Law Of Large Numbers
large numbers, in the long term, averages of independent trials will
tend to approach the expected value. This is very true for the casino,
they deal in nothing but long term outcomes.
But your average player will never even approach anything remotely
like the large number of trials needed to prove the law of large numbers.
We play in the extreme short term, where basically anything can happen.
Realistically, the law of large numbers can't apply to the player. There
are no laws or theories that apply to short term play. The casino can
lump all the players together and get a long term number. On a player
to player basis, however, they're lost. Nothing can apply to the next bet
you make in a game of random outcomes.
Anybody want to guess where I'm going with this?
You're starting a new thread on an old and overdone topic to bring the "strategy" proponents out of the woodwork, stir the pot and get attention?Quote: EvenBob
Anybody want to guess where I'm going with this?
Seeing that your statement
is false, that's my best guess.Quote: EvenBobNothing can apply to the next bet
you make in a game of random outcomes.
Let's say you have a bag of 10 colored balls where 9 are red and 1 is blue. If I stick my hand into the bag and pull one out at random, I know before I pull out the ball that there's a 90% chance it will be a red ball. Sure, anything can happen but it doesn't change the math of the situation. The guy betting you will pull out a red ball always has the best odds of being right and you pulling out the blue ball on your first draw doesn't change that. The same math applies to roulette or any casino game where the house has a built in mathematical advantage albeit with slightly different odds.
Quote: TheNightflyLet's say you have a bag of 10 colored balls where 9 are red and 1 is blue. >>> The same math applies to roulette or any casino game where the house has a built in mathematical advantage albeit with slightly different odds.
You're two examples aren't remotely related. 9 out of 10 is
a huge advantage for the 9 red balls. The casinos advantage
on roulette is tiny by comparison.
Ok, let's say the bag has 38 balls of which 20 are red and 18 are blue. The guy betting on red still has over a 5% advantage. What's your point? There's no way of knowing what ball he'll pull but you'd have to be a pretty big moron to bet on blue.Quote: EvenBobYou're two examples aren't remotely related. 9 out of 10 is
a huge advantage for the 9 red balls. The casinos advantage
on roulette is tiny by comparison.
Quote: TheNightflyThere's no way of knowing what ball he'll pull but you'd have to be a pretty big moron to bet on blue.
So red is 'due' because there are 20 reds and only 18 blues?
As for the Roulette/Bag example, red isn't "due". Just red is more likely. Over time (and time is not the HUGE long term) the red will help you tend to finish up in profit.
"Anything can happen" is true. It's just most of the time, not much unusual does happen.
Gee Bob, let me think a moment... no.Quote: EvenBobSo red is 'due' because there are 20 reds and only 18 blues?
Quote: thecesspit"Anything can happen" is true. It's just most of the time, not much unusual does happen.
My point is, nothing governs short term play. The
law of large numbers doesn't enter into it. The
'laws' of games like roulette involve huge numbers
of outcomes, far more than any one player will
see in their lifetime of playing. You can't nail short
term play down or make it behave in any predictable
manner.
The laws of probability come into. You just see such a tiny snippet of time, things don't have the large range to see the big patterns. But I will again say, the "long term" is much quicker most of the time (again, outliers happen... course they do). If you make 20 spins, most of the time you'll win between 8 and 12 of them. Course I can't pin down WHICH of those. That's the deal with a random number series (which I'm assuming roulette is). It still has it's constraints and laws (any of 38 numbers will come up, and the next number doesn't rely on any of the previous numbers).
Anyways, I have no idea where you are going with this, to answer the first question :)
Once again, incorrect. Math governs all play in casino games of chance where the games operate within design parameters and there is no cheating on either side.Quote: EvenBobMy point is, nothing governs short term play.
If you sit down at a 00 roulette wheel and put $10 on red, your odds of winning your bet are 18/38. No matter how you look at it, you are at a distinct disadvantage every time that ball falls into the wheel. Of course it is VERY possible that you will win your bet BUT you will only get paid even money, even though it was not an even wager. How does anyone not grasp this concept?
EVERY time you place that roulette wager, the odds of winning are the same. Regardless of what happened in the past and how you attempt to use past results to direct your future wagering decisions, you are ALWAYS at the same mathematical disadvantage for each and every individual spin. Can you be ahead of the game at any time? Sure. The question is, what is the MORE likely outcome? Nothing is ever "due" but something is "ALWAYS" more likely and that has NOTHING to do with what happened before.
Is it possible to increase and vary your wagers in an attempt to recoup losses? Yes. Will this work? Sometimes. Is there a strategy of wagering on roulette that will put the odds in your favor at any time? No. Each spin is independent of every other spin and the money you place on the layout is ALWAYS at a disadvantage.
If you place a single dollar chip on 35 individual numbers do you think you now have an advantage? Sure, it is more likely that one of those numbers will hit than it is that one of the other 3 numbers will hit BUT when you do hit in that situation you will receive less than equitable odds on your wager. You are at a 5.26% disadvantage on EVERY spin.
Quote: thecesspitSomething does govern short term play, the odds of the game.
On a spin to spin basis, with the game resetting
itself after every spin, which it automatically does, anything
can happen on the next spin. Thats if you have an equal
number of reds and blacks, for instance. Forget the
zeros for the moment. The odds are 50/50. How does
that effect the next outcome? All the odds do is make
it equally likely to be red or black. Throw in a couple
zeros; if the odds govern the next spin, which will it
be, red black or green?
Quote: TheNightflyMath governs all play in casino games of chance where the games operate within design parameters and there is no cheating on either side.<<<If you sit down at a 00 roulette wheel and put $10 on red, your odds of winning your bet are 18/38.
OK, whats the next spin going to be, then. You know the math,
you know the odds. Will it be red black or green?
In your example, the odds are 18/38 it will be red, 18/38 it will be black and 2/38 it will be green.Quote: EvenBobOn a spin to spin basis, with the game resetting
itself after every spin, which it automatically does, anything
can happen on the next spin. Thats if you have an equal
number of reds and blacks, for instance. Forget the
zeros for the moment. The odds are 50/50. How does
that effect the next outcome? All the odds do is make
it equally likely to be red or black. Throw in a couple
zeros; if the odds govern the next spin, which will it
be, red black or green?
The fact that neither you nor anyone else knows what the result of the next spin will be doesn't change these odds or their effect on your wager.
The effect will be this:
If you bet on red you have less than a 50% chance (47.368%) of being right but if you are right you will be paid even money.
If you bet on black you have less than a 50% chance (47.368%) of being right but if you are right you will be paid even money.
If you bet on either of the 2 green numbers you have less than a 2.632% chance of being right but if you are right you will only be paid 35 to 1 and have your original wager returned to you which means you were paid at 94.74% of full value.
In every case and for every spin, it doesn't matter where you put your money or the fact that you MAY win the bet, the house always pays you less than the full value of even money. The house will make money because you will lose (choose wrong) more often than you will win and they will take your money every time you are wrong (over 50% of the time) and pay you 1 to 1 (or the mathematical equivalent) when you are right which will be less than 50% of the time.
Quote: TheNightflyThe fact that neither you nor anyone else knows what the result of the next spin
And that says it all. I could care less what the long
term 'effect' is, I'm concerned with the next outcome
and only the next outcome. Thats where we play the
game, not on the next hundred spins or the next 10
spins, the casino only lets us bet on the NEXT spin.
Thats where all our attention should be. The law of
large numbers has nothing to do with just one spin,
where the game is actually played.
Quote: duckmankillaAs has been posted previously, math governs all casino games on each and every individual spin
OK, if thats true, whats the next spin? If math governs
each individual spin, what does math say the answer is?
Quote: TheNightflyIn your example, the odds are 18/38 it will be red, 18/38 it will be black and 2/38 it will be green.
The fact that neither you nor anyone else knows what the result of the next spin will be doesn't change these odds or their effect on your wager.
The effect will be this:
If you bet on red you have less than a 50% chance (47.368%) of being right but if you are right you will be paid even money.
If you bet on black you have less than a 50% chance (47.368%) of being right but if you are right you will be paid even money.
If you bet on either of the 2 green numbers you have less than a 2.632% chance of being right but if you are right you will only be paid 35 to 1 and have your original wager returned to you which means you were paid at 94.74% of full value.
In every case and for every spin, it doesn't matter where you put your money or the fact that you MAY win the bet, the house always pays you less than the full value of even money. The house will make money because you will lose (choose wrong) more often than you will win and they will take your money every time you are wrong (over 50% of the time) and pay you 1 to 1 (or the mathematical equivalent) when you are right which will be less than 50% of the time.
So, now a question for you. When you play roulette, how can you possibly imagine being able to place your wagers in any manner that will result in you making more money than you lose? You've just said it:
Quote: EvenBobI'm concerned with the next outcome
and only the next outcome. Thats where we play the
game, not on the next hundred spins or the next 10
spins, the casino only lets us bet on the NEXT spin.
Thats where all our attention should be. The law of
large numbers has nothing to do with just one spin,
where the game is actually played.
So, knowing that it is all about the next spin only, how do you propose to place a wager where the outcome gives you any advantage? How do you propose to place your wager in such a way that it will eliminate the house edge of 5.26%?
The only honest and sane answer to that question is obvious. You cannot.
Quote: EvenBobOK, whats the next spin going to be, then. You know the math,
you know the odds. Will it be red black or green?
Yes.
Quote: TheNightflyYou must have missed my last post bob so I'll paste it here.
I didn't miss it, its about the long term, which doesn't
apply to the next spin.
All casino math is fuzzy math, its probability math.
It has nothing to do with the next hand or the next
spin. Its all about the next 10,000 or 50,000 outcomes.
Probability math is totally dependent on the LLN. The
next spin is dependent on nothing. Math doesn't touch
it. If it did, roulette would have been beaten with math
200 years ago.
Quote: duckmankillaThe math does not necessarily need to provide an answer. It simply tells you what the most likely outcome will be.
But it doesn't. Where does the math ever tell
you if its going to be red or black and be right
more often than wrong.
I'll ask my question again then.Quote: EvenBobI didn't miss it, its about the long term, which doesn't
apply to the next spin.
All casino math is fuzzy math, its probability math.
It has nothing to do with the next hand or the next
spin. Its all about the next 10,000 or 50,000 outcomes.
Probability math is totally dependent on the LLN. The
next spin is dependent on nothing. Math doesn't touch
it. If it did, roulette would have been beaten with math
200 years ago.
Knowing that it is all about the next spin only, how do you propose to place a wager where the outcome gives you any advantage? How do you propose to place your wager in such a way that it will eliminate the house edge of 5.26%? What strategy beyond a simple guess or coin flip or random toss would a player employ to decide the best place to put his wager on the next spin?
Math will not and cannot tell you whether the next spin will be red or black but it DOES assure you that GREEN will come up 2 times out of 38 spins on the average which means you will lose your wager 1 time in 19 on the average whether you are betting red or black.
As you've said (repeatedly), it is all about the next spin and no other spin has any bearing on that fact or the result of that spin. Knowing that for every individual spin there is less than a 50% chance of the result being red OR black, which do you choose and why? Which choice eliminates the disadvantage due to there being 2 green numbers on the wheel?
Quote: EvenBobBut it doesn't. Where does the math ever tell
you if its going to be red or black and be right
more often than wrong.
The math of adding up the outcomes and dividing them by the possibility of each... binomial progressions will tell you how likely a sequence is. How likely you are to be right 10 times out 20. Etc. It is as you say fuzzy, and tendencies at the low level. But they are there.
There's no need for the Law of Large Numbers to be involved here (which merely states that as you approach infinity the ratio of distributions tends towards the precise ones defined by the game). The Law of Large numbers is derived for the core rules of probabilty (and the rules for each individual spin of the wheel).
Anything can happen is a misnomer. The roulette ball won't jump out and squirt cider in your ear. You know it's tendencies (like on a hand of VP as well), and those may guide your play. If you bet a single rather than a evens bet, you know it's less likely you will hit. But indeed it just might.
But what IS your point? The Math can't predict the precise outcome of the next spin? That's EXACTLY what random means (if we define it to mean unassociated with a previous spin etc etc). That's exactly what probabilty math tells us. We can't know. We can just say what might happen (and won't won't happen at all, and whats unlikely to happen, etc...).
Quote: TheNightflyWhat strategy beyond a simple guess
An educated guess.
And what kind of information have you used to educate yourself on where that ball may or may not land?Quote: EvenBobAn educated guess.
Quote: TheNightflyAnd what kind of information have you used to educate yourself on where that ball may or may not land?
Guessing is all you have. By studying probability you can
make an educated guess as to the next outcome. Can
math prove guessing doesn't work?
Steve Wynn said in an interview that the math that runs
his casino is unreliable on a month to month basis,
but is very reliable on a year to year basis. Imagine
what it is on a spin to spin basis. Its nonexistant.
Well, you've proven you have no concept of probability so logic isn't going to make a dent.Quote: EvenBobGuessing is all you have. By studying probability you can
make an educated guess as to the next outcome. Can
math prove guessing doesn't work?
I can prove that guessing will have less than a 50% chance of being right. How about that? Anyone here who knows anything about probability can prove that guessing the outcome will result in being right less than 50% of the time.
I'm done. Obtuse doesn't begin to describe this guy. Is it possible that he owns property and has been permitted to procreate? As sharp as a wet diaper he is.
Bob, congratulations. You have gone in circles of illogic long enough for me to stop making an effort to use reason with you. You have proven that you refuse to accept the mathematical facts and physical laws of the universe in which you live. When you're ready to make a substantial wager proving that you have any kind of strategy to consistently win money at roulette I'll happily put my money where my mouth is. Until then, enjoy Gilligan's Island.
Quote: TheNightflyWell, you've proven you have no concept of probability
Really? Educate me. Tell me what probability says about the
next outcome.
The player who sits down and makes a bet is making a
guess. Are you saying that no matter what he does, no
matter how much research he does to educate himself
on his guessing method, he has absolutely no chance
of improvement?
Quote: EvenBobAre you saying that no matter what he does, no matter how much research he does to educate himself on his guessing method, he has absolutely no chance of improvement?
That is right. Thre is no hope. Might as well just plunk your money down and then go out and get drunk.
Quote: EvenBob
Probability math is totally dependent on the LLN.
You got it backwards. Law of large numbers is the result (just one of many) of what you call "probability math", not the essence or the foundation of it.
Just like "probability math" says that betting roulette you are about 11% more likely to lose than to win, it also says that if you play "long enough", you'll lose about 5.6% of the money you bet.
Quote:Math doesn't touch it. If it did, roulette would have been beaten with math
200 years ago.
You seem to think that anything that cannot be beaten is not "touched" by math. This is a false assumption. Math purpose is to describe (model) various processes, not to "beat" them. When it comes to games, what math tells you is what is the best strategy, and what is the likely outcome.
You can play tic-tac-toe, and never lose if you use a good strategy, but you will never win either unless your opponent is an idiot. It is not math's fault you cannot win, it is the nature of the game.
We can't predict the next number, or even values of a short string of numbers. There is no educated guess to be made IF we accept that each number is truly random.
However, if we can make an educated guess, what information would we be using?
If we use previous results, we are essentially saying that previous results DO effect the next result, which means the roulette wheel is NOT random (whereas it could still show a mathematically believable set of results in the long term if we look at the probability density function (*)), which means are axiom is wrong, so any conclusions we make about the law of large numbers applying (and before that, basic probability calculations) are fallacious.
If we use wheel bias, then again, each number doesn't have equal probability, there for our initial axiom was false (and the probability function over the longer term will look skewed).
If we use spin/wheel tracking, again we are saying that the pick isn't random.
There may be other sources we can use to make that educated guess. But I can't see how any of them don't break those base assumptions about a random roulette wheel, which means conclusions on the long term are then invalid. I'm happy to shown where I've made an error in this argument though.
I like seeing emergent phenomena from simple rules (a roulette wheel isn't a very interest example of this, in my opinion, but still), and find it fascinating and a source of inspiration for game design (not casino games).
(*) a chi squared analysis, or similar sort of thing that looks at predecessors to a number to show a certain pair/triple/quadruple string is more or less likely should show up over the long term if this the case).
Quote: SOOPOOthe simple concept of 'you can't beat a negative EV game without a technique (hole carding, counting, etc) that turns it into a positive EV game' .
What makes you think I don't understand that? I'm simply pointing out
the math everybody brings up doesn't apply to the next outcome. There's
no math you can point to that says the next spin can't be guessed correctly.
And please spare me the thinly veiled insults about my intelligence, all
you're doing is revealing your ignorance. Instead of pointing out that
an 8 year old is smarter than me, why not show me you're smarter and
reveal what math governs the next outcome. What math says I won't
guess it corrctly.
The fact that you cannot say exactly which cigarette will kill you does not mean that smoking is a safe practice. Similarly, the fact that mathematics cannot tell you exactly what will be the very next outcome in a random series of events does not mean that the mathematics do not govern the process.
Quote: thecesspit
If we use previous results, we are essentially saying that previous results DO effect the next result.
Why do you say that? If you're a general and you study previous wars,
does that mean the current war is effected by previous wars? Why does
studying past results of anything mean they effect current results. The
past simply points to the future, if you learn to interpret it. It doesn't
effect it. And please don't bother saying random results are independent,
thats different. The past is the past, clues are always there if you know
how to look for them.
Quote: DocSimilarly, the fact that mathematics cannot tell you exactly what will be the very next outcome in a random series of events does not mean that the mathematics do not govern the process.
What math says I can't make the next guess correctly? Everybody always says
math governs the process, but they never say what the math is. Whats the equation
or formula that says I will be right or wrong on the next bet. Not how I'll do on
the next 1000, but on the very next outcome. The casino won't let you bet on the
next 1000, so my only concern is the next bet.
Quote: weaselmanYou got it backwards. Law of large numbers is the result (just one of many) of what you call "probability math", not the essence or the foundation of it.
.
Chicken or the egg.
Quote: EvenBobThe past is the past, clues are always there if you know how to look for them.
I think that summarizes the belief that EvenBob and a couple of other roulette enthusiasts on this forum hold, and one that most on this forum reject when it is used to imply that watching a fair roulette wheel gives an indication of the result of a specific future spin. I don't understand why such enthusiasts/believers aren't spending all of their time at the roulette table amassing huge fortunes.
Quote: weaselmanYou got it backwards. Law of large numbers is the result (just one of many) of what you call "probability math", not the essence or the foundation of it.
Just like "probability math" says that betting roulette you are about 11% more likely to lose than to win, it also says that if you play "long enough", you'll lose about 5.6% of the money you bet.
You seem to think that anything that cannot be beaten is not "touched" by math. This is a false assumption. Math purpose is to describe (model) various processes, not to "beat" them. When it comes to games, what math tells you is what is the best strategy, and what is the likely outcome.
You can play tic-tac-toe, and never lose if you use a good strategy, but you will never win either unless your opponent is an idiot. It is not math's fault you cannot win, it is the nature of the game.
Dead on - beautifully stated.
Quote: EvenBobWhat makes you think I don't understand that? I'm simply pointing out
the math everybody brings up doesn't apply to the next outcome. There's
no math you can point to that says the next spin can't be guessed correctly.
And please spare me the thinly veiled insults about my intelligence, all
you're doing is revealing your ignorance. Instead of pointing out that
an 8 year old is smarter than me, why not show me you're smarter and
reveal what math governs the next outcome. What math says I won't
guess it corrctly.
Math tells you the exact, precise expectation of your next guess. That's all.
Quote: DocI don't understand why such enthusiasts/believers aren't spending all of their time at the roulette table amassing huge fortunes.
I don't understand why, when the earth was believed by everybody
to be flat, that somebody didn't go to the edge and set up a viewing
stand and get rich by charging people to look into the abyss.
Quote: WeaselmanYou got it backwards. Law of large numbers is the result (just one of many) of what you call "probability math", not the essence or the foundation of it.
Just like "probability math" says that betting roulette you are about 11% more likely to lose than to win, it also says that if you play "long enough", you'll lose about 5.6% of the money you bet.
You seem to think that anything that cannot be beaten is not "touched" by math. This is a false assumption. Math purpose is to describe (model) various processes, not to "beat" them. When it comes to games, what math tells you is what is the best strategy, and what is the likely outcome.
You can play tic-tac-toe, and never lose if you use a good strategy, but you will never win either unless your opponent is an idiot. It is not math's fault you cannot win, it is the nature of the game.
We said!
Quote: EvenBobThe past is the past, clues are always there if you know how to look for them.
I'm sure there are a lot of baccarat players would would agree with you. However, don't expect much support for your statement here.
We can easily say that, on a 00 wheel, over 1,520 spins, betting on a single number, the odds of having a winning session (43 or more wins) is 28.16%. 1,520 spins represents about 50 hours of roulette action at a spin every two minutes. Given that the average gambling session is about 4 hours, someone going once a month would experience about that number of spins over a year.
If on the other hand that same person was betting red or black for the same number of sessions, the odds of having a winning session (760 or more wins) is only 1.88%. That's because the variance is much lower.
So, indeed, if you are betting on red or black over a night (114 spins), your odds of coming out ahead (up 2 units or more) is 20.0%. If you are betting a dollar single number over that same time, the odds of losing $114 is 4.78%, of losing $78 is 14.7%, of losing $42 is 22.50%, of losing $6 is 22.70%, of winning $30 is 17.02%, of winning $66 is 10.12% of winning $102 is 4.97%, and so on and so forth. The odds of you breaking even (losing $6) or winning is 34.3% and the odds of winning is 19.2% but the variance is so much higher.
It's all measurable. So my answer to this is that Bob is right with the game of roulette depending on the bet that you make. Even over a year, betting on a single number has a 28% chance of being a winning proposition. In fact, if you stuck 38 roulette players and each of them hung around for 1,520 spins betting on the same different number, 13 of them would walk away winners but the casino would walk way with 3,040 gaming units each and every time.
Quote: EvenBobWhat math says I won't guess it correctly.
None what so ever. Why do you think the math says you won't?
If you are PURELY guessing, the math clearly states you have a just less than even shot of guessing correctly. Sometimes you'll be right, sometimes you'll be wrong. That's what it says. Your comment about chicken and egg is very revealing. The Law of Large numbers is EMERGENT from the basic probability of the game. The chicken and egg is here solved.... the low level behaviour came first.
Quote: EvenBobWhy do you say that? If you're a general and you study previous wars,
does that mean the current war is effected by previous wars? Why does
studying past results of anything mean they effect current results.
and this...
Quote:The
past simply points to the future, if you learn to interpret it. It doesn't
effect it.
... do not follow. You would have to give me a concrete example here to make your point.
Quote:And please don't bother saying random results are independent,
thats different.
Different from what? My previous argument was that if random results are independent, the past doesn't matter AT ALL. If however we claim the past has information we can use, then the events ARE NOT RANDOM, so any axiom we use to start an argument saying "these results are random thus Law of Large Numbers" is meaningless. The law of large numbers ONLY applies to random, independent events.
Quote:The past is the past, clues are always there if you know
how to look for them.
Ignore the wars example. IF there is data and clues in the past spins of a roulette wheel of what may happen in the future, these past events must have a bearing on the future. If you claim by looking at previous events there is something that will help you guess the next spin (and therefore be better than slightly under evens) you are stating past events are effecting future events.
I'm sorry, without a concrete example of what you are talking about, I can't follow what you are stating.
(and actually, past wars do effect current wars, as past wars modify tactics and strategy people will use in the current war, and past battles help future battles. D-Day would not have been as successful with out the Dieppe raid, for example).
Quote: EvenBobI don't understand why, when the earth was believed by everybody
to be flat, that somebody didn't go to the edge and set up a viewing
stand and get rich by charging people to look into the abyss.
Because that belief was false. Exactly Doc's point.
Quote: EvenBobWhat math says I can't make the next guess correctly? Everybody always says
math governs the process, but they never say what the math is. Whats the equation
or formula that says I will be right or wrong on the next bet.
The math is called "Probability Space". It lists the possible outcomes for the roulette wheel spin, defines what an event is (one spin, say), and how likely that event is.
How likely each event is is governed by complicated rotational physics (also a type of math). Naturally, it is close to uniformly distributed across all outcomes.
Neither can tell you whether you will be right or wrong on the next bet. In fact, that's the whole point.
That's it for me: logging off.
Quote: thecesspitIf you claim by looking at previous events there is something that will help you guess the next spin you are stating past events are effecting future events.
Past events can point to future events without effecting them.
Quote: EvenBobPast events can point to future events without effecting them.
Please give me an example relating to a Roulette wheel, or other random number sequence.
For this to be true one of the axioms about random numbers I keep mentioning must be wrong. That's fine, I'm trying to work out which one it is.
If you can't give a concrete example, that's fine, just don't expect me to agree with you.
