I have simplified the above by calling it the "Rule of 495." If there has been another individual who has previously used that term, my apologies there is no plagerism intended.

To my knowledge, this math question has never been accurately answered, though there have been attempts which have not satisfied me. I have even sent an e-mail to the Wizard asking the question which follows, but he is extremely busy and may not have had the time.

The Problem: The Rule of 495 REQUIRES the "perfect" math as shown in the formula of 244 wins vs 251 losses in 495 PL outcomes. WHAT ARE THE ODDS OR PROBABILITIES of actually producing the "perfect" 495??

Example: The first 20 PL wagers produce seven losses. Are the next 224 PL wagers winners?

One could create scenario after scenario changing those numbers as above.

It is my hypothesis that the odds of producing the "perfect" Rule of 495 for the desired outcome of 244/251 are so astronomical as to be labeled a hoax. I also believe that the Rule of 495 has never be a documented or witnessed accomplishment at any casino at any time or anywhere.

I would be grateful for any intellectually and mathematically accrurate feedback.

tuttigym

tuttigym

If you roll the dice 495 times, there are many specific ways that the dice can fall. The numbers you put up are the most likely on a minority basis up against other specific results. However, the probability of any specific result, including what is technically the most likely, is very long. If you graphed the results, the curve will peak at 244 wins and 251 losses, but the total occurence of the other results will be far, far greater.

Over time, the results will get closer and closer to an average win/loss spread (HA) of 1.41 percent. But after 495 rolls, it would be very rare to see you lose any specific result predicted earlier, including exactly 1.41 percent of your total bets, or 251 losses against 244 wins.

Quote:tuttigymThe formula for that HA is also readily available, and broken down to its simplest form, states that out of 495 PL plays there will be 244 PL wins against 251 PL losses.

This is not true. It is never stated like this. Any place where the house edge is stated that way is presenting false information.

The formula for the Rule of 495 is often posted including right here under MATH.

tuttigym

Did you say '224' because 244 - 20 = 224?Quote:tuttigymExample: The first 20 PL wagers produce seven losses. Are the next 224 PL wagers winners?

If so, then you don't understand your own statements of probability.

In the 'perfect world' you are looking for, 20 losses would mean that out of the 475 remaining pass line bets, you would expect most to win. After all, your probability said there would be 251 losses and 244 wins. Since you already had 20 losses, you're more likely to win because you already had 20 of your 251 losses - but that's only in the 'perfect world' you created. In the real world, 20 losses happens, and is no prediction on the future events.

I guess with your response you cannot accomplish the calculations. Right?

tuttigym

Quote:tuttigympocketaces: PL wagers or outcomes are NOT the same as "rolls of the dice." A PL outcome is either a natural Come Out winner (7 or 11); a Come out loser (craps 2,3, or 12); a 7 out after establishing a point; or a point conversion (point winner) regardless of the number of tosses made to do either of the last two examples.

The formula for the Rule of 495 is often posted including right here under MATH.

tuttigym

I said rolls, should have said results or outcomes. Same thing.

And to you second paragraph, there is no such thing as the 'rule of 495' posted right here. Remember, you admitted you made it up, and it is based on a misinterpretation to say it is what the house edge figure states will happen.

You are not on to anything here - trust me. You would be better to try to understand what the math is actually talking about then connecting dots that can't be connected.

tuttigym

Quote:tuttigymahiromu: Your "guarantee" holds little validity in that neither you nor I would live long enough to experience "495 million" PL outcomes. However, I do believe that given an infinite amount of time and an infinite number of PL outcomes, the Rule of 495 might be accomplished. If that is correct, then the 1.41% HA truly is a hoax.

I guess with your response you cannot accomplish the calculations. Right?

tuttigym

Actually you can, open up matlab (for me) and make a quick and simple program with if/then statements that posts information into a matrix. Then look through that matrix for however many points in a row you want to.

Please link me to where it says that formula for the Rule of 495 states "out of 495 PL plays there will be 244 PL wins against 251 PL losses." If that was so, you could track the results, and on the 495th roll bet your entire life on the sure thing that was about to be rolled. I don't think that is posted right here under MATH.

Obviously, after one decision, the rule is wrong. After 2 decisions, it is wrong. At 10 decisions, it will be more precise, but could still be 10-0 one way or the other. At 100 decisions, it could be pretty close, but it could still be 95-5. At 1,000 decisions, it should be getting pretty close, and at 495,000,000 decisions it should be close enough to satisfy the rule.

The math is what it is. It didn't change into something else when you started looking at it. It is an accurate depiction of the way the world works. Some folks built some mighty big casinos on that 1.41%.

Quote:tuttigymahiromu: Your "guarantee" holds little validity in that neither you nor I would live long enough to experience "495 million" PL outcomes. However, I do believe that given an infinite amount of time and an infinite number of PL outcomes, the Rule of 495 might be accomplished. If that is correct, then the 1.41% HA truly is a hoax.

I guess with your response you cannot accomplish the calculations. Right?

tuttigym

I know this isn't directed at me, but I have to ask what exactly you are talking about. If you want to know the chance of getting exactly 244 pass line wins in 495 random trials then maybe someone can calculate it for you. Are you asking this? I can tell you it has happened before - it happens all the time. Like any specific result, its uncommon, but it happens. If I ran a million trials of exactly 495 rolls, some of them would end up with exactly 244 pass line wins. The casinos are essentially running these random trials run everyday.

Other than fleshing that part out of your post, I have absolutely no idea what you are saying with regards to a 'hoax.

The term Rule of 495 is only used for convenience sake because the explanation of the 244/251 is so convolutedly long.

I would like to "trust" you, but in every craps book, article, conversation, etc. the 1.41% HA on PL bets is ALWAYS shouted out to the masses yearning to win big $$$. You too seem to be saying that it really does not exist (hoax?) and the other "math" is more important. Then why do virtually all the "experts," pundits, authors, and "pros" tout it?

tuttigym

Quote:tuttigympocketaces: Thanks, I was pretty sure you were refering to outcomes.

The term Rule of 495 is only used for convenience sake because the explanation of the 244/251 is so convolutedly long.

I would like to "trust" you, but in every craps book, article, conversation, etc. the 1.41% HA on PL bets is ALWAYS shouted out to the masses yearning to win big $$$. You too seem to be saying that it really does not exist (hoax?) and the other "math" is more important. Then why do virtually all the "experts," pundits, authors, and "pros" tout it?

tuttigym

You know what? You don't have to believe it if you don't want to. I don't care. But if you want to convince ME that it is a "hoax", you are going to have to show it to me with numbers rather than words. Shouting it down and simply calling it a hoax will not work.

Put up the math, or go on your way.

Or provide a link?

Thanks.

Lets look at this in the game of craps, flat betting. We know for the exact reasons you stated in your first post that the pass line is slightly more likely to lose than win. So, this means:

On an individual trial, we are slightly more likely to lose than win, but can still very easily win.

On a longer trial (say 500 results) we are significantly more likely to lose overall than win, but can still fairly easily win overall.

This trend continues, until:

On a very long trial (say a million results) we have no chance of winning overall, and will find our results becoming very, very close to 1.41 percent of our total amount bet.

Quote:tuttigymDJTeddyBear: The Rule of 495 allows only seven losses in 495 PL outcomes. Isn't that what the 244/251 purports to show to create the 1.41% HA? The example provided those seven losses in the first 20 outcomes leaving 220 outcomes to be consecutive winners. If there were more losers during the next PL outcomes the HA would be greater based on the additional number of losers produced. OR after there are seven PL losers, whenever they occur, does a new 495 PL outcomes start??

You are confused here. You are saying you can only lose 7 times, then must have 200+ wins.

I think I see where you are getting the number seven... 251 - 244 = 7. That is simply the extra number of losses vs. wins out of 495. There are 251 total losses in 495 PL outcomes.

Your original post, I think, asked... "What are the chances that, in 495 PL outcomes, exactly 244 will win, and exactly 251 will win, disregarding the order they happen?"

I think you could ask a parallel question... "What are the chances that, in 500 fair coin flips, exactly 250 will be heads, and exactly 250 will be tails, disregarding order?"

Both of the above questions have an answer, and they will both be very, very small.

Does that mean there is not a House Advantage of 1.41%? No.

Does that mean the odds of flipping heads is not 50%? No.

Getting an exact number of results is very unlikely for large amounts of trials... But, the number will converge to that percentage over a larger and larger number of trials.

Quote:DweenQuote:tuttigymDJTeddyBear: The Rule of 495 allows only seven losses in 495 PL outcomes. Isn't that what the 244/251 purports to show to create the 1.41% HA? The example provided those seven losses in the first 20 outcomes leaving 220 outcomes to be consecutive winners. If there were more losers during the next PL outcomes the HA would be greater based on the additional number of losers produced. OR after there are seven PL losers, whenever they occur, does a new 495 PL outcomes start??

You are confused here. You are saying you can only lose 7 times, then must have 200+ wins.

I think I see where you are getting the number seven... 251 - 244 = 7. That is simply the extra number of losses vs. wins out of 495. There are 251 total losses in 495 PL outcomes.

Your original post, I think, asked... "What are the chances that, in 495 PL outcomes, exactly 244 will win, and exactly 251 will win, disregarding the order they happen?"

I think you could ask a parallel question... "What are the chances that, in 500 fair coin flips, exactly 250 will be heads, and exactly 250 will be tails, disregarding order?"

Both of the above questions have an answer, and they will both be very, very small.

Does that mean there is not a House Advantage of 1.41%? No.

Does that mean the odds of flipping heads is not 50%? No.

Getting an exact number of results is very unlikely for large amounts of trials... But, the number will converge to that percentage over a larger and larger number of trials.

Nice explanation dween, especially with the coin flip analogy.

It should be noted too, that in the heads and tails example, there are lots of different sequences of flips that get you to a 50/50 split of results. The chance is slim, but very possible. Of course the sum of the other results are more likely, but if we were forced to choose one specific result to wager on, the exactly 50/50 split would be the best bet. Its far more likely than truly improbable events like 500 heads and 0 tails, and slightly more likely than other specific events that are close to a 50/50 split.

In a similar breath, in those 495 craps bets, 244/251 is the most likely specific result. But variance and the large number of other possible results, many only slighly less likely, mean that its still an individually rare event. But not extremely rare in any sense and it would happen a ton given enough trials of 495 bets.

Hoax? Hardly. Astronomical? That depends upon how far your head is in the clouds.Quote:tuttigymIt is my hypothesis that the odds of producing the "perfect" Rule of 495 for the desired outcome of 244/251 are so astronomical as to be labeled a hoax.

If you were to plot the results a million trials of 495 pass line bets, you'll get a result that looks like a bell curve. 244/251 will be at the peak of that curve. But there are large numbers of results on either side.

Personally, if you were to offer me a bet that the next 495 pass bets would result in a 244/251 split, I'd half the farm bet on 'false' every time. Why only half the farm? Because with my dumb luck, I'll hit it first time out of the gate!

Just because it's usaually false, doesn't mean it's a hoax.

FYI: Similarly, I'll bet half the farm that 100 coin tosses will NOT be a 50/50 result.

The probability that you get exactly 244 out of 495 trials given a probability of success of 244/495 is 0.035847.

The house advantage is (244-251)/495 = 1.414%

Odds of rolling a 2 and 12: 1/36 results x 2 in -1

Odds of rolling a 3: 2/36 results -1

Odds of rolling a 11: 2/36 results +1

Odds of rolling a 7: 6/36 results +1

Odds of rolling a 4 or 10 and winning: 3/36 x 3/9 results +1

Odds of rolling a 4 or 10 and losing: 3/36 x 6/9 results -1

Odds of rolling a 5 or 9 and winning: 4/36 x 4/10 results +1

Odds of rolling a 5 or 9 and losing: 4/36 x 6/10 results -1

Odds of rolling a 6 or 8 and winning: 5/36 x 5/11 results +1

Odds of rolling a 6 or 8 and losing: 5/36 x 6/11 results -1.

Add em all up: -4/36 + 8/36 + 6/36 ((3-6)/9) + 8/36 ((4-6)/10) + 10/36 ((5-6)/11)

=1/9 - (18/36)/9 - (16/36)/10 - (10/36)/11

=1/9 - 1/18 - 2/45 - 5/198

= 1/90 - 5/198

= (198-450)/17820 = -252/17820 = -7/495

The house advantage is long term, not short term. You cannot calculate short term odds because of variance. However, as the number of samples increase, you are more likely to reach the expected value of -7/495.

tuttigym

(Diverging from the topic a little.) During a relatively long roll, this same guy suddenly laid the 5 and 9, he confided in me that he was counting -- "don't tell them (the crew) that."

Counting? As in applying the concept of BJ card counting to dice? That's as funny as the guy how bets on Red after 'x' spins in a row of Black!Quote:seattledice...During a relatively long roll, this same guy suddenly laid the 5 and 9, he confided in me that he was counting -- "don't tell them (the crew) that."

Thanks. I needed that laugh!

Oh, yeah. Don't tell the crew. They might back him off! In reality, they would probably start pushing the comps!

There have been hundreds of questions directed to the Wizard asking about the odds of this occurrance or the odds of that occurrance. Most of the time he sets out to explain or redefine the question(s), and then he proceeds to show how he came to a given answer by providing a formula that creates his answer.

For some reason here and regarding this question, there are rebuttals to the question and brick walls have been erected to get an answer. It has not been stated that the 1.41% HA does not exist just that its existence is so remote as to create, for me, a sucker bet to those who play the game.

All of us want to win. Hopefully these discussions will give us a better shot at winning more often and perhaps higher monetary amounts. The Wizard stated in an answer to a PL question on Feb. 2000 that AFTER THE POINT IS ESTABLISHED PL wagers along with their associated FO bets have up to a 67% HA over the player depending on the point (paraphrased). With that statement in mind, isn't it important to examine the reality that even though the "math" says a 1.41% HA on PL outcomes is always touted, it is highly misleading?

Taking verbal shots at me because I am calling the PL 1.41% HA a "hoax" is not providing any clarity on the question. The vast majority of craps players will come to the table, buy in, and start to play by betting the PL; establish the point; place the FO; maybe place other bets; and hope for a point conversion, but in both the long and short term will lose much more often than win.

Asking again, why the resistence?

I will continue to respond individually to your thoughts and posts, but think about the play at the tables and how the few winning sessions are based solely on that "hot" shooter that converts points and throws lots of numbers before the eventual 7 out.

Comments? tuttigym

No business can survive on a 1.41% gross profit which is what some are eluding to that might represent the HA. Businesses have operating expenses which far exceed the portions of gross profits posted by a business. The resultant amount becomes the net profit. That 1.41% might buy tiolet tissue for a casino for a week.

You need to define "long term" and "short term." Obama says the "stimulus" will create jobs in the "long term." What is that?

tuttigym

Quote:tuttigym... isn't it important to examine the reality that even though the "math" says a 1.41% HA on PL outcomes is always touted, it is highly misleading? ...

Comments? tuttigym

If you'll excuse my language, it seems pretty clear you have a hard-on for the Pass Line bet. I have had my moments with it too, but it's still what I go back to (plus taking the odds). I'll assume you aren't just making a case against the House having an edge in general. May I ask what it is you prefer to bet on at a Craps Table?

You stated that it is "uncommon" but "it happens." That statement lacks specificity.

You stated that in a "million trials" "some" sets of 495 PL outcomes will show as 244/251. Those generalizations, "uncommon" and "some," are meaningless when players have their money at risk. The 1.41% HA is a finite number which many rely upon to be accurate. If the 244/251 is truly "uncommon," then that HA is going to increase often. So define "uncommon" and "some" in the context of your response. Gross generalizations can be costly. Kinda like Obama saying that the "stimulus" will work in the "long term." What is that?

tuttigym

tuttigym

Quote: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.

Quote:tuttigymMosca: The "math": After the point is established, fully 65% or more of craps betting and play, the HA becomes huge. The player's chances of winning diminish those PL/FO, if bet, by up to 67% depending on the point according to the Wizard. Feb. 2000.

tuttigym

Your math is faulty. Review the entire analysis and see why; it is not my job to show you why it is wrong. It's not like you've found something the professionals have missed over the last 300 years.

But, believe as you will.

Quote:tuttigymMosca: Look at page 3 on this thread. The second post shows part of the monstrous equation and number configurations.

No business can survive on a 1.41% gross profit which is what some are eluding to that might represent the HA. Businesses have operating expenses which far exceed the portions of gross profits posted by a business. The resultant amount becomes the net profit. That 1.41% might buy tiolet tissue for a casino for a week.

You need to define "long term" and "short term." Obama says the "stimulus" will create jobs in the "long term." What is that?

tuttigym

I have read that if the only bets anyone made at the craps table were the line bets (pass, don't pass, come, and don't come -- all with HA <= 1.41%) then the craps tables would be shut down because they wouldn't make enough money to cover the cost of running the game. I don't know if that's true, but it seems reasonable. Many bets are made on the higher HA place bets (1.52-6.67% HA) and the center "sucker" bets (up to 16.67% HA).

All bets except the free odds are losing propositions for the player. The line bets are simply the best bets you can make.

The "hold" at a craps table is much higher than 1.41% - I don't have a source handy, but I think this is more like 15% of chips bought by players are won back by the casino. This is due to the higher HA bets and the way most people gamble -- I'm certain that most of us will play until a bet has lost. Even if we are ahead, we don't leave until the win streak ends, which means our last bet lost. If you only walked up to the table and made some fixed number of pass line bets and then left regardless of whether you were up or down, I think that after thousands of sessions you would see the 1.41% HA reflected in your bankroll.

Suppose that a couple of million people all play 495 passline decisions. Their win-loss records will be distributed in the familiar bell-shaped curve, with 244 wins as the mean, or very, very close to it. Although coming out 244-251 is not very likely (odds of 27-1 against it), it is MORE likely than any other SINGLE W-L record. It's sort of like horse-racing odds: the favorite may go off at 3-1, but the other horses have longer odds. It's fairly rare for a horse to be an "odds-on" favorite, favored over the entire field. (Of course, horse-racing odds are not actually probabilities, or even the bookies' estimate of probabilities.)

The 1.4% is not a hoax. It is simply the difference between the probability of winning a passline bet and the probability of losing it.

.49293 - .50707 = -.01414

It's like you have a 495-sided die (remember Dungeon Dice?): 244 of the surfaces have a 'W', and the other 251 have an 'L'.

Actually, if you want to cover all the "bases" in integers, you need 1980 decisions, which I call the "perfect 1980):

440 comeout win

220 comeout loss

125 win on 6

150 lose on 6

125 win on 8

150 lose on 8

88 win on 5

132 lose on 5

88 win on 9

132 lose on 9

55 win on 4

110 lose on 4

55 win on 10

110 lose on 10

----

1980, of which 976 are winners, 1004 losers, 784 are seven-outs, so the probability of sevening out on any given bet is 784/1980 = .396

One can learn a lot by studying the "perfect 1980".

Cheers,

Alan Shank

Quote:goatcabin

440 comeout win

220 comeout loss

125 win on 6

150 lose on 6

125 win on 8

150 lose on 8

88 win on 5

132 lose on 5

88 win on 9

132 lose on 9

55 win on 4

110 lose on 4

55 win on 10

110 lose on 10

----

1980, of which 976 are winners, 1004 losers, 784 are seven-outs, so the probability of sevening out on any given bet is 784/1980 = .396

About the HA after a point is established. You can easily derive the correct numbers. Note that if you add up all the "win on n" and "lose on n" they sum to 1320. 1320 / 1980 = .667, so two thirds of the time a point is established, on average. Of those, there are 536 winners and 784 losers, so the weighted probability of winning a point (on the "right" side, of course) is 536 / 1980 = .406, the specific probabilities being .4545 on the 6/8, .4 on the 5/9 and .333 on the 4/10. However, on the comeout the pass/come has a 2:1 advantage, 440 to 220 (8 ways to win vs. 4 to lose). That is why, once you make a passline bet and a point is established, you cannot take the bet down or reduce it; it's a "contract" bet. It's also why you cannot make a don't pass bet after a point has been established. The casino is not going to let you "cherry pick" the stage of the bet where the player, not the casino, has an advantage.

Cheers,

Alan Shank

Quote:tuttigympocketaces: Yes, I want to know the chances, the odds, the probabilities of exactly having 244 wins against 251 losses in 495 PL outcomes.

You stated that it is "uncommon" but "it happens." That statement lacks specificity.

You stated that in a "million trials" "some" sets of 495 PL outcomes will show as 244/251. Those generalizations, "uncommon" and "some," are meaningless when players have their money at risk. The 1.41% HA is a finite number which many rely upon to be accurate. If the 244/251 is truly "uncommon," then that HA is going to increase often. So define "uncommon" and "some" in the context of your response. Gross generalizations can be costly. Kinda like Obama saying that the "stimulus" will work in the "long term." What is that?

tuttigym

OK, per above, 1 in 28. I was trying to speak in laymans terms since you seemed quite opposed to mathematical concepts.

Quote:tuttigmNo business can survive on a 1.41% gross profit which is what some are eluding to that might represent the HA. Businesses have operating expenses which far exceed the portions of gross profits posted by a business. The resultant amount becomes the net profit. That 1.41% might buy tiolet tissue for a casino for a week.

Except that each person will make many bets at that 1.41 percent rate, and the effect becomes cumulative. Again, you are applying one concept and trying to connect it to another different concept in an incorrect way. If every person who went to vegas made ONE bet at a 1.41 percent HA, vegas would be a bunch of tumbleweeds. But they don't, and the casino bases revenue from gaming from an individual on one main factor:

Your average bet, multiplied by the hands per hour, hours spent playing (can be a decimal below 1) and house advantage of the bet(s).

The 'hold' figure is based off this, and truly represents their potential profit per customer. It is far higher than the house advantage of one single bet.

Of course many bets are far more lucrative to the casino than 1.41 percent, but no table games offer much more than 5 percent on average and some (like blackjack) offer far lower. The constant churning of bets is the main thing that drives revenue on all of these games.

We all know that the 7 can be rolled more time than any other number, so once the point is established, PL/FO players chances of winning those bets diminish dractically. That so called 1.41% HA now becomes, depending on the point, up to a 67% HA which renews with every new point.

Based on the 244/251 1.41% HA, only about 22% of those PL bets are natural winners ( 7 or 11).

Why place yourself and your money at such a disadvantage with a contract bet? I know the FO bets are not contract, but they are never taken down once placed.

The coin toss examples that are illustrated actually increase the validity of my thoughts because while the odds are 50/50 and the probabilities for that exact outcome on a large sample are slim, there are still only two outcomes available at 50/50. The PL/FO outcomes have greater margins for loss and those margins renew with each point at various possible deficits advantages for the player.

The reason the house offers 10X or whatever is exactly because of that HA upward swing, and therefore, the so-called very low published HA wins create a false sense of well being in the player. After the point is established, the house ALWAYS has six ways to win, and the player has that many ways to lose which exceeds his opportunities to win on any given point (PL/FO).

For me, to answer your last question, once that point is established, I have up to 30 ways to win and only 6 ways to lose on any given roll of the dice. My betting starts then and I create betting patterns that will provide me more ways to win than to lose. Can one lose doing that? of course, it is called gambling. The difference for me is discipline.

tuttigym

Again, I recognize that the 1.41% HA exists based on the 244/251 PL outcomes, however, removing the Come Out naturals for both winning and losing or about 34% must necessarily skew those results heavily to the house side of the equation which renew with every point, right?

tuttigym

Of those 660 points:

- the point will be 6 or 8 on 10/24 combinations or 275 times. Of those 275 times, on average, the point will be rolled before the seven 125 times and the seven before the point 150 times for a loss of 25 units. With 275 units bet, that is a house advantage of (25/275) 9.0909%, on the points of 6 or 8.

- the point will be 5 or 9 on 8/24 combinations or 220 times. Of those times, on average, the point will be rolled before the seven 88 times and the seven before the point 132 times for a loss of 44 units. With 220 units bet, that is a house advantage of (44/220) 20%, on the points of 5 or 9.

- the point will be a 4 or 10 on 6/24 combinations or 165 times. Of those times, on average, the point will be rolled before the seven 55 times and the seven before the point 110 times for a loss of 55 units. With 165 units bet, that is a house advantage of (55/165) 33.333% on the points of 4 or 10.

When you add it all up, on 660 points, the point will come before the seven 268 times and the seven before the point 392 points. With a bet of one unit, you will lose a total of 124 units over 660 points, for a HOUSE advantage on a point being 124/660 or 18.7879%.

Of the other 330 rolls, you will win on average 220 - 110 units = 110 units of a player advantage of 110/330 = 33.3333%

The total house advantage then, for the table, is (110 - 124) / 990 = 14/990 or 1.4141%.

So, to recap, then, the HA on the 4 and 10 is 33.33%, not 50% or 67%, because out of 3 4 and 10 rolls, you will win one and lose 2 for a loss of 1/3. The HA on the 5 and 9 is 20%. The HA on the 6 or 8 is 9.09090%.

The free odds is used to lower the house advantage. Even though the point is working against you, the fact is the odds are paid according to the frequency of the dice. That is, for $1 odds on a 4 or 10, on three points of 4 or 10, you will win $2 once and lose $1 twice for an average loss on the odds alone of ZERO. That's why they are called "Free Odds".

Quote:tuttigym

For me, to answer your last question, once that point is established, I have up to 30 ways to win and only 6 ways to lose on any given roll of the dice. My betting starts then and I create betting patterns that will provide me more ways to win than to lose. Can one lose doing that? of course, it is called gambling. The difference for me is discipline.

tuttigym

I did not see where you explained your strategy which gives you 30 chances to win and 6 to lose. One way would be to bet across and on the horn after the point is established and take all place bets down after one roll.

This yields a HA = 2.3% which is effective on the larger amount you would be betting - $36 vs $5 for the pass line - so this method will give the house more of your money over the same period of time.

number | bet | win | return | # rolls out of 36 | weighted return |

4 | 5 | 9 | 41 | 3 | 123 |

5 | 5 | 7 | 39 | 4 | 156 |

6 | 6 | 7 | 39 | 5 | 195 |

8 | 6 | 7 | 39 | 5 | 195 |

9 | 5 | 7 | 39 | 4 | 156 |

10 | 5 | 9 | 41 | 3 | 123 |

2 | 1 | 30 | 63 | 1 | 63 |

3 | 1 | 15 | 48 | 2 | 96 |

11 | 1 | 15 | 48 | 2 | 96 |

12 | 1 | 30 | 63 | 1 | 63 |

7 | 0 | 0 | 0 | 6 | 0 |

total return | 1266 | ||||

total bet | 1296 | ||||

loss | 30 | ||||

HA | 2.3% |

You can make similar calculations for whatever startegy you employ.

For me, to answer your last question, once that point is established, I have up to 30 ways to win and only 6 ways to lose on any given roll of the dice. My betting starts then and I create betting patterns that will provide me more ways to win than to lose. Can one lose doing that? of course, it is called gambling. The difference for me is discipline."

You remind me of a guy on rec.gambling.craps who insisted the "free" odds were a casino lie because after a point is established the pass/come player has less than a 50% chance to win the bet, ignoring the fact that the casino pays more than the bet amount when the player wins. The 1.41% applies ONLY to the flat portion of the bet and, as I and others have shown, is a weighted average of all the possible outcomes, including those resolved on the comeout and those going to a point. The less-than-50% chance of winning those points is exactly balanced by the payouts, 6 to 5, 3 to 2 and 2 to 1, which mirror the true odds.

When it was pointed out to him that the DP/DC player, once a point is established, has a greater-than-50% chance to win, so that, per his reasoning, there should be a player advantage, he said, "Yes, but the casino pays you less than the bet." So the payout was relevant here, but not on the "right" side. Duh!

As to your having 30 ways to win vs. 6 to lose, I assume you're talking about covering all the point numbers with place bets. Here again, it's not just a matter of ways to win vs. ways to lose. When the seven shows, you lose ALL of those other bets, not just one. Not only that, but the HA is higher on place bets than on the flat part of pass/come/DP/DC bets, 1.515% on 6/8, 4% on 5/9 and 6.67% on 4/10 (should be buy bets instead, of course).

Of course, the place bets have other advantages, mainly flexibility, since you can make them at any time, remove them at any time and pick which numbers to bet on. OTOH, some people do not like the fact that the dealer has to place them for you.

It's a matter of personal preference, but I do believe it's a good idea to understand where the HA comes from and take into account all the outcomes and their relative probabilities.

Cheers,

Alan Shank

Quote:tuttigym... once the point is established, PL/FO players chances of winning those bets diminish dractically...Why place yourself and your money at such a disadvantage with a contract bet? I know the FO bets are not contract, but they are never taken down once placed.

It is not an even bet, but pays up to 2:1. Perhaps you stick to the old dictum "never take the small end of the odds". Oddly enough this is one time that gets thrown out the window. And actually you *can* take Free Odds bets down.

Quote:tuttigymThe coin toss examples that are illustrated actually increase the validity of my thoughts because ...there are still only two outcomes available at 50/50. The PL/FO outcomes have greater margins for loss and those margins renew with each point ...

Again, I think I am starting to understand your objection. It is certainly quite possible to have one heck of a losing streak.

the other follow-up questions I might have asked have already just been posed.

Quote:tuttigymJB: Okay. Now since we know that 65% of all table action is after the point is established, can you provide the HA for PL/FO bets based solely on winning and losing those bets to either point conversions or 7 outs?

Again, I recognize that the 1.41% HA exists based on the 244/251 PL outcomes, however, removing the Come Out naturals for both winning and losing or about 34% must necessarily skew those results heavily to the house side of the equation which renew with every point, right?

tuttigym

To use a video poker analogy, what you are asking is akin to saying "I understand Jacks or Better returns 99.5439%, but what about those deals that contain no high cards, such as 2-5-6-8-9 offsuit? Surely those hands don't return 99.5439%."

It is correct to say that every unique situation has its own expected value, but the house edge has already taken all of these situations into consideration. The house edge for a bet is the average house edge of every possible outcome for that bet.

Since you never know which situation you will end up with, the house edge you are up against is always the same at the time you place your bet.

For example, with video poker, you could be dealt unsuited 2-5-6-8-9, four of a kind, or a royal flush. Obviously a royal flush is a much better hand than unsuited 2-5-6-8-9, but you don't know until AFTER you place your bet what you are dealt, thus, the house edge you are up against when you place your bet is always 0.4561%.

Likewise, with the Pass Line bet in craps, some outcomes are rolling a 7 on the come-out roll (a win), establishing a point of 4 (not so good), and establishing a point of 8 (not too bad). Each of those three situations have different expected values, but the house edge already incorporates them. When you place a Pass Line bet on the come-out roll, the house edge you are up against is always 1.414%. The fact that it changes later on is irrelevant, and has already been accounted for.

Quote:odiousgambit

Again, I think I am starting to understand your objection. It is certainly quite possible to have one heck of a losing streak.

Of course it is. Even in a coin flip, it is possible. However, the same thing goes for place bets, which resolve with the same probabilities as points on pass/come, but don't pay true odds. Let's examine three aspects of bets on the point number six:

pass line point of six: probability of winning .4545, payoff 1:1

place bet on six: probability of winning .4545, payoff 7:6

odds bet on point of six: probability of winning, .4545, payoff 6:5

#1 and #3 go together, since you can't make the odds bet without a flat bet

Suppose you have $5 on the passline and $10 odds

5 ways to win $ 17 = 85

6 ways to lose $15 = -90

----

-5 / 11 * 15 = -.0303

Compare to $12 on place 6

5 ways to win $14 = 70

6 ways to lose $12 = -72

----

-2 / 11 * 12 = -.01515

So, AT THAT POINT IN TIME, the place bet looks like a better deal. However, people who tout the place bets over pass/come/odds always seem to overlook the comeout roll, where the pass/come bettor has the advantage:

8 ways to win $5 = 40

4 ways to lose $5 = -20

----

20 / 12 * 5 = +.3333

The "wrong" bettor is in the opposite situation, having a positive expectation after a point is established, but a big disadvantage on the comeout:

8 ways to lose $5 = -40

3 ways to win $5 = 15

---

-25 / 11 * 5 = -.4545 OR, if you count the push

-25 / 12 * 5 = -.4167

If you take a high enough odds multiple, you can get the HA down to equal (5X odds) or lower (> 5X) than the place, even after a point is established, but only by risking a lot more money. The odds bets add volatility without adding to the expected loss.

In comparing bets:

1) always take all the possibilities into account

2) always consider the volatility as well as the HA, especially if you are playing with a relatively small bankroll

Cheers,

Alan Shank

tuttigym

WIN VS LOSES = PERCENTAGE and party advantage

Come Out Roll: 8 ways to win and 4 ways to lose = 2 to 1 or player advantage of 50%

Point 6 or 8: 5 ways to win and 6 ways to lose = 16 2/3% house advantage

Point 5 or 9: 4 ways to win and 6 ways to lose = 33 1/3% house advantage

Point 4 or 10: 3 ways to win and 6 ways to lose = 2 to 1 house advantage of 50%

Why do you or the Wizard or anyone else calculate the Come out one way and the point conversion house advantage another way especially since the FO "true odds" payouts reflect the above and not the 4/10 of 67% house advantage? Why the lack of consistency in creating these calculations and "odds"?

tuttigym

Quote:tuttigymJB: Does that 3.5+% represent the fact that the "perfect math" will present itself three and one half times out of 100 attempts of 495 PL outcomes? Please clarify. Thanks

tuttigym

On average, yes. It doesn't mean you won't see 500 sets of 495 PL outcomes go by with none of them being "perfect" as you call it. When it comes to gambling, the only thing you can rely on is averages.

Ladies and gentlemen while the "hoax" does not really exist, the calculations posted by JB with the addendum clarification shown above basically throws the 1.41% HA on PL outcomes under the bus.

tuttigym

...And isn't the average a HA of 1.41%?Quote:JBWhen it comes to gambling, the only thing you can rely on is averages.

If you're saying it a nearly impossible to hit the average, you're right. And that has nothing to do with craps. In any event of probabilities, it's hard for an individual to hit the statistical average.Quote:tuttigymLadies and gentlemen while the "hoax" does not really exist, the calculations posted by JB with the addendum clarification shown above basically throws the 1.41% HA on PL outcomes under the bus.

But that doesn't change the fact that the average is a fair prediction of expected results.

How can you agree that the hoax doesn't exist and still throw the 1.41 HA under the bus?

FYI: The only thing under the bus is your argument.

Quote:DJTeddyBear...And isn't the average a HA of 1.41%?

Yes.

Quote:DJTeddyBearIf you're saying it a nearly impossible to hit the average, you're right. And that has nothing to do with craps. In any event of probabilities, it's hard for an individual to hit the statistical average.

But that doesn't change the fact that the average is a fair prediction of expected results.

How can you agree that the hoax doesn't exist and still throw the 1.41 HA under the bus?

FYI: The only thing under the bus is your argument.

I agree with all of the above. I'm not sure what he was trying to prove.

There is one other thing you can rely on when it comes to gambling, and that is that everybody is an "expert". (eyes rolling)