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

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.

Hoax? Hardly. Astronomical? That depends upon how far your head is in the clouds.

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.

For any statistical trial where there is a Yes/No results and an expected result, you can plug it into a binomial calculator.

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.

ahiromu: I am a computer dunce with no apologies. An old, short, fat, dumpy guy with very little computer skills, so creating a "program" for me, would be like trying to build an engine from scratch. Is it matlab or mathlab? But thanks for the suggestion; it is appreciated.

tuttigym

Just last night I stood next a guy who told me the pass line was the WORST bet on the table!! During the short time we were playing, the dice "proved" him right with a surplus of craps rolls on the come out and far too many quick 7-outs for my liking. He said something about how many ways to win vs. lose, but I knew that standing at the rail was not the right time to go through the math. Rather than play the pass line he placed the point.

(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."

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."

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!

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!

To All: I really appreciate your taking the time to provide the posts herein about this subject.

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

Mosca: 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

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?

pocketaces: 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

Mosca: 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