The hoax that is the 1.41% house advantage on pass line bets
Quote: HeadlockNobody discovered the 1.41% HA, it's determined by the laws of probability. All the sims you guys run are pointless because tuttigym (sevenshooter) doesn't believe in the 100's of years of mathematical principles developed.
Really Headlock which "laws" of probability? I mean, did it somehow mystically appear on the table in a casino or come down from a voice on high or what and who and where?
sevenshooter believes in dice influence and lives to roll. I do not do either. "Sims" can NOT do random. Sims can only do programs and models.
tuttigym
Quote: tuttigymAgain, did any of the references you have read or any other "expert" display the fact that the 1.41% HA have a 3.5% "expectation" of happening or did all those references INFER to all who would come to play that the HA was so "small" as to be not worrysome? Additionally, did any of the books or references you know of with the exception of blogs such as this one even describe the 244/251 ooutcomes?? I ask because beginners such as Raleighcraps and, I believe, thousands of others who play are clueless.
The references I have read did not specifically treat the distribution of 495 passline outcomes. The 1.414% HA can be arrived at in various ways. Actually, as I've said, I use the "perfect 1980", which is just four times the 495 and allows one to express all the possible outcomes in the form of integers. Interestingly enough, in the movie "The Big Town" (1987), with Matt Dillon, Diane Lane, Tommy Lee Jones, Bruce Dern and Lee Grant, J C Cullen (Dillon) is a young craps hotshot who comes to town and wants to work for Ferguson Edwards (Grant). During the interview, she asks him "How many bets does it take to work out all the odds?" His answer, "1980", of which 440 are comeout wins..." etc.,etc.
Of course, you are still confusing the meaning of the 1.4%. Try thinking about it this way: for any given session that you play, if you keep track of all your bets, you can figure out the house (or player) advantage for the session. Just take your net result and divide it by the total amount of all your bets (bet handle, it's called). (Don't use your starting bankroll.) If you did that for many, many sessions, and added up all the net outcomes and all the bet handles, then divided the total net by the total bet handle, it would come quite close to 1.4%.
Quote: tuttigymQuote: goat: What do you think the HA on placing the six is? How would you figure it?
tuttigym
Just like you showed five ways to win and six ways to lose or 16 2/3% or .167 HA just like when the house pays the FO bet (true odds) of paying the player $6 for the $5 bet.
OK, I see what you're doing. It's completely wrong, of course. If you believed that placing the six actually had an HA of 16.7%, why would you EVER make such a bet? Nothing about your calculation is correct. If there are five ways to win and six to lose, there are 11 ways to resolve the bet, right? So, the probability of winning is 5/11 and losing is 6/11. Your .167 is just the probability of a seven rolling, out of all 36 combinations. I'm afraid you are hopeless. Sorry. I am done.
Cheers,
Alan Shank
Quote: goatcabinI am going to take one more shot at this, a different approach having occurred to me.
Now, tuttigym is fond of stating that the probability of ending up 244-251 after 495 passline bets is only .035 (actually .035847716), making it a "false promise" or even a "hoax". But that probability is actually higher than the probability of the 12 coming up on any roll of two dice. The odds against 244-251 occurring are only 27 to 1. Does tuttigym think that the 12 is a rare event?
What about the seven? The probability of the seven coming up is only .1667. So, is it a "false promise", too? The seven is far less likely to come up than all the other numbers combined, right? That's why tuttigym likes to bet $64 across, because he has 30 ways to win and only six to lose.
Tuttigym, try to understand that the 12 and the passline are both binary events; you either roll a 12 or you don't, you either win your passline bet or you don't, you either come out 244-251 or you don't.
Cheers,
Alan Shank
JB said it is 28 to 1. Are you saying that our illustrious administrator is wrong?
Actually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164. I know that your sensibilities will be screaming and that somehow you will come up with a formula that shows that the HA is 17,432 to 1 against me, but then your mindset would leave all the bets on the table until the 7 showed and wiped out the chips. I mean, if you played on a $25 table with 5X odds and you bet $25 PL; the 6 became the point and then a FO bet (5X) of $125, the amount at risk is close to similar. Any three rolls that are no the point provides a win of about $30 or so X 3. A 7 out I lose a net $74; you of course lose $150. Now since the rules allow me to bring down all my Place bets during the point and since my discipline tells me to bring my bets down after three rolls. I win $90 and have no further exposure. You get to wait it out and hope that the math is wrong and the point is converted. If it happens, we are both happy. If not,......
244/251 or you don't? Try this math which is derived from your own calculations:
495 PL outcomes are achieved by rolling the dice (using an SRR of 6.0) 2,970 times on "average."
6 X 495= 2,970.
It takes 2,264 sets of 495 PL outcomes with a 99.5% "certainty" to get the exact 244/251 ratio. (Your post 2-13-10)
Therefore, it would require 6,724,080 rolls of the dice to exact just one 244/251 PL outcome ratio. 2,970 X 2,264 = 6,724,080
Rolling the dice 24/7 with a full table at all times (one minute between rolls) would take 12.8 years to accomplish. Now I know that the 244/251 ratio could happen in less time and with fewer rolls, but who's counting?
That 1.41% HA "average" really looks good to me now. How can I possibly refuse to play it with those very reasonable "expectations"?
tuttigym
Quote: HeadlockI should have said probability theory rather than laws of probability. I apologize. The 1.41% HA on a pass line bet is based on the assumption that there are 36 possible outcomes when rolling 2 6 sided dice that are weighted such that no one side is more or less likely to show.
I was confident that it was a simple misspeak and you knew the "theory" of how 1.41 was derived. The apology was unnecessary but very nice.
Having been hammered so often, I sort of wanted to hammer back. My apologies to you too.
tuttigym
Quote: goatcabinQuote: tuttigymAgain, did any of the references you have read or any other "expert" display the fact that the 1.41% HA have a 3.5% "expectation" of happening or did all those references INFER to all who would come to play that the HA was so "small" as to be not worrysome? Additionally, did any of the books or references you know of with the exception of blogs such as this one even describe the 244/251 ooutcomes?? I ask because beginners such as Raleighcraps and, I believe, thousands of others who play are clueless.
The references I have read did not specifically treat the distribution of 495 passline outcomes. The 1.414% HA can be arrived at in various ways. Actually, as I've said, I use the "perfect 1980", which is just four times the 495 and allows one to express all the possible outcomes in the form of integers. Interestingly enough, in the movie "The Big Town" (1987), with Matt Dillon, Diane Lane, Tommy Lee Jones, Bruce Dern and Lee Grant, J C Cullen (Dillon) is a young craps hotshot who comes to town and wants to work for Ferguson Edwards (Grant). During the interview, she asks him "How many bets does it take to work out all the odds?" His answer, "1980", of which 440 are comeout wins..." etc.,etc.
Of course, you are still confusing the meaning of the 1.4%. Try thinking about it this way: for any given session that you play, if you keep track of all your bets, you can figure out the house (or player) advantage for the session. Just take your net result and divide it by the total amount of all your bets (bet handle, it's called). (Don't use your starting bankroll.) If you did that for many, many sessions, and added up all the net outcomes and all the bet handles, then divided the total net by the total bet handle, it would come quite close to 1.4%.Quote: tuttigymQuote: goat: What do you think the HA on placing the six is? How would you figure it?
tuttigymQuote: tuttigymQuote: goatJust like you showed five ways to win and six ways to lose or 16 2/3% or .167 HA just like when the house pays the FO bet (true odds) of paying the player $6 for the $5 bet.
OK, I see what you're doing. It's completely wrong, of course. If you believed that placing the six actually had an HA of 16.7%, why would you EVER make such a bet? Nothing about your calculation is correct. If there are five ways to win and six to lose, there are 11 ways to resolve the bet, right? So, the probability of winning is 5/11 and losing is 6/11. Your .167 is just the probability of a seven rolling, out of all 36 combinations. I'm afraid you are hopeless. Sorry. I am done.
Cheers,
Alan Shank
I know that you and others have believe that I am wrong on the HA on the 6 or 8 at 16 2/3%, and that it is much more palitable to believe that the HA is only 1.51% because you asked the question "why would you EVER make such a bet (meaning PL/FO)? You see I knew you would get it --yes .167 HA. After all the ONLY two numbers that are relevant to the bet is the 6 (Place) and the 7 (loser). Thanks for affirming the correct math.
tuttigym
Quote: tuttigymQuote: boymimboNO! The house advantage on 6 or 8 is 5/11 * 7/6 - 6/11 = 1.5151515151515%
There are 11 different outcomes of a six or eight (not six) and you have to add all of the outsomes together to get house advantage not take 5/6 - 6/6 = -1/6!
So why not calculate 5/36 * 7/6 - 6/36 = ???? That is the "true" formula using ALL possible outcomes.
5/36 * 7/6 - 6/36 = .463% which happens to be the PER ROLL house advantage on the 6 or 8. You got one right for a change.
5/11 * 7/6 - 6/11 = 1.51515% IS the house advantage on the 6 or 8 when you let the bet go to resolution (ie, a 6 or 8 vs a seven).
You see, when I go to a casino, I know that house advantage of every single bet on the craps table. I know that there is variance to what is expected to happen and that I will not come out to that exact expectation every time. But I know that a $30 horn bet will lose, on average, far more money on average (about 10 times more money) then a $30 line bet or a $5 line bet with $25 odds. That's why the person is selling the bets in the center.
But what that means is that I expect to lose when I walk in the door and sit down at any slot machine or table. The only way I am going to win is if I am lucky. And I know the way that I will lose the least over time is to make the smartest bets: those with the lowest house advantage.
I don't pretend to think that there is a system with 30 ways to win and 6 ways to lose that will overcome anything that the casino will throw at me. I know that no system will overcome the house advantage at craps. The math demonstrates that. Craps exists because of that. Thousands have tried. All have failed.
So go for it. Believe what you will.
Quote: tuttigymQuote: goatcabinI am going to take one more shot at this, a different approach having occurred to me.
Now, tuttigym is fond of stating that the probability of ending up 244-251 after 495 passline bets is only .035 (actually .035847716), making it a "false promise" or even a "hoax". But that probability is actually higher than the probability of the 12 coming up on any roll of two dice. The odds against 244-251 occurring are only 27 to 1. Does tuttigym think that the 12 is a rare event?
What about the seven? The probability of the seven coming up is only .1667. So, is it a "false promise", too? The seven is far less likely to come up than all the other numbers combined, right? That's why tuttigym likes to bet $64 across, because he has 30 ways to win and only six to lose.
Tuttigym, try to understand that the 12 and the passline are both binary events; you either roll a 12 or you don't, you either win your passline bet or you don't, you either come out 244-251 or you don't.
Cheers,
Alan Shank
JB said it is 28 to 1. Are you saying that our illustrious administrator is wrong?
Once again, you misquote. Here is JB's statement:
"3.5848%, or approximately one "chunk" of 495 Pass Line resolutions out of 28 "chunks" of 495 Pass Line resolutions."
So, if the result in one "chunk" out of 28 "chunks", the odds against it occurring are 27 to 1. You don't understand the most basic ideas about odds, do you?
Of course, this was probably just a way to dodge the issue of the 12, which is less likely than the 244-251. Why didn't you address that?
Quote: tuttigymActually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164. I know that your sensibilities will be screaming and that somehow you will come up with a formula that shows that the HA is 17,432 to 1 against me, but then your mindset would leave all the bets on the table until the 7 showed and wiped out the chips. I mean, if you played on a $25 table with 5X odds and you bet $25 PL; the 6 became the point and then a FO bet (5X) of $125, the amount at risk is close to similar. Any three rolls that are no the point provides a win of about $30 or so X 3. A 7 out I lose a net $74; you of course lose $150. Now since the rules allow me to bring down all my Place bets during the point and since my discipline tells me to bring my bets down after three rolls. I win $90 and have no further exposure. You get to wait it out and hope that the math is wrong and the point is converted. If it happens, we are both happy. If not,......
Your "discipline" tells you to take place bets down after three rolls? It's the Gambler's Fallacy that tells you that. Well, you did something dishonest like this before, but just using the $64 across, then carefully selecting a scenario that favored that over PL/FO. No matter how you cut it, especially adding a high-HA bet like the horn, which of course loses on any of your place numbers as well as the seven, your method has a MUCH higher house advantage as well as more volatility.
The fact that you take bets down just means that you delay the resolution. If you believe the probability of the seven showing changes over time, then you are deluded about that, too. What taking bets down or calling them off does is lower your expected loss per unit time. However, those bets are no more likely to lose after some number of rolls as when you put them up again. You are a hopelessly confused individual when it comes to probability.
Quote: tuttigym244/251 or you don't? Try this math which is derived from your own calculations:
495 PL outcomes are achieved by rolling the dice (using an SRR of 6.0) 2,970 times on "average."
6 X 495= 2,970.
This is also totally wrong. A passline bet is resolved, on average, every 3.375 rolls, not every six. Have you ever heard of the comeout seven, the "winner seven"?
Quote: tuttigymIt takes 2,264 sets of 495 PL outcomes with a 99.5% "certainty" to get the exact 244/251 ratio. (Your post 2-13-10)
Therefore, it would require 6,724,080 rolls of the dice to exact just one 244/251 PL outcome ratio. 2,970 X 2,264 = 6,724,080
Rolling the dice 24/7 with a full table at all times (one minute between rolls) would take 12.8 years to accomplish. Now I know that the 244/251 ratio could happen in less time and with fewer rolls, but who's counting?
Wrong again. Apparently you interpreted my being a member since 2/13/10 as the date of my post, which was many days later. You make it very difficult to communicate well, don't you?
Here is my quote: "So, it would take 296 sets of 495 passline decisions to have a 50% chance of getting one at exactly 270-225, but 2264 sets to get a 99.5% chance of having one occur. For 270 OR MORE wins, it takes just 63 trials for a 50% chance, 483 for a 99.5% chance."
So, this was not talking about 244-251, but about a less likely W-L of 270-225. So, all of your figures are incorrect. Is anyone surprised? >:-) Regardless of which W-L record we're talking about, you also equate the (vastly overstated) number of rolls to get a 99.5% chance of an occurrence with it taking that many of rolls for it to occur. Of course, the 244/251 could occur on your first time; it could occur many times in 2264 sets of 495.
Cheers,
Alan Shank
Quote: tuttigymQuote: HeadlockNobody discovered the 1.41% HA, it's determined by the laws of probability. All the sims you guys run are pointless because tuttigym (sevenshooter) doesn't believe in the 100's of years of mathematical principles developed.
Really Headlock which "laws" of probability? I mean, did it somehow mystically appear on the table in a casino or come down from a voice on high or what and who and where?
tuttigym
Statistics is the mathematical science involving the collection, analysis and interpretation of data. A number of specialties have evolved to apply statistical theory and methods to various disciplines. Here are the main disciplines where the laws of probability and statistics, the same ones used at the craps table, are applied.
- Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. Your insurance rates are governed by the same laws of probability that drives the odds at the craps table.
- Biostatistics is a branch of biology that studies biological phenomena and observations by means of statistical analysis, and includes medical statistics. Likely a great deal of advances in medical sciences is driven by the same laws of probability that drive the odds at the craps table.
- Demography is the statistical study of all populations. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space.
- Environmental statistics is the application of statistical methods to environmental science. Weather, climate, air and water quality are included, as are studies of plant and animal populations.
- Epidemiology is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine.
- Geostatistics is a branch of geography that deals with the analysis of data from disciplines such as petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geography.
- Psychometrics is the theory and technique of educational and psychological measurement of knowledge, abilities, attitudes, and personality traits.
- Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.
- Statistical physics is one of the fundamental theories of physics, and uses methods of statistics in solving physical problems.
You see, when Mr Shank presents you with statistics that say that the pass line house advantage is 1.41%, we understand it to mean the same thing as say that your life expectancy at age 40 is 44 years. Not everyone dies at 84. In fact, only 6% of people might die at 84. But it's the MOST probable answer. When the bank comes to me and offers me a mortgage at 4%, I understand that they are using my credit rating, my income, and my age to calculate that rate. When they offer me that rate and calculating the most that I can afford, they are calculating a probablility that I am going to pay back the loan and determining the interest rate based on PROBABILITY. They don't know that I will be laid off tomorrow and will never repay the loan. They do know that a few people will and they make everyone in the risk pool pay a premium on the rate to cover the defaulters.
When I go out and get life insurance, the rate I pay is based on demographics and the profit margin that the life insurance wants -- all statistics, which is science that has been developed over hundreds of years. They are, in effect, actually, theorems, based on observations.
Really, when you say that the house advantage is not 1.414%, it's really insulting, especially to someone like me who has taken a number of statistics and calculus courses and understands this stuff. An entire branch of science is not wrong.
Quote: tuttigym
Actually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164. I know that your sensibilities will be screaming and that somehow you will come up with a formula that shows that the HA is 17,432 to 1 against me, but then your mindset would leave all the bets on the table until the 7 showed and wiped out the chips. I mean, if you played on a $25 table with 5X odds and you bet $25 PL; the 6 became the point and then a FO bet (5X) of $125, the amount at risk is close to similar. Any three rolls that are no the point provides a win of about $30 or so X 3. A 7 out I lose a net $74; you of course lose $150. Now since the rules allow me to bring down all my Place bets during the point and since my discipline tells me to bring my bets down after three rolls. I win $90 and have no further exposure. You get to wait it out and hope that the math is wrong and the point is converted. If it happens, we are both happy. If not,......
tuttigym
These simple calculations can be done using pencil and paper, although I used a keyboard and a calculator.
The HA for the across + horn where you take down all bets after one roll was derived on page 4 of this thread: 2.3%.
This was for a different total bet amount; using the strategy and bet and win amounts you provided here:
There is an outcome on every number that can roll. Each roll has a 30/36 probability of not being a seven.
Immediate seven out: 6/36 = 16.7% and on average the across + horn will lose 16.7% * 164 = $27.39
One non seven followd by a seven: 30/36 * 6/36 = 13.9%; average loss 13.9% * (164-30) = $18.63
Two non sevens followed by a seven: (30/36)^2 * 6/36 = 11.6%; average loss = 11.6% * (164-60) = $12.06
Three non sevens (now we don't care what happens next, because the bets are taken down: (30/36)^3 = 57.9%; average win = 57.9% * 90 = 52.11.
Net average win: 52.11 - 27.39 - 18.63 - 12.06 = -6.57. This is a loss even with your discipline to take down your bets after three rolls.
HA = 6.57/164 = 4%
For the pass line 6 with 5x odds, played out until it is resolved, it wins 5 times and loses 6 times.
Win: 5/11 = 45.5% of the time there is a $175 win; on average = 79.54.
Lose: 6/11 = 54.5% of the time there is a $150 loss: on average = 81.75
Net average win = 79.54 - 81.75 = -2.21
HA = 2.21 / 150 = 1.47% (NOTE that this neglects the effects on the come out roll on the flat bet, which reduces the overall HA because it wins more often than it loses.)
I'm not trying to argue that one way is better than the other, just that they both favor the house, and, measuring strictly by the average amount the house makes off each bet, the pass line 6 + FO loses less than the across + horn.
There are other ways to look at these bets and consider various scenarios. We can both lose it all on an immediate seven out -- 16.7% of the time. I can more than double my money on one roll -- 13.9% of the time while you can win only $30. For me, it is a binary event, I win $175 or lose $150. You have a range of possible outcomes. I could win after a dozen rolls while you are sitting on the sideline happy with your $90. When a person understands the HA, and takes into account the probabilities of the different outcomes (or the variance) he can make a choice about how he is going to bet.
Quote: tuttigymQuote: goatcabin: What do you think the HA on placing the six is? How would you figure it?
Quote: tuttigymJust like you showed five ways to win and six ways to lose or 16 2/3% or .167 HA just like when the house pays the FO bet (true odds) of paying the player $6 for the $5 bet.
Quote: goatcabinOK, I see what you're doing. It's completely wrong, of course. If you believed that placing the six actually had an HA of 16.7%, why would you EVER make such a bet? Nothing about your calculation is correct. If there are five ways to win and six to lose, there are 11 ways to resolve the bet, right? So, the probability of winning is 5/11 and losing is 6/11. Your .167 is just the probability of a seven rolling, out of all 36 combinations. I'm afraid you are hopeless. Sorry. I am done.
I know that you and others have believe that I am wrong on the HA on the 6 or 8 at 16 2/3%, and that it is much more palitable to believe that the HA is only 1.51% because you asked the question "why would you EVER make such a bet (meaning PL/FO)?
No, meaning placing the six, if you believe that the HA is .167, which, oddly enough, is the HA on the Any 7 bet.
Quote: tuttigymYou see I knew you would get it --yes .167 HA. After all the ONLY two numbers that are relevant to the bet is the 6 (Place) and the 7 (loser). Thanks for affirming the correct math.
tuttigym
Well, if the only relevant numbers are 6 and 7, then the probability of the 7 occurring, compared to ALL the other numbers is irrelevant, isn't it? The probability of the 7 showing BEFORE a 6 is 6/11 = .5454. The probability of the 6 showing before a 7 is 5/11 = .4545. The difference between them is .0909, which actually IS the HA for the Big 6/Big 8, since that's an even-money bet. For an even-money bet, the HA is simply the difference between the probabilities of winning and losing. For a relevant example, the passline probability of winning is .492929 and losing is .507071, and the difference is .01414, quite a recognizable figure, no?
BTW, since you believe that the payoff is not part of the issue, why in the name of sense do you bother to bet the extra $2 on the 6 and 8 when you place $64 across. Surely you don't care that you need that to get the 7:6 payout do you? It's bullshit, isn't it? You are hilarious! You see, I'm not only smiling; I'm laughing.
Cheers,
Alan Shank
Quote: tuttigym
Actually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164. I know that your sensibilities will be screaming and that somehow you will come up with a formula that shows that the HA is 17,432 to 1 against me, but then your mindset would leave all the bets on the table until the 7 showed and wiped out the chips. I mean, if you played on a $25 table with 5X odds and you bet $25 PL; the 6 became the point and then a FO bet (5X) of $125, the amount at risk is close to similar. Any three rolls that are no the point provides a win of about $30 or so X 3. A 7 out I lose a net $74; you of course lose $150. Now since the rules allow me to bring down all my Place bets during the point and since my discipline tells me to bring my bets down after three rolls. I win $90 and have no further exposure. You get to wait it out and hope that the math is wrong and the point is converted. If it happens, we are both happy. If not,......
tuttigym
Wait a minute! Are you saying that you bet $64 across and $100 on the horn? That would be $25 each on the 2, 3, 11 and 12. Or maybe the $164 is made up of different components. Please clarify.
However, assuming you bet $64 across and $100 on the horn, here are the possible results of one roll:
2 -- win $750 on the 2, lose $75 = +$675
12 -- same thing
3 -- win $375 on the 3, lose $75 = +$300
11 -- same thing
6 or 8 -- win $14 on 6 or 8, lose $100 = -$86
5 or 9 -- same thing
4 or 10 -- win $18, lose $100 = -$82
7 -- lose $164
If you weight these by their probabilities, they come out to a loss of $8.61, but with a huge variance.
So, please clarify these things:
1) Specify each bet, i.e. $10 place 4, $10 place 5, $12 place 6.... etc. and how much on the horn
2) The horn is a one-roll bet; do you replace it when it loses (for the three rolls, that is)? Do you leave the bet up when it wins?
3) After you call your bets off (or take them down), do you wait for the next shooter and a point before putting bets up (calling them "On") again?
Another point:
I find it pretty hilarious that you are, apparently, putting $25 each on the 2 and 12, which each have only a 2.78% chance to win, actually less than the probability of the "perfect 244-251" that you so vociferously deride.
Hey, I've got an idea! Why don't you add an Any 7 bet to your arsenal so you'd win at least one bet on EVERY ROLL!!! You couldn't lose, could you?
Cheers,
Alan Shank
Quote: goatcabinQuote: tuttigym
Actually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164. I know that your sensibilities will be screaming and that somehow you will come up with a formula that shows that the HA is 17,432 to 1 against me, but then your mindset would leave all the bets on the table until the 7 showed and wiped out the chips. I mean, if you played on a $25 table with 5X odds and you bet $25 PL; the 6 became the point and then a FO bet (5X) of $125, the amount at risk is close to similar. Any three rolls that are no the point provides a win of about $30 or so X 3. A 7 out I lose a net $74; you of course lose $150. Now since the rules allow me to bring down all my Place bets during the point and since my discipline tells me to bring my bets down after three rolls. I win $90 and have no further exposure. You get to wait it out and hope that the math is wrong and the point is converted. If it happens, we are both happy. If not,......
tuttigym
Wait a minute! Are you saying that you bet $64 across and $100 on the horn? That would be $25 each on the 2, 3, 11 and 12. Or maybe the $164 is made up of different components. Please clarify.
However, assuming you bet $64 across and $100 on the horn, here are the possible results of one roll:
2 -- win $750 on the 2, lose $75 = +$675
12 -- same thing
3 -- win $375 on the 3, lose $75 = +$300
11 -- same thing
6 or 8 -- win $14 on 6 or 8, lose $100 = -$86
5 or 9 -- same thing
4 or 10 -- win $18, lose $100 = -$82
7 -- lose $164
If you weight these by their probabilities, they come out to a loss of $8.61, but with a huge variance.
So, please clarify these things:
1) Specify each bet, i.e. $10 place 4, $10 place 5, $12 place 6.... etc. and how much on the horn
2) The horn is a one-roll bet; do you replace it when it loses (for the three rolls, that is)? Do you leave the bet up when it wins?
3) After you call your bets off (or take them down), do you wait for the next shooter and a point before putting bets up (calling them "On") again?
Another point:
I find it pretty hilarious that you are, apparently, putting $25 each on the 2 and 12, which each have only a 2.78% chance to win, actually less than the probability of the "perfect 244-251" that you so vociferously deride.
Hey, I've got an idea! Why don't you add an Any 7 bet to your arsenal so you'd win at least one bet on EVERY ROLL!!! You couldn't lose, could you?
Cheers,
Alan Shank
No Alan the bet is $160 across the board at $30 on each the 6 & 8 plus $25 each on the 4, 5, 9, and 10 plus $4 on the horn. Gee Alan I thought your math skills were better than that, but then again someone who is invested the PL/FO strategy at 3x, 4x, and 5x depending on the point and actually believes in the 1.41% HA that requires over 6 million rolls of the dice for a 99.5% certainty just might have some trouble with the simple dispursement of $164 to the player's advantage.
tuttigym
Quote: boymimboTutti, I am sorry that you don't understand math, probability or statistics. I'm convinced that you don't.
You see, when I go to a casino, I know that house advantage of every single bet on the craps table. I know that there is variance to what is expected to happen and that I will not come out to that exact expectation every time. But I know that a $30 horn bet will lose, on average, far more money on average (about 10 times more money) then a $30 line bet or a $5 line bet with $25 odds. That's why the person is selling the bets in the center.
But what that means is that I expect to lose when I walk in the door and sit down at any slot machine or table. The only way I am going to win is if I am lucky. And I know the way that I will lose the least over time is to make the smartest bets: those with the lowest house advantage.
I don't pretend to think that there is a system with 30 ways to win and 6 ways to lose that will overcome anything that the casino will throw at me. I know that no system will overcome the house advantage at craps. The math demonstrates that. Craps exists because of that. Thousands have tried. All have failed.
So go for it. Believe what you will.
I realize this might be a bit off topic, but when Tiger Woods enters a tournament he believes he is going to win. His preparation and mindset and skills make his beliefs happen. His winning percentage has exceeded any other golfer ever to play the game. At 33 yrs of age, he is 2nd in total PGA wins, 2nd in total major wins, and first in percentage.
When I enter a casino, I believe I will win at the craps table. My preparation and mindset and of course some luck allows me to have a very favorable winning percentage.
I know you play to win, but if you believe you are going to lose, you are never disappointed and you do.
tuttigym
Quote: JBQuote: tuttigymI want to know the chances, the odds, the probabilities of exactly having 244 wins against 251 losses in 495 PL outcomes.
3.5848%, or approximately one "chunk" of 495 Pass Line resolutions out of 28 "chunks" of 495 Pass Line resolutions.
The exact formula is: 495!/(244! × 251!) × (244/495)244 × (251/495)251
To address the notion that the house advantage is a hoax, consider a coin toss. The chance of it landing on heads is 50%, and the chance of it landing on tails is the other 50%. But the probability of exactly 250 heads and 250 tails in 500 coin tosses is 3.5665%, also roughly 1 in 28. Does this mean that the probability of heads being 50% and tails being 50% is a hoax? Of course not. In the short term, anything can happen. But over time, the results will approach expectations (50% heads, 50% tails). It's no different with the Pass Line bet in craps. In the short term, anything can happen, but over time you will win 49.2929% of the time and lose 50.7071% of the time. Just because every sequence of 495 rolls doesn't produce exactly 244 wins and 251 losses does not make it a hoax.
"Also roughly 1 in 28" referring to the coin toss and the PL 1.41% HA. 1 in 27 works out to .037037 and 1 in 28 works out to .0357142, so it is 1 in 28 "roughly."
tuttigym
Quote: tuttigym...someone who is invested the PL/FO strategy....
You've written this several times, that the reason everyone is telling you you are wrong is because we are "invested in this strategy". I feel comfortable speaking for everyone in saying that no one is defending it because they are invested in it; we invest in it because over time it is the strategy most likely to win, or at least most likely to lose least.
Quote: tuttigymWhen I enter a casino, I believe I will win at the craps table. My preparation and mindset and of course some luck allows me to have a very favorable winning percentage.
That's heartwarming. Your mindset has nothing to do with it, unless you are psychic. If what you've written here is your "preparation", and you have a favorable winning percentage, then I need to stand next to you. But I doubt do not believe that your winning percentage over several years' time is as good as any pass/don't pass + odds player. In order to overcome your strategy, which is essentially the equivalent of betting in US currency but taking your winnings in Canadian, you need to have more than "some" luck.
Believe it or not... and for some reason, you do not... the world really does follow the math. You do not UNDERSTAND the math. It is hard for me to believe that you do not understand it; but I actually believe that it is more likely that you actually think you are right, rather than that you are doing this to see how long it will last.
Quote: tuttigymQuote: goatcabinQuote: tuttigym
Actually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164.
tuttigym
Wait a minute! Are you saying that you bet $64 across and $100 on the horn? That would be $25 each on the 2, 3, 11 and 12. Or maybe the $164 is made up of different components. Please clarify.
So, please clarify these things:
1) Specify each bet, i.e. $10 place 4, $10 place 5, $12 place 6.... etc. and how much on the horn
2) The horn is a one-roll bet; do you replace it when it loses (for the three rolls, that is)? Do you leave the bet up when it wins?
3) After you call your bets off (or take them down), do you wait for the next shooter and a point before putting bets up (calling them "On") again?
Cheers,
Alan Shank
No Alan the bet is $160 across the board at $30 on each the 6 & 8 plus $25 each on the 4, 5, 9, and 10 plus $4 on the horn.
OK, that's more like it. Your other post about this method talked about placing $64 across, so I was starting from there, since you did not say otherwise. The information you provide is often inadequate to evaluate what you say.
Quote: tuttigymGee Alan I thought your math skills were better than that,...
tuttigym
Nothing to do with my math skills, I was just going back to your $64 across example.
BTW, you did not answer the question about replacing the horn bet.
Cheers,
Alan Shank
Quote: tuttigymNo Alan the bet is $160 across the board at $30 on each the 6 & 8 plus $25 each on the 4, 5, 9, and 10 plus $4 on the horn.
tuttigym
OK, so here's what can happen on one roll of the dice:
2 -- win $30 on the 2, lose $3 = +$27
12 -- same thing
3 -- win $15 on the 3, lose $3 = +$12
11 -- same thing
6 or 8 -- win $35 on the 6/8, lose $4 = +$31
5 or 9 -- win $35 on the 5/9, lose $4 = +$31
4 or 10 -- win $45 on 4/10,lose $4 = +$41
7 -- lose $164
weighted net outcome -$2.167
bets
6/36 * 4 = .66667
10/36 * 34 = 9.444
14/36 * 29 = 11.277
6/36 * 164 = 27.333
weighted bet handle - $48.722
-2.167 / 48.722 = -.0445 or 4.45%
So, I programmed a WinCraps auto-bet file with these parameters:
starting bankroll $2500
no bets on comeout roll
when a point is established:
bet $25, $25, $30, $30, $25, $25 on all point numbers
bet $4 horn
winning bets - same bet
losing bets - replace
After three non-seven rolls, call place bets "Off", do not replace horn bet, so NO ACTION until shooter sevens out. If shoot makes his point, no horn bet on comeout roll, place bets Off automatically.
Session ends before first comeout roll after 200 rolls, or if there is not $164 left.
I ran 10,000 sessions; here are the results:
| parameter | |
|---|---|
| avg. num. rolls | 202.5 |
| avg. num. bets | 224 |
| avg. bet handle | 3958 |
| mean net result | -$179 |
| median net result | -$152 |
| mode of net result | -$188 to -$148 |
| standard deviation | $636 |
| mean house advantage | -4.51% |
| winning sessions | 4034 |
| breakeven sessions | 2 |
| losing sessions | 5964 |
| number of busts | 12 |
| lost more than $1000 | 1052 |
| lost more than $500 | 2955 |
| won more than $100 | 3451 |
| won more than $250 | 2589 |
| won more than $500 | 1396 |
| won more than $1000 | 244 |
| biggest win | $1821 |
So, it looks like $2500 is plenty to keep you going for a couple of hours, unless you are very unlucky; however, your chances of breaking even or better are only about 40%, with almost a 30% chance of losing $500 or more. In fact, your probability of losing at least $500 is greater than your probability of winning $250 or more.
Here is a picture from WinCraps of the distribution of net outcomes:
How about that?
Cheers,
Alan Shank
For comparison sake, can you put up the distribution for a passline bet that has ~$164 at risk?
Perhaps $30 pass line with $120 odds.
If you had the same seed as you just used for tutti, that would be awesome.
Quote: goatcabinQuote: tuttigymQuote: goatcabin: What do you think the HA on placing the six is? How would you figure it?
Quote: tuttigymJust like you showed five ways to win and six ways to lose or 16 2/3% or .167 HA just like when the house pays the FO bet (true odds) of paying the player $6 for the $5 bet.
Quote: goatcabinOK, I see what you're doing. It's completely wrong, of course. If you believed that placing the six actually had an HA of 16.7%, why would you EVER make such a bet? Nothing about your calculation is correct. If there are five ways to win and six to lose, there are 11 ways to resolve the bet, right? So, the probability of winning is 5/11 and losing is 6/11. Your .167 is just the probability of a seven rolling, out of all 36 combinations. I'm afraid you are hopeless. Sorry. I am done.
I know that you and others have believe that I am wrong on the HA on the 6 or 8 at 16 2/3%, and that it is much more palitable to believe that the HA is only 1.51% because you asked the question "why would you EVER make such a bet (meaning PL/FO)?
No, meaning placing the six, if you believe that the HA is .167, which, oddly enough, is the HA on the Any 7 bet.Quote: tuttigymYou see I knew you would get it --yes .167 HA. After all the ONLY two numbers that are relevant to the bet is the 6 (Place) and the 7 (loser). Thanks for affirming the correct math.
tuttigymQuote: goatWell, if the only relevant numbers are 6 and 7, then the probability of the 7 occurring, compared to ALL the other numbers is irrelevant, isn't it? The probability of the 7 showing BEFORE a 6 is 6/11 = .5454. The probability of the 6 showing before a 7 is 5/11 = .4545.
Again, you continue to forge out ratios (6/11, etc.) that have nothing to do with the actuality of winning a bet. The player's only concern should be to win any given bet based on the true ratio of ways to win over ways to lose, i.e., 6/7. If your goal is to confuse a newcomer or even someone who has been playing a long time that has never really dug into the "math," then why not show them 5/36? After all, it is possible to throw the other numbers w/o losing; neutral numbers right? That way you can really distort your percentage (5/36 = .138888 on any given roll of the dice).
The difference between them is .0909, which actually IS the HA for the Big 6/Big 8, since that's an even-money bet. For an even-money bet, the HA is simply the difference between the probabilities of winning and losing. For a relevant example, the passline probability of winning is .492929 and losing is .507071, and the difference is .01414, quite a recognizable figure, no?Quote: goatBTW, since you believe that the payoff is not part of the issue, why in the name of sense do you bother to bet the extra $2 on the 6 and 8 when you place $64 across. Surely you don't care that you need that to get the 7:6 payout do you?
Again, you misrepresent what I have said. The additional winning payments due to the odds do not relate to the winning % (ways to win vs ways to lose). But you and yours actually believe the FO bet levels the field for winning and losing bets. Right?Quote: goatIt's bullshit, isn't it?
The only BS shown here is twofold: (1) The FO bet somehow reduces the risk of loss because "the house no longer has an advantage" and somehow the point conversion is a 50/50 proposition like the coin flip, and (2) the 1.41% HA, which is just the average of the possible ways to win and lose a PL bet, provides the "expectation" of winning at a similar rate of the coin flip.
By the way, since there is no HA with the placement of the FO bets, why would you play a lesser FO bet on the 4/10 than on the 6/8? Everybody keeps stating that there is NO HA with the FO bets. Now that is really laughable.
You are hilarious! You see, I'm not only smiling; I'm laughing.
Cheers,
Alan Shank
Quote: seattlediceQuote: tuttigym
Actually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164. I know that your sensibilities will be screaming and that somehow you will come up with a formula that shows that the HA is 17,432 to 1 against me, but then your mindset would leave all the bets on the table until the 7 showed and wiped out the chips. I mean, if you played on a $25 table with 5X odds and you bet $25 PL; the 6 became the point and then a FO bet (5X) of $125, the amount at risk is close to similar. Any three rolls that are no the point provides a win of about $30 or so X 3. A 7 out I lose a net $74; you of course lose $150. Now since the rules allow me to bring down all my Place bets during the point and since my discipline tells me to bring my bets down after three rolls. I win $90 and have no further exposure. You get to wait it out and hope that the math is wrong and the point is converted. If it happens, we are both happy. If not,......
tuttigymQuote: SDThese simple calculations can be done using pencil and paper, although I used a keyboard and a calculator.
The HA for the across + horn where you take down all bets after one roll was derived on page 4 of this thread: 2.3%.
This was for a different total bet amount; using the strategy and bet and win amounts you provided here:
There is an outcome on every number that can roll. Each roll has a 30/36 probability of not being a seven.
Immediate seven out: 6/36 = 16.7% and on average the across + horn will lose 16.7% * 164 = $27.39
One non seven followd by a seven: 30/36 * 6/36 = 13.9%; average loss 13.9% * (164-30) = $18.63
Two non sevens followed by a seven: (30/36)^2 * 6/36 = 11.6%; average loss = 11.6% * (164-60) = $12.06
Three non sevens (now we don't care what happens next, because the bets are taken down: (30/36)^3 = 57.9%; average win = 57.9% * 90 = 52.11.
Net average win: 52.11 - 27.39 - 18.63 - 12.06 = -6.57. This is a loss even with your discipline to take down your bets after three rolls.
HA = 6.57/164 = 4%
For the pass line 6 with 5x odds, played out until it is resolved, it wins 5 times and loses 6 times.
Win: 5/11 = 45.5% of the time there is a $175 win; on average = 79.54.
Lose: 6/11 = 54.5% of the time there is a $150 loss: on average = 81.75
Net average win = 79.54 - 81.75 = -2.21
HA = 2.21 / 150 = 1.47% (NOTE that this neglects the effects on the come out roll on the flat bet, which reduces the overall HA because it wins more often than it loses.)
Here is what you need to do when teaching you 21 year old grandson or granddaughter to play the game of craps. First, show them all of the above "math" from boymimbo, goatcabin, and yourself just as it is presented here. Second, wake them up from their sleep of deep bordom, and third try to convince them that walking away from your diatribes is no way to treat their grandfather who is trying to teach them the game of craps and how easy it is to play and win.
I'm not trying to argue that one way is better than the other, just that they both favor the house, and, measuring strictly by the average amount the house makes off each bet, the pass line 6 + FO loses less than the across + horn.
There are other ways to look at these bets and consider various scenarios. We can both lose it all on an immediate seven out -- 16.7% of the time. I can more than double my money on one roll -- 13.9% of the time while you can win only $30. For me, it is a binary event, I win $175 or lose $150. You have a range of possible outcomes. I could win after a dozen rolls while you are sitting on the sideline happy with your $90. When a person understands the HA, and takes into account the probabilities of the different outcomes (or the variance) he can make a choice about how he is going to bet.
The house edge is calculted on the result from all 36 combintions of the dice. Since the lowest common denomintor is 160 the formula is as follows 36x160= 5760 to figure the house edge from the pass line it is:
2 3 4 5 6 7 8 9 10 11 12
160 320 480 640 800 960 800 640 480 320 160
It is a perfect bell shaped curve. To plot the edge
-160 -320 -160 -128 -72 +960 -72 -128 -160 +320 -160 = -80
-80/5760= -1.388%
For the don't pass
+160 +320 +160 +128 +72 -960 +72 +128 +160 -320 PUSH = -80
-80/5760 = -1.388%
The house edge on all other bets is greater than this.
Quote: MoscaQuote: tuttigym...someone who is invested the PL/FO strategy....
Quote: MoscaYou've written this several times, that the reason everyone is telling you you are wrong is because we are "invested in this strategy". I feel comfortable speaking for everyone in saying that no one is defending it because they are invested in it; we invest in it because over time it is the strategy most likely to win, or at least most likely to lose least.
Do you suppose the others can show similar successes that mirror your play during the past eight years?? What you have proven to me, anyway, is that the strategy you are currently employing just is not rewarding your loyalties to the prevailing "math" wisdom. Look, I know you are a really good person, because you have taken the time to jump in here and put yourself out to provide your point of view plus show us your sense of humor and talent with the cartoons. I just think you can be more successful.Quote: tuttigymWhen I enter a casino, I believe I will win at the craps table. My preparation and mindset and of course some luck allows me to have a very favorable winning percentage.
Quote: MoscaThat's heartwarming. Your mindset has nothing to do with it, unless you are psychic. If what you've written here is your "preparation", and you have a favorable winning percentage, then I need to stand next to you. But I doubt do not believe that your winning percentage over several years' time is as good as any pass/don't pass + odds player. In order to overcome your strategy, which is essentially the equivalent of betting in US currency but taking your winnings in Canadian, you need to have more than "some" luck.
My "preparation" is to practice every day on a free craps play web site like the W of O. I can experiment with different wagers, patterns, and play. Every day for at least an hour, I practice. When I play for real, it is easy; I can switch up my play and bets; I am comfortable. The reality of the table many times exhibits the computer play and sometimes not. The randomness never dublicates the computer, but the "preparation" prepares me for the randomness.
Quote: MoscaBelieve it or not... and for some reason, you do not... the world really does follow the math. You do not UNDERSTAND the math. It is hard for me to believe that you do not understand it; but I actually believe that it is more likely that you actually think you are right, rather than that you are doing this to see how long it will last.
I UNDERSTAND the math associated with the 1.41% HA on PL bets resolves itself only 3.5% of the time. I UNDERSTAND that it takes 146 SETS of 495 PL outcomes to actually produce the 1.41% HA.
I UNDERSTAND that at 3.375 ave rolls/PL outcome that comes out to 243,966 rolls of the dice. I REALLY UNDERSTAND that those odds and figures will desimate one's pocketbook.
tuttigym
Quote: tuttigymYou see I knew you would get it --yes .167 HA. After all the ONLY two numbers that are relevant to the bet is the 6 (Place) and the 7 (loser). Thanks for affirming the correct math.
tuttigym
Quote: goatcabinWell, if the only relevant numbers are 6 and 7, then the probability of the 7 occurring, compared to ALL the other numbers is irrelevant, isn't it? The probability of the 7 showing BEFORE a 6 is 6/11 = .5454. The probability of the 6 showing before a 7 is 5/11 = .4545.
Quote: tuttigymAgain, you continue to forge out ratios (6/11, etc.) that have nothing to do with the actuality of winning a bet. The player's only concern should be to win any given bet based on the true ratio of ways to win over ways to lose, i.e., 6/7. If your goal is to confuse a newcomer or even someone who has been playing a long time that has never really dug into the "math," then why not show them 5/36? After all, it is possible to throw the other numbers w/o losing; neutral numbers right? That way you can really distort your percentage (5/36 = .138888 on any given roll of the dice).
First, you say that the only two numbers relevant are the six and seven. That is correct. But the probability of winning or losing that bet is dependent on the probabilities of getting a six and seven RELATIVE TO EACH OTHER. So you cannot use 36 as the divisor. There are five ways to roll a six and six ways to roll a seven, so the divisor is their sum - 11. You don't care about any other rolls, right? So, p(6 before 7) is 5/11, p(7 before 6) is 6/11. I still don't see how you ever came up with .167, in any case. And, of course, the ways are not 6 and 7 at all. Your confusion is incredible!
Quote: goatBTW, since you believe that the payoff is not part of the issue, why in the name of sense do you bother to bet the extra $2 on the 6 and 8 when you place $64 across. Surely you don't care that you need that to get the 7:6 payout do you?
Quote: tuttigymAgain, you misrepresent what I have said. The additional winning payments due to the odds do not relate to the winning % (ways to win vs ways to lose). But you and yours actually believe the FO bet levels the field for winning and losing bets. Right?
The payoff does not affect the probability of winning a bet. Since you think the only relevant thing is the probability of winning a bet, I ask again: "Why do you bother to bet $12 on place 6/8, while you bet $10 on 5/9/4/10?"
Quote: tuttigymBy the way, since there is no HA with the placement of the FO bets, why would you play a lesser FO bet on the 4/10 than on the 6/8? Everybody keeps stating that there is NO HA with the FO bets. Now that is really laughable.
Who would play a lesser FO bet on the 4/10? Not I, unless I am taking max odds at a 3,4,5X table. Do you understand why 3, 4, 5X odds are now more-or-less standard? It's because the payoff is always 6 units, i.e. it's easier on the dealers. Also, there is more variance on the outside numbers, due to the increased, 2:1 payoff, and the casinos do not like to give too much variance for free.
I guess you simply are not intelligent enough to understand that the evaluation of a bet must include BOTH its probability of being won and the payoff relative to the amount bet.
A coin-flip game:
heads you pay me $5
tails I pay you $5
OR
heads you pay me $6
tails I pay you $5
Are these equally fair?
If not, why not?
Cheers,
Alan Shank
Quote: SPOOS1tuttigym:
The house edge is calculted on the result from all 36 combintions of the dice. Since the lowest common denomintor is 160 the formula is as follows 36x160= 5760 to figure the house edge from the pass line it is:
2 3 4 5 6 7 8 9 10 11 12
160 320 480 640 800 960 800 640 480 320 160
It is a perfect bell shaped curve. To plot the edge
-160 -320 -160 -128 -72 +960 -72 -128 -160 +320 -160 = -80
-80/5760= -1.388%
For the don't pass
+160 +320 +160 +128 +72 -960 +72 +128 +160 -320 PUSH = -80
-80/5760 = -1.388%
The house edge on all other bets is greater than this.
These are not correct. I'm not sure how you came up with the values for each number, but: In the first place, you can express all the possible outcomes as integers with 1980 bets as below:
| result | ways | comment |
|---|---|---|
| comeout win | 440 | |
| comeout loss | 220 | 660 comeout decisions |
| win on 6 | 125 | |
| loss on 6 | 150 | |
| win on 8 | 125 | |
| loss on 8 | 150 | |
| win on 5 | 88 | |
| loss on 5 | 132 | |
| win on 9 | 88 | |
| loss on 9 | 132 | |
| win on 4 | 55 | |
| loss on 4 | 110 | 1320 point decisions |
| win on 10 | 55 | 536 point wins |
| loss on 10 | 110 | 784 seven-outs |
| ---- | ||
| 1980 |
If you add them all up, you get -28 / 1980 = -.01414. For the don't pass, it's -27 / 1925 = -.01403 (some books consider the 55 ways for the 12 as "risked", and show -27 / 1980 = -.01364).
Cheers,
Alan Shank
Quote: SPOOS1tuttigym:
The house edge is calculted on the result from all 36 combintions of the dice. Since the lowest common denomintor is 160 the formula is as follows 36x160= 5760 to figure the house edge from the pass line it is:
2 3 4 5 6 7 8 9 10 11 12
160 320 480 640 800 960 800 640 480 320 160Quote: SPOOS1It is a perfect bell shaped curve.
Nice to have you join in and welcome to the "insanity." How many SETS of the -80/5760 does it take to create your "perfect bell shaped curve"? Does the 5760 represent the number of dice rolls? How is that different that the "Rule of 495"? Is the "house edge" and the HA the same thing? Are we talking PL outcomes? If so, why is your house edge different at 1.388% than everyone else's 1.41% HA?
tuttigym
To plot the edge
-160 -320 -160 -128 -72 +960 -72 -128 -160 +320 -160 = -80
-80/5760= -1.388%
For the don't pass
+160 +320 +160 +128 +72 -960 +72 +128 +160 -320 PUSH = -80
-80/5760 = -1.388%
The house edge on all other bets is greater than this.
Quote: RaleighCrapsAlan,
For comparison sake, can you put up the distribution for a passline bet that has ~$164 at risk?
Perhaps $30 pass line with $120 odds.
If you had the same seed as you just used for tutti, that would be awesome.
Keep in mind that the odds bet is only made 2/3 of the time, so in order to get an average bet of around $164, you have to go up substantially from $30 plus $120.
I ended up trying $40 pass with 5X odds, which results in an average of over $173 for each passline bet. Of course, that is going to be a LOT more variance than tutti's game, where he stops betting after 3 rolls. The results indicate this clearly:
| parameter | |
|---|---|
| mean num. rolls | 188.6 |
| mean num. bets | 93 |
| mean bet handle | 9683 |
| mean net result | -$43.44 |
| median net result | -100 |
| mode of net result | -2300 to -2220 |
| standard deviation | $1718 |
| mean house advantage | -0.45% |
| winning sessions | 4768 |
| breakeven sessions | 40 |
| losing sessions | 5192 |
| number of busts | 1991 |
| lost more than $1000 | 3188 |
| lost more than $500 | 4163 |
| won more than $500 | 3743 |
| won more than $1000 | 2778 |
| won more than $2000 | 1260 |
| biggest win | $7420 |
So, this has almost three times the volatility as tutti's $164 method. In my simulation of tutti's method, in about the save average time (# of rolls), about 225 bets were resolved, but those bets were for a maximum of $30 of some of them only $4. In this sim, an average of 93 bets were resolved per session, but they averaged $173. Note that the mean bet handle was almost 2 1/2 times higher with PL/FO at this level. OTOH, despite the huge bet handle, the mean loss was over four times higher with tutti's method, and the probability of a winning session was .403, compared to .477. That is how the relationship between expected loss and variance works: the lower the ratio of ev / SD, the higher the probability of breaking even or better. In tutti's case, 179 / 636 = .281, while 43.4 / 1718 = .025. Of course, the higher the variance, the higher the "penalty" for having bad luck. There is no "magic bullet". If you squeeze a balloon on one side, it puffs out on the other. Gambling is the same.
Here's something else to consider. If you know the expected loss and SD for two strategies, you can figure out the degree of luck where one method comes out better than the other, IOW the "breakeven point".
In this case, suppose both players have exactly average luck, i.e. each player experiences the expected value from a session (like the 244-251 that's been beaten to death here).
tutti: -179
PL/FO: -43, so the advantage at average luck is $136 to PL/FO
Now, the difference in the SDs is 1718 - 636 = 1082
This means that, for every one SD of "good luck", the PL/FO gets more ahead by $1082.
If tutti has one SD of good luck, he comes out -179 + 636 = +$457.
If PL/FO has one SD of good luck, which is equally likely, he comes out -43 + 1718 = +$1675.
However, what if they have equal degrees of bad luck?
If tutti has one SD of bad luck, he comes out -179 - 636 = -$815
If PL/FO has one SD of bad luck, which is equally likely, he comes out -43 - 1718 = -$1761.
So at -1 SD, PL/FO is more badly off. Somewhere in between +1 SD and -1 SD, then, there must be a "crossover point" where the heavy variance in the PL/FO method makes it come out worse. We can find it by dividing the "initial advantage", i.e. the advantage of the PL/FO at average luck, by the difference in the standard deviations. So:
136 / 1082 = .1257
So, if they have average or better luck, the PL/FO comes out ahead, the more good luck the farther ahead (note the $7420 biggest win, compared to $1821 for tutti). However, if they both come out .1257 SD WORSE than average, then tutti is going to lose LESS, the worse the luck, the more less, so to speak. This is why the bust rate is much higher for the PL/FO.
Let's check our figures:
-179 - (.1257 * 636) = -259 for tutti
-43 - (.1257 * 1718) = -259 for PL/FO
Below that, the PL/FO at that level gets hammered worse and worse. The probability of coming out .13 SD OR MORE WORSE than the mean expectation is .448. So, the PL/FO has a .552 probability of doing better than the "tutti method", with a much, much higher "up side" but a much, much lower downside.
Each individual's tolerance for volatility is different; if you can afford (and are willing) to lose $2500 in a quest for winning $1000 or more (PL/FO has a probability of .28 of doing that), then I am happy for you. >:-)
For my taste, tutti's method has too much expected loss and too much variance, both, because of the relatively high HA and the amount of the bets.
The key, in my view, is to understand what the session-outcome probabilities are, just like one (except tuttigym) understands the probabilities of winning the different bets and the probabilities of the dice rolls. Then you can come up with a strategy that gives you the best chance to achieve what you want to achieve, whether it's to minimize losses and stay at the table, to win a certain amount of money, or whatever.
Cheers,
Alan Shank
Quote: tuttigym
No Alan the bet is $160 across the board at $30 on each the 6 & 8 plus $25 each on the 4, 5, 9, and 10 plus $4 on the horn. Gee Alan I thought your math skills were better than that, but then again someone who is invested the PL/FO strategy at 3x, 4x, and 5x depending on the point and actually believes in the 1.41% HA that requires over 6 million rolls of the dice for a 99.5% certainty just might have some trouble with the simple dispursement of $164 to the player's advantage.
tuttigym
House advantage, with 30 ways to win, 6 ways to lose, as specified.
Your expected loss, per roll:
HA per roll =(1/36 * 30 - 35/36 + 2/36 * 15 - 34/36) * 2 + 25 * 3/36 * 9/5 * 2 + 25 * 4/36 * 7/5 * 2 + 30 * 5/36 * 7/6 * 2 - 160 * 1/6
= -$2.166667 PER ROLL, (HA per roll, 1.321%).
= YOU LOSE.
No betting system can beat the house. Why? Because the house always pays you less than the true odds on the dice.
Here's a bet for you. I have ONE unbiased dice with six sides. You bet $6 and get to pick 5 numbers. If one of the numbers hit, I pay you $1. This is why craps works in the house advantage.
Here's another bet for you. I have a roulette wheel with 37 numbers. You get to pick every number but zero and I'll pay you $1 each time a number hits. Of course if the single zero hits you lose everything. Is the hoax that the single zero roulette house advantage is 2.702703%? Should we open another thread? Craps is the same. Just because there are two dice doesn't mean there aren't 36 combinations.
The house advantage is easily calculable. It doesn't require any sampling at all. Just because you don't get the expected result on 495 rolls doesn't mean it isn't so. That's what variance is all about.
Edit:
Tutti, a word of advice to help you out on your $160 across bet. Find a casino where you only buy the 4 and 10 and pay the commission only when you win. A $25 buy 4 or 10 will pay you $49 while a $25 place 4 or 10 will pay you $45. They are both the same bet.
"HA =(1/36 * 30 - 35/36 + 2/36 * 15 - 34/36) * 2 + 25 * 3/36 * 49/25 * 2 + 25 * 4/36 * 7/5 * 2 + 30 * 5/36 * 7/6 * 2 - 160 * 1/6
= -$1.50 PER ROLL, (HA per roll, 0.915%).
= YOU LOSE LESS. "
More advice:
Drop the $4 horn bet.
HA = 25 * 4/36 * 7/5 * 2 + 30 * 5/36 * 7/6 * 2 - 160 * 1/6
= -$1.00 PER ROLL, (HA per roll, 0.625%).
= YOU LOSE EVEN LESS.
Quote: tuttigym
I realize this might be a bit off topic, but when Tiger Woods enters a tournament he believes he is going to win. His preparation and mindset and skills make his beliefs happen. His winning percentage has exceeded any other golfer ever to play the game. At 33 yrs of age, he is 2nd in total PGA wins, 2nd in total major wins, and first in percentage.
When I enter a casino, I believe I will win at the craps table. My preparation and mindset and of course some luck allows me to have a very favorable winning percentage.
I know you play to win, but if you believe you are going to lose, you are never disappointed and you do.
tuttigym
Tutti, golf is a game of skill. Tiger practices his golf swing for his entire life to be where he is today. Do you think you have a chance to beat Tiger at golf?
Craps is a game of chance where every single roll of the dice is in the casino's favor, because the casino has set the payback of EVERY SINGLE roll at less than the true odds of the dice appearing. I am sorry that you believe that you are going to win at the craps table. Preparation and mindset will not do you any good. Only luck will help you, and when I say luck, I mean the variance of the dice from its true odds and your presence at the table when the dice are "in your favor". It is math and statistics and probability that rules every single game at the casino. The only times you have an advantage over the casino is when they let you.
Craps has been beaten to death by every single system out there, including yours, to no success.
I don't play to win. I play to have fun, and at that, I am never disappointed. But to have more fun, my money needs to last. For my money to last, I play the games with the least house advantage at a level I can afford balancing it out against the fun I personally have playing the game. Bacarrat carries some of the lowest house advantages but it is no fun. Pai Gow carries a house advantage at 2.66% range but it is fun and goes very slowly so my expected loss per house is low. I will even throw $20 into a slot machine if the game looks to be fun.
I win some, and I lose some, and I am fine with that. If I play with the expectation to win, I will be disappointed. If I can play for a long time and have fun, win or lose, I am happy.
Quote: tuttigymQuote: seattlediceQuote: tuttigym
Actually when I do bet across the board, I play the "horn" also, giving me 30 ways to win and 6 ways to lose. The bet total is $164. I know that your sensibilities will be screaming and that somehow you will come up with a formula that shows that the HA is 17,432 to 1 against me, but then your mindset would leave all the bets on the table until the 7 showed and wiped out the chips. I mean, if you played on a $25 table with 5X odds and you bet $25 PL; the 6 became the point and then a FO bet (5X) of $125, the amount at risk is close to similar. Any three rolls that are no the point provides a win of about $30 or so X 3. A 7 out I lose a net $74; you of course lose $150. Now since the rules allow me to bring down all my Place bets during the point and since my discipline tells me to bring my bets down after three rolls. I win $90 and have no further exposure. You get to wait it out and hope that the math is wrong and the point is converted. If it happens, we are both happy. If not,......
tuttigym
These simple calculations can be done using pencil and paper, although I used a keyboard and a calculator.
The HA for the across + horn where you take down all bets after one roll was derived on page 4 of this thread: 2.3%.
This was for a different total bet amount; using the strategy and bet and win amounts you provided here:
There is an outcome on every number that can roll. Each roll has a 30/36 probability of not being a seven.
Immediate seven out: 6/36 = 16.7% and on average the across + horn will lose 16.7% * 164 = $27.39
One non seven followd by a seven: 30/36 * 6/36 = 13.9%; average loss 13.9% * (164-30) = $18.63
Two non sevens followed by a seven: (30/36)^2 * 6/36 = 11.6%; average loss = 11.6% * (164-60) = $12.06
Three non sevens (now we don't care what happens next, because the bets are taken down: (30/36)^3 = 57.9%; average win = 57.9% * 90 = 52.11.
Net average win: 52.11 - 27.39 - 18.63 - 12.06 = -6.57. This is a loss even with your discipline to take down your bets after three rolls.
HA = 6.57/164 = 4%
For the pass line 6 with 5x odds, played out until it is resolved, it wins 5 times and loses 6 times.
Win: 5/11 = 45.5% of the time there is a $175 win; on average = 79.54.
Lose: 6/11 = 54.5% of the time there is a $150 loss: on average = 81.75
Net average win = 79.54 - 81.75 = -2.21
HA = 2.21 / 150 = 1.47% (NOTE that this neglects the effects on the come out roll on the flat bet, which reduces the overall HA because it wins more often than it loses.)
Here is what you need to do when teaching you 21 year old grandson or granddaughter to play the game of craps. First, show them all of the above "math" from boymimbo, goatcabin, and yourself just as it is presented here. Second, wake them up from their sleep of deep bordom, and third try to convince them that walking away from your diatribes is no way to treat their grandfather who is trying to teach them the game of craps and how easy it is to play and win.
I'm not sure what point you are trying to make. Also, you have somehow quoted me and added your statements to make it appear that I wrote them. The corrected quote sequence is above.
If I were to teach my grandchildren about craps (which I would probably leave up to their parents, but let's go with your premise) I doubt I would have to do more than give them a pair of dice, the payouts of the various bets, and let them work out the probablilities on their own, and they would ask, "Grandpa, what is the point of playing craps when you can't win?"
Usually when one quotes a single word, as you quoted the word "math", it is a shorthand way of saying you don't believe it is really what it appears to be, as in "so called math." Are you bored by the math that you have been shown? What boy, goat, me and many others have tried to show is the real math of the probabilities of craps. We have done it in different ways - some lengthy derivations of overall probabilities, some simple treatments of specific strategies that you have put forth - yet all of our calculations arrive at the same result. You have cited your own "math" (yes, I mean "so called math") to back up your opinions, and we have carefully and, for the most part, patiently shown you where your math is wrong.
It is one thing to claim that your own experience does not match the math. That very same math tells us that it is possible to win sometimes, and even possible to be ahead over a long period of play. It is another thing entirely to claim that the math we have shown you is wrong, and the "math" you use to support your claims is right. Do you really believe that you and a few others have found a way to beat the casinos? Your ideas have been around for a long time and they have been tried, analyzed, and simulated, and if they really worked the casino owners would have changed the rules of the game because they don't want to go bankrupt.
The only person trying to teach that you can play craps and win over the long haul is you. In my last post I showed that the two betting strategies have a house advantage, and one has a higher HA than the other. I did this by accounting for all possible outcomes of the two strategies. Others have taken your strategies and run simulations of tens of thousands of rolls, and come up with the same result.
Diatribe. The word has roots in the Latin "diatriba" (learned discourse) and Greek "diatribe" (pastime, lecture) but it's most common current definition is "A bitter, abusive denunciation" and given this definition, the only thing resembing a diatribe throughout this thread is your abuse of pure mathematics.
I am sure that I am not alone in thinking that you will never believe what we are telling you. I don't know if it's because you are unwilling to put in the time to really understand the math, or unable to grasp the concepts, or perhaps some other reason. We probably should have given up long ago, but you continue to misquote us, and apply faulty reasoning. One reason I replied was that you cited two strategies and selected a small set of outcomes to "prove" that one was clearly superior; I wanted to make sure other readers see how these strategies work over all possible outcomes.
If you don't believe me run a random number generator for 5760 comeout rolls using the rules of any craps game and you will find at the end of each cycle if you bet the pass you will be down 80+/ units and if you bet the don't you will be down 80+/ units.
The bell shaped curve is simply the 36 roll curve. Because the 6 and 8 win .45454% of the time it is much easier to see the results if you roll them 800 times. So in 5760 comeout rolls you will roll a 6 (5/36 x 5760) 800 times if you are a do player you will win 364 times and "seven out" 436 times for a net loss of 72 units. The inverse for the don't player +72.
So to look at a module 5760 comeout rolls you have a perfect bell shaped curve. The mean is the number 7 and the other numbers represent deviations from the mean. If you were an option trader the number 7 would be considered the At the Money Strike and all of the other numbers would be higher or lower strike prices on the curve. The 2 and the 12 would be the "teenies"(.0277%.)
2 160
3 320
4 480
5 640
6 800
7 960
9 800
10 480
11 320
12 160
5760
So here is a question to stir up the pot. What is the difference between the edge and the "drop"?
Several pages back, I provided a brief instruction on using forum tags and editing quotes. Tutti couldn't figure it out.Quote: seattledice...you have somehow quoted me and added your statements to make it appear that I wrote them. The corrected quote sequence is above.
...
I am sure that I am not alone in thinking that you will never believe what we are telling you. I don't know if it's because you are unwilling to put in the time to really understand the math, or unable to grasp the concepts, or perhaps some other reason.
Whether he is unable or unwilling to grasp that concept is probably an indication of why he is unable or unwilling to grasp the concept of the 1.41%
"Seeing the light" is difficult. I had a hard time with it back a month or so ago with the Monty Hall Paradox thread. But the funny thing is, once I figured it out, I am now able to explain it in terms that are so simple, I'm surprised that nobody explained it that way before.
Sooner or later, Tutti is gonna see the light on the 1.41%. I shudder to think of what will happen on that day.
Mathematically, they should be the same.Quote: SPOOS1So here is a question to stir up the pot. What is the difference between the edge and the "drop"?
FYI: The drop is the actual difference between the cash taken in, and the cash paid out.
The reason they are not the same is because of variance, and the human habit of playing the same cash over and over before finally walking away.
Note: Unless I'm mistaken, "Edge" refers to the House Advatage. If not, then ignore this post. And give me a better definition, so I stop making that mistake!
In a sense the casino's are like a racetrack that has a mutual take averaging greater than 17%. Their natural edge is built in, and all they want is the most money bet on each race. The Casino loves action the more the merrier. They have position limits, so no one shooter can knock them out of the box.
Quote: tuttigymHere is what you need to do when teaching you 21 year old grandson or granddaughter to play the game of craps. First, show them all of the above "math" from boymimbo, goatcabin, and yourself just as it is presented here. Second, wake them up from their sleep of deep boredom, and third try to convince them that walking away from your diatribes is no way to treat their grandfather who is trying to teach them the game of craps and how easy it is to play and win.
Didn't see this one.
I've already talked to my child about gambling. She sees me going to the casino (as many of my friends and family do) as a waste of money. What I tell my child is that gambling is a form of entertainment which has cost (similar to a movie, bowling, golf, buying i-tunes, going to a concert, etc) just like other forms of entertainment. The difference in gambling is that the cost is not set where as the other forms of entertainment are. When measuring the value of your entertainment, I tell my child that the amount I expect to lose and budget is the number of hours I play times the amount I play with times the house advantage.
I do not tell my child that it's easy to win. I tell my child that it's a form of entertainment and that you can win and lose and that you should only play with what you can afford to lose, BUT that the casino is there to make money off you and that every bet in the casino is designed to take everyone's money gradually away. Some will win, more will lose.
When my kid gets older, if she gets a desire to gamble, I will tell her to visit the Wizard's sites and tell her to work out the odds for any particular system herself.
All of your scenarios so far (30 ways to win, 6 ways to lose, all of the place bets) show that you will on average, lose money, and in fact far faster than the pass line with odds. Most people who play craps do not just play that bet. I certainly don't. I add come bets (also a -1.414% HA as well, less with odds) and I will place the 6 and 8 (1.52%), as these are the best bets on the table. When I feel like not risking much money, I'll put $1 or $2 each on the hard 6 and 8 which has the same expected loss (but greater house advantage) as a $9 / $18 place bet (instead of placing the 6 and 8). Overall, my per roll expected value is $.19, or about $12/hour and I get to play 4 numbers. Compare this with your system which right now at $164/bet will lose you $2.17/roll (if you remove the horn and buy your 4 and 10 where the winning is paid on the vig only it will only be $1.00 / roll). I don't need action on every roll to keep me excited.
I compare this to blackjack with an expected value of about $5/hour ($10 x 100 hands/hr x .5%), pai gow with an expected value of $12/hour ($15 x 30 hands/hr x 2.66%), video poker (5/6/9 DB) with an expected value of $10/hour ($1.25 x 360 hands / hr x 2.2%). When I compare all of that with a movie ($22 including drinks and popcorn for 2 hours), golf ($60 / round + lost balls and tees for 4 hours), theatre ($$$ for three hours), or other forms of entertainment, gambling to me at any of the games above becomes a very valid form of entertainment.
Quote: SPOOS1My numbers are absolutely correct!! They express the "true odds" in a craps game in terms of units won and lost in any 36 roll cycle. Because the number 12 is neutral for the don't player it must be taken into consideration.
If you don't believe me run a random number generator for 5760 comeout rolls using the rules of any craps game and you will find at the end of each cycle if you bet the pass you will be down 80+/ units and if you bet the don't you will be down 80+/ units.
The bell shaped curve is simply the 36 roll curve. Because the 6 and 8 win .45454% of the time it is much easier to see the results if you roll them 800 times. So in 5760 comeout rolls you will roll a 6 (5/36 x 5760) 800 times if you are a do player you will win 364 times and "seven out" 436 times for a net loss of 72 units. The inverse for the don't player +72.
The trouble with your figures is rounding. For each point, the error is small, but it results in a cumulative error of a couple of percent. With the "perfect 1980" there is no rounding problem. Please review the figures I posted; they are exact. The edge is 1.414% for the pass and 1.403 for the don't pass (or 1.364 if you count the 55 units of comeout 12 as "risked"). You can find these figures in any book on craps or on mathematics of gambling. The expected value of 1980 pass bets is -28 units, -27 for don't pass.
Quote: SPOOS1So here is a question to stir up the pot. What is the difference between the edge and the "drop"?
The edge is the percentage the casino expects to win (the players to lose) out of every unit bet. More precisely, the edge is the "expected value" divided by the amount bet. The key to understanding this is that it applies to the total bet handle, not just to the player's starting bankroll. To put it another way, the expected value is the edge times the "bet handle".
Too much emphasis is placed, in my view, on the edge, or "HA", which is important but perhaps not as important as variance.
Cheers,
Alan Shank
Quote: tuttigym
I UNDERSTAND the math associated with the 1.41% HA on PL bets resolves itself only 3.5% of the time. I UNDERSTAND that it takes 146 SETS of 495 PL outcomes to actually produce the 1.41% HA.
Of course, it only takes one set of 495 to produce a 244-251 outcome, just as it only takes one set to produce 243-252, or 242-253. 244-251 is more likely than any other specific outcome. You UNDERSTAND nothing, unfortunately.
Cheers,
Alan Shank
I was looking forward to this thread just dropping off the bottom, into forum oblivion.
i haven't read anything on this thread so don't know whats going on, but maybe my post will kill this thread. i have that power you know. :)
And just to be sure.......
It's almost like Hitler is still alive and Populating this thread.
Damn Nazi's.
[/godwinslaw]
Should get the longest thread record now. [/evillaugh]
Sigh... I think the Wiz will need to lock the thread to make that happen.Quote: boymimboIt still burns.
I was looking forward to this thread just dropping off the bottom, into forum oblivion.
Hmmm.... Is it my immagination, or has the Wiz made NO posts in this thread? Sounds like he had the right idea....
Quote: goatWho would play a lesser FO bet on the 4/10? Not I, unless I am taking max odds at a 3,4,5X table. Do you understand why 3, 4, 5X odds are now more-or-less standard? It's because the payoff is always 6 units, i.e. it's easier on the dealers. Also, there is more variance on the outside numbers, due to the increased, 2:1 payoff, and the casinos do not like to give too much variance for free.
Nice reach, i.e., "easier on the dealers." The Box person and the player makes sure the payouts are correct. Where I play, 20X odds is the "standard." The 4/10 payout reflects the 2:1 HA on the winning the bet. So if you are at my casino at 20X on a minimum $10 table and the point is 4, you would bet $10 PL and then $200 FO because there is NO HA on the bet? Right.
Quote: goatI guess you simply are not intelligent enough to understand that the evaluation of a bet must include BOTH its probability of being won and the payoff relative to the amount bet.
Nope, guess not!
Quote: goatA coin-flip game:
heads you pay me $5
tails I pay you $5
OR
heads you pay me $6
tails I pay you $5
Are these equally fair?
If not, why not?
That would be a fair deal if you threw the dice to determine which side showed up, i.e., if a 7 is thrown you lose and if a 6 is thrown you win but only on the head/tail called. If the 6 is tossed and you called heads but the coin is a tail, you also lose. I think that would be fair.
tuttigym
Quote: DorothyGale
Really nice teeth. I do not have all of mine.
tuttigym
Use dice to determine the results of a coin flip? My head hurts.Quote: tuttigymThat would be a fair deal if you threw the dice to determine which side showed up, i.e., if a 7 is thrown you lose and if a 6 is thrown you win but only on the head/tail called. If the 6 is tossed and you called heads but the coin is a tail, you also lose. I think that would be fair.
But, on the plus side, Tutti has figured out how to use the quote feature! Woo hoo?
Does that mean he might be on the very of accepting the 1.41% house advantage? Sigh. I wouldn't bet on it....
Quote: goatcabinQuote: tuttigymNo Alan the bet is $160 across the board at $30 on each the 6 & 8 plus $25 each on the 4, 5, 9, and 10 plus $4 on the horn.
tuttigym
OK, so here's what can happen on one roll of the dice:
2 -- win $30 on the 2, lose $3 = +$27
12 -- same thing
3 -- win $15 on the 3, lose $3 = +$12
11 -- same thing
6 or 8 -- win $35 on the 6/8, lose $4 = +$31
5 or 9 -- win $35 on the 5/9, lose $4 = +$31
4 or 10 -- win $45 on 4/10,lose $4 = +$41
7 -- lose $164
weighted net outcome -$2.167
bets
6/36 * 4 = .66667
10/36 * 34 = 9.444
14/36 * 29 = 11.277
6/36 * 164 = 27.333
weighted bet handle - $48.722
-2.167 / 48.722 = -.0445 or 4.45%
So, I programmed a WinCraps auto-bet file with these parameters:
starting bankroll $2500
no bets on comeout roll
when a point is established:
bet $25, $25, $30, $30, $25, $25 on all point numbers
bet $4 horn
winning bets - same bet
losing bets - replace
After three non-seven rolls, call place bets "Off", do not replace horn bet, so NO ACTION until shooter sevens out. If shoot makes his point, no horn bet on comeout roll, place bets Off automatically.
Session ends before first comeout roll after 200 rolls, or if there is not $164 left.
I ran 10,000 sessions; here are the results:
parameter avg. num. rolls 202.5 avg. num. bets 224 avg. bet handle 3958 mean net result -$179 median net result -$152 mode of net result -$188 to -$148 standard deviation $636 mean house advantage -4.51% winning sessions 4034 breakeven sessions 2 losing sessions 5964 number of busts 12 lost more than $1000 1052 lost more than $500 2955 won more than $100 3451 won more than $250 2589 won more than $500 1396 won more than $1000 244 biggest win $1821
So, it looks like $2500 is plenty to keep you going for a couple of hours, unless you are very unlucky; however, your chances of breaking even or better are only about 40%, with almost a 30% chance of losing $500 or more. In fact, your probability of losing at least $500 is greater than your probability of winning $250 or more.
Here is a picture from WinCraps of the distribution of net outcomes:
How about that?
Cheers,
Alan Shank
Very nice, very professional, very colorful and it is something my computer challenged skills could not replicate. So tell me, do you suppose that anyone might live long enough to actually perform this experiment? Relying on Win Craps or any computer model which "parrots" a simulation based on thousands/ millions of games/points/bets/outcomes might create for you some semblance of reality, but for me, stupid, hard-headed me, it only serves to reinforce the simple fact that when it comes to games of chance and the true randomness of such, it falls woefully short. But I want you to know that I do appreciate the incredible time, intellect, and talent you have exhibited by posting the above. At no time will I diminish what you are trying to convey.
I know that you believe in the law of large numbers as in actuarial theory, but insurance companies using those theories are constantly raising their rates in casualty areas because their theories, i.e., models are wrong. BTW do you know why flood and "earth movement" (earthquake) are not covered in property coverages? Only in life insurance have the rates gone down because there can only be ONE claim and people are actually living longer than their 10-20 year old models.
tuttigym
Quote: boymimboTutti, I am sorry that you don't understand math, probability or statistics. I'm convinced that you don't.
You see, when I go to a casino, I know that house advantage of every single bet on the craps table. I know that there is variance to what is expected to happen and that I will not come out to that exact expectation every time. But I know that a $30 horn bet will lose, on average, far more money on average (about 10 times more money) then a $30 line bet or a $5 line bet with $25 odds. That's why the person is selling the bets in the center.
But what that means is that I expect to lose when I walk in the door and sit down at any slot machine or table. The only way I am going to win is if I am lucky. And I know the way that I will lose the least over time is to make the smartest bets: those with the lowest house advantage.
I don't pretend to think that there is a system with 30 ways to win and 6 ways to lose that will overcome anything that the casino will throw at me. I know that no system will overcome the house advantage at craps. The math demonstrates that. Craps exists because of that. Thousands have tried. All have failed.
So go for it. Believe what you will.
Let me see if I understand you correctly, boymimbo, you hammer me and berate everything I have said regarding the HA, and you then tell the world that you go to the casino just to LOSE. You basically do not believe you can win, and if you do, it is an anomaly because you are there for the entertainment value you get out of seeing how long your buy in will last. You see there ARE 30 ways to win and only 6 ways to lose, however, I did NOT say that that ratio will OVERCOME ANYTHING or any adverities of gambling. The mindset of all here posting is that I play each point the same way everytime with perhaps little variations per session. Actually I vary my bets and patterns with every shooter and sometimes differentiate my play between points. There is very little that is consistent with the play at the tables, and that is why I practice daily; that is why my preparation results in mostly positive sessions.
tuttigym
