The hoax that is the 1.41% house advantage on pass line bets

Alan,
Fascinating stuff, the perfect 1980!!! Tell me please, what is the HA on the roll, immediately following the established point, being a seven?
What would probability say about that same sequence happening multiple times consecutively?

Thanks,
Bill

Quote: tuttigym

DJTeddyBear: 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??

I think you are confused with "net losses" versus "actual losses" here. This rule accounts for 251 losses and 244 wins in a 495 PL outcome scenario. Seven losses in 20 trials would not account for an expected result of 220 wins, nor would 50 consecutive losses. Each PL bet resolved has an expected house edge of 1.41%, but what happened previously has no effect on what will happen in the future. As multiple people before have posted, the idea of actually hitting 244 winners and 251 losses over a given 495 PL bet stretch is fairly slim, but over a much larger figure this will be accurate.

Think of it this way. The oddsmakers for sports contests are tasked with taking in an enormous amount of information to create a "line" that they feel will be the closest to the actual result as possible. These people are the best in the world at what they do, but there are variables in such a short timeframe (one week of a season or a single game) that they cannot account for. How many times do the games match the spread exactly (+ or - .5 points)? Far fewer than when they do not get it exactly right.

The house advantage is not a steadfast rule since you cannot experience a 1.41% loss on your pass line bet, and you will either experience wild variation in the expected value no matter what happens with that single bet. If you win, you are experiencing results that are 101.41% over the expectation but if you lose that one bet, you are 98.59% under expected value. Thus, the rule can only apply for the long-term.

Quote: bruski

First, while we are speculating because your set-up is wrong, a 495 sided coin would be almost impossible to mint in a size small enough to fit into the average human's pocket. Also, with an odd number of sides, it would likely be very difficult to create a roll to package the coins in for banking purposes.

The coin is mental, not literal, representing an abstraction of the game. A toss of the coin is one settled Pass Line. The concepts are equivalent.

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2012 update.
This thread actually has some good information and math hidden in it, especially from "goatcabin".

I spent some dead time at work today and read and listed the posts that should come to the top.
Would make for a good summary page if I find time later.

By BF asked ME a Craps Q today about the HE of the pass line.
It was easy to answer about the pass line bet.

But in looking for the answer I came across "tuttigym" over at the Craps Forum. He is back at it again. Just did not learn. he goes by "falcon"

some quotes:
Posted: 27 January 2012 04:09 PM
"The fictional 1.41% or 1.42% “house advantage” begs for a definition which gets the tutor back to that obscene math as above"
and
"I know that you honestly believe in the HA approach to wagering at the table but since we all play in the short term, those “expected” results rarely if ever occur."

I guess I could sign up over there and let those members know who "falcon" or "tuttigym" is... Yeah
funny stuff

Page one, tuttigym asks one question, has one hypothesis and offers one claim.

Here they are and the links to the answers and the results.
(Yes, he has surfaced again at another forum with the same old lines. Too bad.)

This should help those that may want to read this thread find the answers that took over 50 pages to show.
There is a lot of drama in this thread and some good math posts also.
Summary of those to follow later on.

Quote: tuttigym

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??

JB answer
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
JB post page 4

Quote: tuttigym

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.

Again from JB's post
about 1 in 28
that is what 3.5848% is.
Not so "astronomical"

Quote: tuttigym

I also believe that the Rule of 495 has never be a documented or witnessed accomplishment at any casino at any time or anywhere.
tuttigym

DeMango suggested it.
7winner on page 41 shows the proof

244/495 in Zumma

I took the dice rolls from the Zumma Craps system tester, my Dad has it, and ran it in WinCraps and Excel (I can color in Excel).
I also came up with the same results as 7winner.

Now, if you are ready to read the entire thread, put on your seat belt and good luck!