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

The house advantage (HA) or edge on Pass Line (PL) bets is unequivically stated at 1.41%. The 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.

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

I think your confusion is between the probability of something occuring and the actual results over a relatively small number of samples (not infinite). If you flip a coin 100 times, you expect that there will be 50 heads and 50 tails. So the probability of any one flip landing on heads is 50%. If you actually flip a coin 100 times, you probably won't get exactly 50 heads. That doesn't mean the math of 50% is wrong.

I'm not really understanding this. The house edge is a probability figure, but cannot predict specific results. Nobody ever purports that it does either. If in some crazy world it could, you could exploit it very easily.

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: tuttigym

The 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.

Very aggressive for someone who has absolutely no idea of what's going on. As stated this is a probability... I guarantee you if you did 495 million pass line bets and divided your win/losses by one million you'd come fairly close.

pocketaces: 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

Quote: tuttigym

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

Did you say '224' because 244 - 20 = 224?

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.

ahiromu: 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

Quote: tuttigym

pocketaces: 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.

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??

tuttigym

Quote: tuttigym

ahiromu: 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.