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

You or I might not be able to roll the dice 495,000,00 times, but I'm sure all the rolls of the dice since say, 1945 just to pick a year have totaled more than 495,000,000. It's not an impossibly large number.

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: 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

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.

pocketaces: 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

So many logical fallacies... my brain hurts

Quote: tuttigym

pocketaces: 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.

I am so confused by this, I can only say: could you list the details of the 'rule of 495'?
Or provide a link?

Thanks.

OK, I think there is just some confusion. The one thing that doesn't exist is using a probability figure (ie the house advantage) to try to definitively predict specific short term results. They are correlated, but not even close to the same. However, this probability figure can determine very accurately long-term results, which in the case of most casino games is millions of trials.

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: 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??

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: Dween

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??

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.

I think one need only consider the rolls at the California Club and at the Borgata which were each over three hours long to know that there simply will be exceptional results in the short term. Even at the history making rolls, the house edge on the pass line bet was 1.414.