Quote:JB Administrator3.5848%, 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.

Webmaster - WizardOfVegas.com

JB: I have thought very often about your analysis and formula above. My conclusion is that the 3.5848% is woefully short. Let me state at the outset of this post that it is MY fault that the answer is wrong. I was dwelling on the proposition that the 1.41% HA on PL decisions were based on the outcomes of 495 PL decisions where there are 244 wins vs 251 loses. That assumption is only a small part of the equation. The 495 PL decisions MUST be made only one time each within the body of the totality of the resolutions.

Therefore, I must ask these pertinent questions:

1. What are the odds of having only seven losses in 495 PL decisions?

2. What are the odds of throwing only one 12 or one 2 natural craps come out losers in 495 PL decisions?

3. What are the odds of throwing only six different natural 7s come out winners in 495 PL decisions?

The questions could go on and on in the same mode.

While the 1.41% HA on PL decisions is the conventional wisdom and perhaps mathematically correct, it is absolutely unachieveable and my guess is that the reality of the odds is 1 to the 495th power to one.

What say you?

tuttigym

Quote:tuttigymWhile the 1.41% HA on PL decisions is the conventional wisdom and perhaps mathematically correct, it is absolutely unachieveable and my guess is that the reality of the odds is 1 to the 495th power to one.

What say you?

I say: study limits and asymptotes. What you're getting into is how a binomial distribution of N independent trials of a random variable (in this case, with p=0.492929) approaches its theoretical mean as N grows. In other words, the Law of Large Numbers. Read this:

http://en.wikipedia.org/wiki/Law_of_large_numbers

So why not just humor me and answer the three questions above especially the first question so that our friends here on this forum will, hopefully, be able to realize that the perceived HA is pretty much a fantasy.

Our mutual objective is to win not to be taken to the cleaners by the house's con regarding the PL wager along with the associated FO bet.

One other thing which goes to some simple math, in order for a player to receive excess $$$ over any given Place bet, the player must risk the PL + 5X odds. Anything less increases the house profit. Somehow we almost never hear about that part of the PL/FO equation. Some casinos only offer 4X odds (AC) and cruise ships offer only 2X odds. How is that for a con?

What say you?

tuttigym

Once again, we will try to get second grade math thru your thick skull.Quote:tuttigym1. What are the odds of having only seven losses in 495 PL decisions?

The math does NOT say that there will, on average, be seven losses per 495 decisions. It says that there will, in average, be seven MORE losses THAN wins.

I.E.

251 wins plus 244 losses = 495 decisions.

251 wins minus 244 losses = 7 more losses than wins.

To answer your question: Very small.

However, when phrased correctly: What are the odds of having seven more losses than wins in 495 PL decisions? Very high.

Quote:DJTeddyBearHowever, when phrased correctly: What are the odds of having seven more losses than wins in 495 PL decisions? Very high.

Well, not absolutely. But relatively, that's the most likely outcome.

Similarly, 5 heads and 5 tails in 10 flips is not very likely at 24.6%, but it's the most likely outcome -- all the others possibilities are less likely than that. The moral of the story is that the top of the bell curve doesn't have to be very high, but it's still the top.

Quote:tuttigymThanks for the offering, however, if the "large number" is beyond comprehension, then the bet as stated by that conventional wisdom becomes a con for the house.

There's nothing beyond comprehension about the number 495. There's also nothing beyond comprehension about the LLN, but for those who haven't taken the time to study it yet. Your lack of study doesn't imply that the "HA is a fantasy". It just means you don't understand it yet.

Upon further reflection, it would seem that you don't believe in the concept of a probability. In order to make any progress on this topic, you have to get the fundamentals down first. For example, do you believe that over many flips of a fair coin, the ratio of heads to flips will converge upon 1/2? If you don't, you can't really begin to dissect the rest.

You are a smart man, the So-Called Free Odds was developed as a marketing ploy to get the players to bet more money...!

I try to point this out to everybody that ask about the PL bet, all the Math guys tell me I am an idiot for not betting on the PL and taking the so-called free odds, I guess it's their new math, that I can't comprehend...!

Their way of thinking is a $10 PL bet on the 10 with $20 in odds is the bet to make, their bet pays them $10 on their flat PL bet and $40 on their so-called free odds total of $50 fantastic....!

My old way of doing math and betting $30 placed bet and to make things simple we will say you had a free buy on the 10, my bet just paid me $60 dumb old me, I could take the bet down at any time and turn it off, I didn't have to wait for the point to be made if the point was something else. If I bet on the 10 because it was the come-out point and I wanted to bet on that number, when the point was hit I didn't have to replace the bet again, if I wanted it to bet the point again! Or I could have regressed the bet down.

I never have a PL bet unless I am paying rent on the table to shoot the dice, I don't care about all the come-out rolls that you all say are the best ways of making money at a craps table.

So please explain why I won more money then you, with your PL bet and your so-called free odds...!

My math and your's must be different, free odds are a joke, you are paying for them with your PL bet, and unless you are taking max odds on the bet they are doing nothing for you!

Most players will never take full odds if they are playing on a 10 x odds table or more, this is a fact, just watch how they play, sure there are a lot of smart players that have the bankroll to take advantage, but the average Joe Blow will not bet full odds!

I never worry what the odds are on a table, and if I forget where I am playing and they have Strip Odds, I just place the point for what ever I want to bet!

If there are any question about playing rent, it's only when you have the dice, and you need a PL bet to shoot the dice, other wise you never have a PL bet!

,,,

Quote:superricktuttigym

You are a smart man, the So-Called Free Odds was developed as a marketing ploy to get the players to bet more money...!

I try to point this out to everybody that ask about the PL bet, all the Math guys tell me I am an idiot for not betting on the PL and taking the so-called free odds, I guess it's their new math, that I can't comprehend...!

Their way of thinking is a $10 PL bet on the 10 with $20 in odds is the bet to make, their bet pays them $10 on their flat PL bet and $40 on their so-called free odds total of $50 fantastic....!

My old way of doing math and betting $30 placed bet and to make things simple we will say you had a free buy on the 10,

If you have a free buy bet, by all means make it, and forget about the pass line w/odds. But, in fact, you are going to pay at least $1 vig on that bet. With the best conditions, a buy 4 or 10 can have a house edge of just 1.11% (vig for $30 bet is $1, collected only on wins), lower than the "hoax" of 1.41% on the pass line. However, that $10 bet on the pass line has an ev of just -$.14, not a whole dollar, and the odds bet has an ev of zero.

Quote:superrickmy bet just paid me $60 dumb old me, I could take the bet down at any time and turn it off, I didn't have to wait for the point to be made if the point was something else. If I bet on the 10 because it was the come-out point and I wanted to bet on that number, when the point was hit I didn't have to replace the bet again, if I wanted it to bet the point again! Or I could have regressed the bet down.

All true. Place and buy bets have flexibility, and many people like that. Of course, odds bets have exactly the same flexibility -- you can call them off, increase/decrease them or take them down any time. You just can't do it with the flat part (except DP/DC).

Quote:superrickI never have a PL bet unless I am paying rent on the table to shoot the dice, I don't care about all the come-out rolls that you all say are the best ways of making money at a craps table.

So, when you DO shoot and bet the pass line, you refuse to accept any comeout wins, right? We don't need no stinkin' comeout wins! We refuse to consider the part of the passline bets where the player has the advantage; otherwise our argument falls apart.

Quote:superrickSo please explain why I won more money then you, with your PL bet and your so-called free odds...!

My math and your's must be different, free odds are a joke, you are paying for them with your PL bet, and unless you are taking max odds on the bet they are doing nothing for you!

You *are* paying for the odds bet with the flat bet, but you are only paying 14 cents, regardless of how much you bet in odds. Your insistence on comparing place/buy bets with only the post-point two-thirds of the passline bet is truly ignorant. On average, for every 36 $10 passline bets made, you net $40 on the 12 resolved on the comeout. But I guess you don't care about that.

Quote:superrickMost players will never take full odds if they are playing on a 10 x odds table or more, this is a fact, just watch how they play, sure there are a lot of smart players that have the bankroll to take advantage, but the average Joe Blow will not bet full odds!

So, what's your point? You might just as well state that place bettors never bet the table max. A player's betting level is presumably based on his/her risk of ruin. Place bets, buy bets and odds bets all have the same probabilities of winning, less than .5, so you need to size your bets so that you can accept some losses without busting your bankroll, else you will be out of the game.

If you bet $30 buy 4, $1 vig collected only on wins 60 times, the ev is -$20, the standard deviation (SD) $325. If you bet $10 pass and take $20 odds on all points 60 times, the ev is -$8, the SD $221, so you'll also less likely to bust. If you take 3, 4, 5X odds the ev is the same, but the SD is now $381. The odds multiple can be chosen so that the risk of ruin is low, but if you have a large bankroll you can increase the variance without increasing the expected loss; you cannot do that with place or buy bets.

Cheers,

Alan Shank

Woodland, CA

Quote:superrickI never have a PL bet unless I am paying rent on the table to shoot the dice, I don't care about all the come-out rolls that you all say are the best ways of making money at a craps table.

"Best" is too subjective. What's true, however, is that you're giving up more to the house on the place bets than a pass bettor is on the line bets, assuming equal wager sizes. You can make subjective arguments about why you like the place bets better, and that's totally fine, but it's simply incorrect that the place bets have a lower house edge than the passline.

What you seem to favor is the immediacy with which you can make (and remove) a place bet, vs. the restrictions placed on line bets. That's a valid procedural complaint, but it's not relevant to the mathematics. If you're at a table with 10x odds, for example, and that table allows put bets, you're always going to be better off making a put bet + odds vs. a place bet. $50 place 5 pays $70, for example, compared to $5 put + $44 odds ($49 total wager) pays $5 + $66 = $71, for $1 less on the bet and $1 more on the win. There's no arguing that the put/odds approach pays better. It turns out that the pass/odds approach has even a lower house edge, but if you prefer not to wait for your point to roll, that's your call. There's nothing wrong with being impatient at the dice table - it'll just cost more money.