Best Mathematical Craps Strategy
The Five-Minute Craps Strategy
- Best Mathematical Craps Strategy Tactics
- Best Mathematical Craps Strategy Games
- Best Mathematical Craps Strategy For Beginners
- Best Mathematical Craps Strategy Strategies
The best strategy for the typical player is the '3 point molly.' Place a bet on the pass line. Once the point is established, back the pass line bet up with at least two times odds, and make a come bet. The strategy outlined below is extremely easy to understand and implement. It’s also as effective as any craps strategy we’ve seen as it combines ‘ease of use’ with a very low house edge. Don’t misconstrue this to think that this strategy will give you the best of it. In craps, that’s mathematically impossible.
Want to learn one of the smartest bets in the casino in the next five minutes?I am not kidding.In the time it takes to read this report, you can learn to make a bet that beats nearly every other wager available in a casino.
Ready?Here's what you'll do -
You are about to learn to make a 'Place Bet' to win on a 6.In a nutshell, this is how it works -
1. Walk up to a craps table and place $6 worth of chips on the layout and tell the dealer you want to 'place the six.'
2. Now, if the six shows on any dice roll before the 7, you win $7 (a 7 to 6 payoff)
3. If the shooter rolls a 7 before the 6, you lose your $6 bet.Any other number rolled has no effect on your wager.
4. Your wager does not normally 'work' on a shooter's come out roll(s), when he is trying to establish a point.
Thus, a 7 rolled then will not cause the loss of your bet, nor will a 6 rolled give you a win.
That's it.You now know how to make one of the best bets in the house.The house edge on this bet is a paltry 1.5%.In other words, you'll get a 98.5% chance of winning this wager.When was the last time you played on a slot machine that returned 98.5%?
If you are unfamiliar with craps, let me give you some pointers.
Craps Etiquette.If you already have casino chips in hand you can just walk up to the table, wait till the shooter throws the dice and then place your chips on the table for your wager.If you don't have any casino chips, wait until the shooter has thrown the dice and place your cash on the layout in front on you, get the dealer's attention, and tell him 'chips please.'He will give your cash to the boxman (seated at the center of the table) who will count it.The dealer will then give you chips.Place the chips in the rail in front of you.Be sure to watch your hands when reaching for your chips as it is considered very bad etiquette for your hand to touch the dice in mid air or on the table.Other players believe this brings bad luck (I am not kidding - just let the dice bounce off your hand one time and listen to the groans from the other players.)
Making the Bet.Look at the craps layout.Forget all the confusing labels.Just look for the large betting area marked 'Come.'Now after the dice have settled and the dealer has paid off winning bets and removed losing ones, place your $6 on the table in the come area and tell the dealer to 'place the six.'The dealer will pick up the chips and position them within the Six Point Box at the top of the layout.If other players are also betting the six, don't worry.The dealer will position your bet so that he knows which wager is yours.
Your Bet's Outcome.Now that your bet is up, all you have to do is wait for it to win or lose. It might take a few rolls before either a six shows which gives you a win, or a 7 is rolled, which will cause you to lose your bet.
A Winning Wager.If your bet wins, it is okay to give out a yell - because you just won!The dealer will pay off other players in turn and when it is your turn will place your $7 ofwinning chips either in the come box or in front of you at the side of the table.He may ask 'Same bet?'If you want to keep the same bet up just say 'Same bet.'If you feel like you would like to remove your bet and sit on your $7 profit, tell him 'Take my bet down.'In the event you feel very lucky you may want to double your bet.In this case, just tell the dealer, 'Press my bet.'If you do, the dealer will only return $1 of your winnings and will place $6 of your winnings with your original bet, bringing it up to $12.Now if the wager wins, you will win $14.
Flexibility.Please note that some craps bets (most notably pass line and come bets) can't be removed once they have been made.However, you have ultimate flexibility with your place bet.You can tell the dealer to 'Take down my bet on the 6' any time and he will return your bet to you.
Best Mathematical Craps Strategy Tactics
Come out rolls. Place bets always work on every roll except come out rolls unless you call them off or have the dealer take them down.However, they are automatically 'Off' on come out rolls.You can recognize a come out roll as no point has been established, and the shooter is trying to roll a point number.Non point numbers are 2, 3, 7, 11 and 12 and anytime the dealer rolls one of these numbers, no point will be established and your place bet on the 6 will not be affected.Once the shooter has rolled a 4, 5, 6, 8, 9 or 10 (a point number) your bet will be working until it loses or you take it down.Just a reminder - The dealer will not take down a winning place bet unless you tell him to.So, if you want to walk up and play for one win, be sure to remember to tell the dealer to take your bet down after you win.
Okay, your five minutes are up.You can now make one of the smartest bets in the casino.
Whenever you are ready for a full fledged winning craps strategy, I have one waiting for you.The 'Automatic Craps Strategy' is one of the easiest and safest winning craps systems I have ever used.
In fact, my wife Diane even likes this system.Last year during the Christmas holidays she used this strategy to pick up a cool $9,839 in profits playing craps online.
I don't know if you will do as well.However, I will tell you that this strategy is very, very safe and wins a high percentage of the time.
And, it is easy enough to use that, even if you don't know beans about craps, you can learn it very quickly.
If you would like to learn more about it, just follow this Link.
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Introduction
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
Number | Final | Highest | Total | Net | Probability | Expected | Expected |
|---|---|---|---|---|---|---|---|
| 0 | Win | 1 | 1 | 1 | 0.49292929 | 0.49292929 | 0.49292929 |
| 1 | Win | 2 | 3 | 1 | 0.24995001 | 0.74985002 | 0.24995001 |
| 2 | Win | 4 | 7 | 1 | 0.12674233 | 0.88719628 | 0.12674233 |
| 3 | Win | 8 | 15 | 1 | 0.06426732 | 0.96400981 | 0.06426732 |
| 4 | Win | 16 | 31 | 1 | 0.03258808 | 1.01023035 | 0.03258808 |
| 5 | Win | 32 | 63 | 1 | 0.01652446 | 1.04104089 | 0.01652446 |
| 6 | Win | 64 | 127 | 1 | 0.00837907 | 1.06414175 | 0.00837907 |
| 7 | Win | 128 | 255 | 1 | 0.00424878 | 1.08343900 | 0.00424878 |
| 8 | Win | 256 | 511 | 1 | 0.00215443 | 1.10091479 | 0.00215443 |
| 9 | Win | 512 | 1023 | 1 | 0.00109245 | 1.11757574 | 0.00109245 |
| 10 | Win | 1024 | 2047 | 1 | 0.00055395 | 1.13393379 | 0.00055395 |
| 10 | Loss | 1024 | 2047 | -2047 | 0.00056984 | 1.16646467 | -1.16646467 |
| Total | 1.00000000 | 11.81172639 | -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 = 0.052668
Player 2
- 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 = 0.052663
Player 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 Money
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 won = 7,182,811,698 (50.4999%)
- Bets lost = 7,040,599,544 (49.5001%)
- Player achieved $1,000,000 first = 79,438 (83.019%)
- Player went bust first = 16,249 (16.981%)
- Average number of bets to reach $1,000,000 = 174,972 (364.5 days at 8 hours per day, 60 bets per hour)
$100 Bankroll, 2% Advantage
- Bets won = 7,027,117,205 (51.0000%)
- Bets lost = 6,751,539,769 (49.0000%)
- Player achieved $1,000,000 first = 215,702 (98.099%)
- Player went bust first = 4,180 (1.901%)
- Average number of bets to reach $1,000,000 = 63,775 (132.9 days at 8 hours per day, 60 bets per hour)
$1,000 Bankroll, 1% Advantage
- Bets won = 5,213,026,190 (50.4999%)
- Bets lost = 5,109,817,544 (49.5001%)
- Player achieved $1,000,000 first = 74,818 (99.0285%)
- Player went bust first = 734 (0.9715%)
- Average number of bets to reach $1,000,000 = 137,208 (285.8 days at 8 hours per day, 60 bets per hour)
$1,000 Bankroll, 2% Advantage
- Bets won = 6,332,837,070 (50.9996%)
- Bets lost = 6,084,596,671 (49.0004%)
- Player achieved $1,000,000 first = 267,445 (99.9996%)
- Player went bust first = 1 (0.0004%)
- Average number of bets to reach $1,000,000 = 46,428 (96.7 days at 8 hours per day, 60 bets per hour)
These simulations prove that with just a small advantage of as little as 1% and a bankroll of as little as $100 you can grind your way to a million dollars through the gambling equivalent of compound interest. Yet you never hear of this actually happening. Could it be that these gambling systems don’t work after all?!
Best Mathematical Craps Strategy Games
Here are some examples of system salesmen who try to take advantage of the mathematically challenged. There are hundreds of sites like these on the Internet, and this list is just a sampling. Frequently these sites vanish in the middle of the night, or suddenly direct traffic to a porn site. Please do let me know if any of these links don’t work or take you to other than the intended place.
Also, be warned that there are many others out there selling get rich quick gambling schemes that claim they are not betting systems. These sites usually throw out lots of fancy physics words like “chaos” and “fractals,” but display no evidence they know what these words mean. In the past, I have listed some such sites above but got angry letters claiming I shouldn’t criticize what I don’t understand. Personally, I feel that every method claiming an easy way to beat the casinos is a scam, and I don’t need to understand whatever the secret is. However, to be totally fair, I’ll only list betting systems above since those have been mathematically debunked by computer simulations. If anyone did find a truly easy way to beat the casinos, why aren’t they getting rich doing it?
The Wizard of Odds Challenge
For about six years, from 1999 to 2005, I offered $20,000 to anyone with a betting system that could show a profit over a one billion hand computer simulation. Here you can find the rules of the challenge. However, in all this time I only had one serious taker and hundreds of people wasting my time, pretending to be interested but never following through. So in January 2005, I took down the offer.
My webmaster, Michael Bluejay, now offers essentially the same challenge on his own site, VegasClick.com. If you accept his challenge, and win, I will be happy to state as such on the front page of this site, for proving the experts wrong.
A Fourth Experiment
On October 19, 2004, Daniel Rainsong accepted my challenge. Mr. Rainsong was so confident he would win he doubled the stakes to my $40,000 against his $4,000. Although the rules of the challenge are based on craps or roulette I allowed this challenge to be based on blackjack rules with a house edge of only 0.26%. Can a betting system beat a game with a house edge this small and a 1,028 bet spread? Visit my Rainsong Challenge page for all the details.
Please, Don't Write
I no longer respond to e-mails that suggest a player can beat a negative expectation game over the long run with a betting system. Such e-mail is deleted on sight. I have said all I have to say on the topic here and in my Gambling FAQ.
If you really want to discuss the topic, then I invite you not to do so at my forum at Wizard of Vegas, but instead one where you will be among like-minded people, like the forum atJohn Patrick's site (Update: This site has, not surprisingly, gone the way of the dodo bird).
Internal Links
- Oscar's Grind betting system.
- Labouchere betting system.
- Fibonacci betting system.
External Links
- Betting Systems and the House Edge, an article by Ph.D. mathematician Eliot Jacobson debunking betting systems.
- Betting Systems, an article by Michael Bluejay of VegasClick.
- German translation of this article.
- Debunking the “No Risk Don’t Come” betting system.