then determine whether you want to try it for real or not.clarkacal
I would suggest a change to your strategy. Go to a craps table and wait until three pass numbers have been made in a row.
Wait for several non-field numbers to come in a row and then start your martingale.
Again wait for a predetermined period of reds/blacks, highs/lows, even/odds to pass by and then start the martingale.
The dice have no memory, nor do they have ears or the ability to answer prayers.AZDuffman
The dice have no memory, nor do they have ears or the ability to answer prayers.
What do you mean? They answer ’NO’ all the time.All animals are equal, but some are more equal than othersclarkacal
What do you mean? They answer ’NO’ all the time.
They are however widely accepted to be feminine.NicksGamingStuff
>And you should know that language such as yours is not tolerated here.
Fuck off.
Thank you! Hey if he wants to use his system I say let him, we can all thank him for offering to share with us a system that will not likely have a huge wipeout, maybe he can take us to dinner with all the money he is making off of it!Martingale System CrapsMartin
The dice have no memory, nor do they have ears or the ability to answer prayers.
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.Martin
Thank you! Hey if he wants to use his system I say let him, we can all thank him for offering to share with us a system that will not likely have a huge wipeout, maybe he can take us to dinner with all the money he is making off of it!
The man asked a simple question - he neither instructed you, begged you, or otherwise attempted to coerce you into using the method he proposed. True to their nature however the Wizard’s Welcoming Warriors jumped on him and stomped him to dust.mkl654321
The man asked a simple question - he neither instructed you, begged you, or otherwise attempted to coerce you into using the method he proposed. True to their nature however the Wizard’s Welcoming Warriors jumped on him and stomped him to dust.
Probably because he’s about the 18,734th person to post his ’Thuper Thystem’ on this board, and 18,721 of those systems have been based on some kind of Martingale, which we are kind of sick of hearing about. Anyone with the tiniest knowledge of mathematics, or gambling, or both, should know that a Martingale can’t work. But we keep getting asked to do a rigourous, extensive mathematical analysis--and when we say, ’No analysis needed. It’s a Martinglae--therefore it can’t work.’ Or--’You can’t beat a negative expectation game with any combination of bets.’ Simple truths--yet all the system posters blow a gasket when we refuse to subject yet another goofball system to rigorous analysis.The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shawmkl654321
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.
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.’The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shawrdw4potus
$5/$1000 table limit, best odds for player (i.e. BJ pays 3:2, etc)..is this game out there with a $5/$1000 limit?
You can find lots of shoe-dealt games with (at least) those limits. They’ll be H17 games, and may not offer late surrender, but they pay 3:2 on BJ and most will allow double after split.’So as the clock ticked and the day passed, opportunity met preparation, and luck happened.’ - Maurice ClarettIntroduction
Not only do betting systems fail to beat casino games with a house advantage, they can’t even dent it. Roulette balls and dice simply have no memory. Every spin in roulette and every toss in craps is independent of all past events. In the short run, you can fool yourself into thinking a betting system works, by risking a lot to win a little. However, in the long run no betting system can withstand the test of time. The longer you play, the ratio of money lost to money bet will get closer to the expectation for that game.
In the many years that run this site, I have received thousands of e-mails from believers in betting systems. Their faith surpasses religious levels. However, in all things, the more ridiculous a belief is the more tenaciously it tends to be held. Gamblers have been looking for a betting system that works for hundreds of years, and yet the casinos are still standing.Gambler’s Fallacy
The biggest gambling myth is that an event that has not happened recently becomes overdue and more likely to occur. This is known as the “gambler’s fallacy.” Thousands of gamblers have devised betting systems that attempt to exploit the gambler’s fallacy by betting the opposite way of recent outcomes. For example, waiting for three reds in roulette and then betting on black. Hucksters sell “guaranteed” get-rich-quick betting systems that are ultimately based on the gambler’s fallacy. None of them work. If you don’t believe me here is what some other sources say on the topic:
A common gamblers’ fallacy called “the doctrine of the maturity of the chances” (or “Monte Carlo fallacy”) falsely assumes that each play in a game of chance is not independent of the others and that a series of outcomes of one sort should be balanced in the short run by other possibilities. A number of “systems” have been invented by gamblers based largely on this fallacy; casino operators are happy to encourage the use of such systems and to exploit any gambler’s neglect of the strict rules of probability and independent plays. — Encyclopedia Britannica (look under “gambling”)
No betting system can convert a subfair game into a profitable enterprise.. — Probability and Measure (second edition, page 94) by Patrick Billingsley
The number of ‘guaranteed’ betting systems, the proliferation of myths and fallacies concerning such systems, and the countless people believing, propagating, venerating, protecting, and swearing by such systems are legion. Betting systems constitute one of the oldest delusions of gambling history. Betting systems votaries are spiritually akin to the proponents of perpetual motion machines, butting their heads against the second law of thermodynamics. — The Theory of Gambling and Statistical Logic (page 53) by Richard A. Epstein
Vegas Click also has a good expose of the gambler’s fallacy.The Martingale
Every week I receive two or three emails asking me about the betting system by which a player doubles his/her bet after a loss. This system is generally played with an even money game such as the red/black bet in roulette or the pass/don’t pass bet in craps and is known as the Martingale. The idea is that by doubling your bet after a loss, you would always win enough to cover all past losses plus one unit. For example, if a player starts at $1 and loses four bets in a row, winning on the fifth, he will have lost $1+$2+$4+$8 = $15 on the four losing bets and won $16 on the fifth bet. The losses were covered and he had a profit of $1. The problem is that it is easier than you think to lose several bets in a row and run out of betting money after you’ve doubled it all away.
In order to prove this point, I created a program that simulated two systems, the Martingale and flat betting, and applied each by betting on the pass line in craps (which has a 49.29% probability of winning). The Martingale bettor would always start with a $1 bet and start the session with $255 which is enough to cover 8 losses in a row. The flat bettor would bet $1 every time. The Martingale player would play for 100 bets, or until he couldn’t cover the amount of a bet. In that case, he would stop playing and leave with the money he had left. In the event his 100th bet was a loss, he would keep betting until he either won a bet or couldn’t cover the next bet. The person flat betting would play 100 bets every time. I repeated this experiment for 1,000,000 sessions for both systems and tabulated the results. The graph below shows the results:
As you can see, the flat bettor has a bell curve with a peak at a loss of $1, and never strays very far from that peak. Usually the Martingale bettor would show a profit represented by the bell curve on the far right, peaking at $51; however, on the far left we see those times when he couldn’t cover a bet and walked away with a substantial loss. That happened for 19.65% of the sessions. Many believers in the Martingale mistakenly believe that the many wins will more than cover the few losses.
In this experiment, the average session loss for the flat bettor was $1.12, but was $4.20 for the Martingale bettor. In both cases, the ratio of money lost to money won was very close to 7/495, which is the house edge on the pass line bet in craps. This is not coincidental. No matter what system is used in the long run, this ratio will always approach the house edge. To prove this point consider the Martingale player on the pass line in craps who only desires to win $1, starts with a bet of $1, and has a bankroll of $2,047 to cover as many as 10 consecutive losses. The table below shows all possible outcomes with each probability, expected bet, and return.Expand
Betting tips football app. Number
of losses
Final
outcome
Highest
bet
Total
bet
Net
outcome
Probability
Expected
bet
Expected
return0Win1110.492929290.492929290.492929291Win2310.249950010.749850020.249950012Win4710.126742330.887196280.126742333Win81510.064267320.964009810.064267324Win163110.032588081.010230350.032588085Win326310.016524461.041040890.016524466Win6412710.008379071.064141750.008379077Win12825510.004248781.083439000.004248788Win25651110.002154431.100914790.002154439Win512102310.001092451.117575740.0010924510Win1024204710.000553951.133933790.0005539510Loss10242047-20470.000569841.16646467-1.16646467Total1.0000000011.81172639-0.16703451
The expected bet is the product of the total bet and the probability. Likewise, the expected return is the product of the total return and the probability. The last row shows this Martingale bettor to have had an average total bet of 11.81172639 and an average loss of 0.16703451. Dividing the average loss by the average bet yields .01414141. We now divide 7 by 495 (the house edge on the pass line) and we again get 0.01414141! This shows that the Martingale is neither better nor worse than flat betting when measured by the ratio of expected loss to expected bet. All betting systems are equal to flat betting when compared this way, as they should be. In other words, all betting systems are equally worthless.
Here is another experiment I conducted earlier which proves the same thing as the experiment above. This one is played against roulette testing three different systems. Player 1 flat bet a $1 each time. He was not using a betting system. Player 2 started a series of trials with a bet of $1 and increased his wager by $1 after every winning bet. A lost bet would constitute the end of a series and the next bet would be $1. Player 3 also started a series of bets with a bet of $1 but used a doubling strategy in that after a losing bet of $x he would bet $2x (the Martingale). A winning bet would constitute the end of a series and the next bet would be $1. To make it realistic I put a maximum bet on player 3 of $200. Below are the results of that experiment:Player 1
*Total amount wagered = $1,000,000,000
*Average wager = $1.00
*Total loss = $52,667,912
*Expected loss = $52,631,579
*Ratio of loss to money wagered = 0.052668Player 2Grand Martingale Craps
*Total amount wagered = $1,899,943,349
*Average wager = $1.90
*Total loss = $100,056,549
*Expected loss = $99,997,018
*Ratio of loss to money wagered = 0.052663Player 3
*Total amount wagered = $5,744,751,450
*Average wager = $5.74
*Total loss = $302,679,372
*Expected loss = $302,355,340
*Ratio of loss to money wagered = 0.052688
As you can see the ratio of money lost to money wagered is always close to the normal house advantage of 1/19 ≈ 0.052632. In conclusion, varying of bet size depending on recent past wins or losses makes no difference in the long run outcome and is no different than always betting the same.A Third Experiment
“An Old Timer’s Guide to Beating the Craps Table” was a betting system that makes big promises about turning the craps tables into your own personal cash register. I offered to test his system for free. Here are the results.The Cancellation Betting System
Despite all my warnings about betting systems, readers continually ask me to suggest one. To satisfy those who enjoy playing systems I have done a full explanation and analysis of the cancellation betting system.Don’t Waste Your MoneyMartingale System Craps Field
The Internet is full of people selling betting systems with promises of beating the casino at games of luck. Those who sell these systems are the present day equivalent of the 19th century snake oil salesmen. Under no circumstances should you waste one penny on any gambling system. Every time one has been put to a computer simulation it failed and showed the same ratio of losses to money bet as flat betting. If you ask a system salesman about this you likely will get a reply such as, “In real life nobody plays millions of trials in the casino.” You’re likely to also hear that his/her system works in real life, but not when used against a computer simulation. It is interesting that professionals use computers to model real-life problems in just about every field of study, yet when it comes to betting systems computer analysis becomes “worthless and unreliable,” as the salesman of one system put it. In any event, such an excuse misses the point; the computer runs billions of trials simply to prove that a system is unsound. If it won’t work on a computer, it won’t work in the casino.
Gambling systems have been around for as long as gambling has. No system has ever been proven to work. From an inside source, I know that system salesmen go from selling one kind of system to another. It is a dirty business by which they steal ideas from each other, and are always attempting to rehash old systems as something new.
System salesmen usually promise ridiculous advantages. For example, even with just a 1% advantage on an even money bet, it would not be difficult to parlay $100 into $1,000,000 by betting in proportion to bankroll. I was asked to prove this claim so I wrote a computer simulation based on the toss of a biased coin, with a 50.5% chance of winning. At all times the player bet 1% of his bankroll, rounded down to the nearest dollar. However, if a winning bet would put the player over $1,000,000 then he only bet as much as he needed to get to exactly $1,000,000. In addition, I ran simulations with a 2% advantage and for a starting bankroll of $1,000. Following are the results of all four tests.$100 Bankroll, 1% Advantage
*Bets
https://diarynote-jp.indered.space
As previously explained, this is the best game to play when it comes to the Martingale system. The only downside is that you need a massive bankroll, but you are also in need of a large win in a short-time period. Did you know that you have the lowest house edge with this game? The martingale style only allows you to establish pass/come bets while grinding out a profit without the risk of losing short of a run of craps rolls(the achilles heal). The thing that differentiates craps bets from all the other casino bets is the line bets hang unresolved for awhile. The Martingale betting system increases your chances of winning in the short term. The catch is that when you do lose, you lose big. For example, starting with $1000 and a starting bet of $5, you’ve got about an 80% chance of turning a profit after one hour at craps or roulette, with an average win of about $100. The Martingale system is one of the oldest and currently most-used betting strategies by players all over the world. The origin of the strategy is yet unknown, but it is named after Mr. Henry Martingale, who was an owner of one of the most famous gambling houses in Britain in the 18th century. In most cases, the system is applied to games of chance that have a near 50/50 win to loss outcomes, such as the Roulette black and red bets or the pass and don’t pass lines at the craps tables. An uncommon but definitely applicable game that the Martingale system can be applied to is Baccarat.MartinAlthough as an frequent visitor to this forum I know that martingales never work I also know that they frequently work but not enough to overcome a loss. The problem is if you lose the 9 hands in a row then you are out 1960. Then you would have to win 49 martingales on the 9th hand (profit of each being 40) or, win a one or two-hand martingale (profit 5) at least 392 times (without a loss) just to break even on the one you lost. Seems like a lot of effort for nothing much. Because of the slowness of the game blackjack might not a good venue for such a play. One of the critical problems with the method suggested is that 66% of the time you get a break even as an outcome. Consequently you are going to spend a lot of time just spinning wheels.
I would suggest a change to your strategy. Go to a craps table and wait until three pass numbers have been made in a row. Then start your martingale on the don’t pass line. It will take some time because very few shooters make three passes in a row. However most craps venues don’t mind you standing there doing nothing as people ’track’ tables all the time.
While it is possible for someone to make 12 passes in a row I’ve never seen it. Of course I’m ignoring the ’pesky odds’ again and have only been playing craps for 40 some odd years so let’s just say the likelihood of this happening is really, really small even though there is a mathematical possibility that it could happen.
Another way to do this and one I’ve seen people actually use is on the field (confession - I’ve even used it). Wait for several non-field numbers to come in a row and then start your martingale. Can’t possibly work but once again I’ve never seen twelve non-field numbers come in a row (I have seen eight) but just because I haven’t seen it doesn’t make the math change.
Another way would be using one of the outside bets at roulette. Again wait for a predetermined period of reds/blacks, highs/lows, even/odds to pass by and then start the martingale.
The Wizard has some free games where you could test these things out and then determine whether you want to try it for real or not.clarkacal
I would suggest a change to your strategy. Go to a craps table and wait until three pass numbers have been made in a row.
Wait for several non-field numbers to come in a row and then start your martingale.
Again wait for a predetermined period of reds/blacks, highs/lows, even/odds to pass by and then start the martingale.
The dice have no memory, nor do they have ears or the ability to answer prayers.AZDuffman
The dice have no memory, nor do they have ears or the ability to answer prayers.
What do you mean? They answer ’NO’ all the time.All animals are equal, but some are more equal than othersclarkacal
What do you mean? They answer ’NO’ all the time.
They are however widely accepted to be feminine.NicksGamingStuff
>And you should know that language such as yours is not tolerated here.
Fuck off.
Thank you! Hey if he wants to use his system I say let him, we can all thank him for offering to share with us a system that will not likely have a huge wipeout, maybe he can take us to dinner with all the money he is making off of it!Martingale System CrapsMartin
The dice have no memory, nor do they have ears or the ability to answer prayers.
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.Martin
Thank you! Hey if he wants to use his system I say let him, we can all thank him for offering to share with us a system that will not likely have a huge wipeout, maybe he can take us to dinner with all the money he is making off of it!
The man asked a simple question - he neither instructed you, begged you, or otherwise attempted to coerce you into using the method he proposed. True to their nature however the Wizard’s Welcoming Warriors jumped on him and stomped him to dust.mkl654321
The man asked a simple question - he neither instructed you, begged you, or otherwise attempted to coerce you into using the method he proposed. True to their nature however the Wizard’s Welcoming Warriors jumped on him and stomped him to dust.
Probably because he’s about the 18,734th person to post his ’Thuper Thystem’ on this board, and 18,721 of those systems have been based on some kind of Martingale, which we are kind of sick of hearing about. Anyone with the tiniest knowledge of mathematics, or gambling, or both, should know that a Martingale can’t work. But we keep getting asked to do a rigourous, extensive mathematical analysis--and when we say, ’No analysis needed. It’s a Martinglae--therefore it can’t work.’ Or--’You can’t beat a negative expectation game with any combination of bets.’ Simple truths--yet all the system posters blow a gasket when we refuse to subject yet another goofball system to rigorous analysis.The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shawmkl654321
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.
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.’The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shawrdw4potus
$5/$1000 table limit, best odds for player (i.e. BJ pays 3:2, etc)..is this game out there with a $5/$1000 limit?
You can find lots of shoe-dealt games with (at least) those limits. They’ll be H17 games, and may not offer late surrender, but they pay 3:2 on BJ and most will allow double after split.’So as the clock ticked and the day passed, opportunity met preparation, and luck happened.’ - Maurice ClarettIntroduction
Not only do betting systems fail to beat casino games with a house advantage, they can’t even dent it. Roulette balls and dice simply have no memory. Every spin in roulette and every toss in craps is independent of all past events. In the short run, you can fool yourself into thinking a betting system works, by risking a lot to win a little. However, in the long run no betting system can withstand the test of time. The longer you play, the ratio of money lost to money bet will get closer to the expectation for that game.
In the many years that run this site, I have received thousands of e-mails from believers in betting systems. Their faith surpasses religious levels. However, in all things, the more ridiculous a belief is the more tenaciously it tends to be held. Gamblers have been looking for a betting system that works for hundreds of years, and yet the casinos are still standing.Gambler’s Fallacy
The biggest gambling myth is that an event that has not happened recently becomes overdue and more likely to occur. This is known as the “gambler’s fallacy.” Thousands of gamblers have devised betting systems that attempt to exploit the gambler’s fallacy by betting the opposite way of recent outcomes. For example, waiting for three reds in roulette and then betting on black. Hucksters sell “guaranteed” get-rich-quick betting systems that are ultimately based on the gambler’s fallacy. None of them work. If you don’t believe me here is what some other sources say on the topic:
A common gamblers’ fallacy called “the doctrine of the maturity of the chances” (or “Monte Carlo fallacy”) falsely assumes that each play in a game of chance is not independent of the others and that a series of outcomes of one sort should be balanced in the short run by other possibilities. A number of “systems” have been invented by gamblers based largely on this fallacy; casino operators are happy to encourage the use of such systems and to exploit any gambler’s neglect of the strict rules of probability and independent plays. — Encyclopedia Britannica (look under “gambling”)
No betting system can convert a subfair game into a profitable enterprise.. — Probability and Measure (second edition, page 94) by Patrick Billingsley
The number of ‘guaranteed’ betting systems, the proliferation of myths and fallacies concerning such systems, and the countless people believing, propagating, venerating, protecting, and swearing by such systems are legion. Betting systems constitute one of the oldest delusions of gambling history. Betting systems votaries are spiritually akin to the proponents of perpetual motion machines, butting their heads against the second law of thermodynamics. — The Theory of Gambling and Statistical Logic (page 53) by Richard A. Epstein
Vegas Click also has a good expose of the gambler’s fallacy.The Martingale
Every week I receive two or three emails asking me about the betting system by which a player doubles his/her bet after a loss. This system is generally played with an even money game such as the red/black bet in roulette or the pass/don’t pass bet in craps and is known as the Martingale. The idea is that by doubling your bet after a loss, you would always win enough to cover all past losses plus one unit. For example, if a player starts at $1 and loses four bets in a row, winning on the fifth, he will have lost $1+$2+$4+$8 = $15 on the four losing bets and won $16 on the fifth bet. The losses were covered and he had a profit of $1. The problem is that it is easier than you think to lose several bets in a row and run out of betting money after you’ve doubled it all away.
In order to prove this point, I created a program that simulated two systems, the Martingale and flat betting, and applied each by betting on the pass line in craps (which has a 49.29% probability of winning). The Martingale bettor would always start with a $1 bet and start the session with $255 which is enough to cover 8 losses in a row. The flat bettor would bet $1 every time. The Martingale player would play for 100 bets, or until he couldn’t cover the amount of a bet. In that case, he would stop playing and leave with the money he had left. In the event his 100th bet was a loss, he would keep betting until he either won a bet or couldn’t cover the next bet. The person flat betting would play 100 bets every time. I repeated this experiment for 1,000,000 sessions for both systems and tabulated the results. The graph below shows the results:
As you can see, the flat bettor has a bell curve with a peak at a loss of $1, and never strays very far from that peak. Usually the Martingale bettor would show a profit represented by the bell curve on the far right, peaking at $51; however, on the far left we see those times when he couldn’t cover a bet and walked away with a substantial loss. That happened for 19.65% of the sessions. Many believers in the Martingale mistakenly believe that the many wins will more than cover the few losses.
In this experiment, the average session loss for the flat bettor was $1.12, but was $4.20 for the Martingale bettor. In both cases, the ratio of money lost to money won was very close to 7/495, which is the house edge on the pass line bet in craps. This is not coincidental. No matter what system is used in the long run, this ratio will always approach the house edge. To prove this point consider the Martingale player on the pass line in craps who only desires to win $1, starts with a bet of $1, and has a bankroll of $2,047 to cover as many as 10 consecutive losses. The table below shows all possible outcomes with each probability, expected bet, and return.Expand
Betting tips football app. Number
of losses
Final
outcome
Highest
bet
Total
bet
Net
outcome
Probability
Expected
bet
Expected
return0Win1110.492929290.492929290.492929291Win2310.249950010.749850020.249950012Win4710.126742330.887196280.126742333Win81510.064267320.964009810.064267324Win163110.032588081.010230350.032588085Win326310.016524461.041040890.016524466Win6412710.008379071.064141750.008379077Win12825510.004248781.083439000.004248788Win25651110.002154431.100914790.002154439Win512102310.001092451.117575740.0010924510Win1024204710.000553951.133933790.0005539510Loss10242047-20470.000569841.16646467-1.16646467Total1.0000000011.81172639-0.16703451
The expected bet is the product of the total bet and the probability. Likewise, the expected return is the product of the total return and the probability. The last row shows this Martingale bettor to have had an average total bet of 11.81172639 and an average loss of 0.16703451. Dividing the average loss by the average bet yields .01414141. We now divide 7 by 495 (the house edge on the pass line) and we again get 0.01414141! This shows that the Martingale is neither better nor worse than flat betting when measured by the ratio of expected loss to expected bet. All betting systems are equal to flat betting when compared this way, as they should be. In other words, all betting systems are equally worthless.
Here is another experiment I conducted earlier which proves the same thing as the experiment above. This one is played against roulette testing three different systems. Player 1 flat bet a $1 each time. He was not using a betting system. Player 2 started a series of trials with a bet of $1 and increased his wager by $1 after every winning bet. A lost bet would constitute the end of a series and the next bet would be $1. Player 3 also started a series of bets with a bet of $1 but used a doubling strategy in that after a losing bet of $x he would bet $2x (the Martingale). A winning bet would constitute the end of a series and the next bet would be $1. To make it realistic I put a maximum bet on player 3 of $200. Below are the results of that experiment:Player 1
*Total amount wagered = $1,000,000,000
*Average wager = $1.00
*Total loss = $52,667,912
*Expected loss = $52,631,579
*Ratio of loss to money wagered = 0.052668Player 2Grand Martingale Craps
*Total amount wagered = $1,899,943,349
*Average wager = $1.90
*Total loss = $100,056,549
*Expected loss = $99,997,018
*Ratio of loss to money wagered = 0.052663Player 3
*Total amount wagered = $5,744,751,450
*Average wager = $5.74
*Total loss = $302,679,372
*Expected loss = $302,355,340
*Ratio of loss to money wagered = 0.052688
As you can see the ratio of money lost to money wagered is always close to the normal house advantage of 1/19 ≈ 0.052632. In conclusion, varying of bet size depending on recent past wins or losses makes no difference in the long run outcome and is no different than always betting the same.A Third Experiment
“An Old Timer’s Guide to Beating the Craps Table” was a betting system that makes big promises about turning the craps tables into your own personal cash register. I offered to test his system for free. Here are the results.The Cancellation Betting System
Despite all my warnings about betting systems, readers continually ask me to suggest one. To satisfy those who enjoy playing systems I have done a full explanation and analysis of the cancellation betting system.Don’t Waste Your MoneyMartingale System Craps Field
The Internet is full of people selling betting systems with promises of beating the casino at games of luck. Those who sell these systems are the present day equivalent of the 19th century snake oil salesmen. Under no circumstances should you waste one penny on any gambling system. Every time one has been put to a computer simulation it failed and showed the same ratio of losses to money bet as flat betting. If you ask a system salesman about this you likely will get a reply such as, “In real life nobody plays millions of trials in the casino.” You’re likely to also hear that his/her system works in real life, but not when used against a computer simulation. It is interesting that professionals use computers to model real-life problems in just about every field of study, yet when it comes to betting systems computer analysis becomes “worthless and unreliable,” as the salesman of one system put it. In any event, such an excuse misses the point; the computer runs billions of trials simply to prove that a system is unsound. If it won’t work on a computer, it won’t work in the casino.
Gambling systems have been around for as long as gambling has. No system has ever been proven to work. From an inside source, I know that system salesmen go from selling one kind of system to another. It is a dirty business by which they steal ideas from each other, and are always attempting to rehash old systems as something new.
System salesmen usually promise ridiculous advantages. For example, even with just a 1% advantage on an even money bet, it would not be difficult to parlay $100 into $1,000,000 by betting in proportion to bankroll. I was asked to prove this claim so I wrote a computer simulation based on the toss of a biased coin, with a 50.5% chance of winning. At all times the player bet 1% of his bankroll, rounded down to the nearest dollar. However, if a winning bet would put the player over $1,000,000 then he only bet as much as he needed to get to exactly $1,000,000. In addition, I ran simulations with a 2% advantage and for a starting bankroll of $1,000. Following are the results of all four tests.$100 Bankroll, 1% Advantage
*Bets
https://diarynote-jp.indered.space
コメント