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Author Topic: Einstein's theory of roulette?
Honey Bunching Oats
I'll Be Home for After Christmas Sales


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[slight hijack]
Albert Einstein visted Las Vegas in 1955. He walks across the casino floor in the Tropacana and passes the craps table. He sees God there.
"Mein Gott!" he shouts, "What are you doing?"

--------------------
"When we talk about democracy, if the people's stomach is empty, democracy is also empty. Democracy cannot be installed by fiat; it must be achieved by the people themselves." Y.C. James Yen (1893-1990)

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vtsquire
I Saw Three Shipments


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I'm headed to Tahoe in 5 days with a $200 bankroll. I'll let you all know how I did.
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pob14
Jingle Bell Hock


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quote:
Originally posted by vtsquire:
I'm headed to Tahoe in 5 days with a $200 bankroll. I'll let you all know how I did.

And let me be the first to say, "The short term doesn't mean anything."

--------------------
Patrick

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vtsquire
I Saw Three Shipments


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it means $150 I didn't go up with [Big Grin]
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Ganzfeld
Let There Be PCs on Earth


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Don't say it so loudly, vt. Everyone will want to use your method.
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Four Kitties
Layaway in a Manger


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Not anyone who understands probability.

--------------------
If swimming is so good for your figure, how do you explain whales?

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BeachLife
The Bills of St. Mary's


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quote:
Originally posted by Four Kitties:
Not anyone who understands probability.

Exactly.

I went to the casino over the weekend, started with $100 ended up with $917 therefor I'm sure I've got a method that works...

Beach...or I'm just spitting out numbers that are totally unverifiable...Life!

--------------------
Wisdom comes with age, but sometimes age comes alone.
Jack Dragon, On Being a Dragon
Confessions of a Dragon's scribe
Diary of my Heart Surgery

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F minor
I'll Be Home for After Christmas Sales


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vtsquire, let's play something called the Monty Hall Game. I'll be the host.
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vtsquire
I Saw Three Shipments


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quote:
Originally posted by F minor:
vtsquire, let's play something called the Monty Hall Game. I'll be the host.

I'll switch.
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F minor
I'll Be Home for After Christmas Sales


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Curses.
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pob14
Jingle Bell Hock


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quote:
Originally posted by vtsquire:
I'm headed to Tahoe in 5 days with a $200 bankroll. I'll let you all know how I did.

So, how did it go?

--------------------
Patrick

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Ganzfeld
Let There Be PCs on Earth


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quote:
Originally posted by pob14:
quote:
Originally posted by vtsquire:
I'm headed to Tahoe in 5 days with a $200 bankroll. I'll let you all know how I did.

So, how did it go?
Wouldn't this be the answer?
quote:
Originally posted by vtsquire:
it means $150 I didn't go up with [Big Grin]


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vtsquire
I Saw Three Shipments


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yes, yes it would be.
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Silas Sparkhammer
I Saw V-Chips Come Sailing In


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quote:
Originally posted by vtsquire:
yes, yes it would be.

Oops... If that means what I think it means, I hope you didn't lose too much...

For my part, I don't completely comprehend your system as described above, but I must say that I agree with all the others: there is no system to beat an honest roulette wheel, and probability events (such as the spin of that wheel) have no "memory." The oddes of RRRRRRR are exactly the same as the odds of RRRRRRB.

For what it's worth...if you ever demonstrate otherwise in practice...you'll have done what a million preachers have failed to do: put gamblers out of business!

Silas

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vtsquire
I Saw Three Shipments


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quote:
Originally posted by Silas Sparkhammer:
quote:
Originally posted by vtsquire:
yes, yes it would be.

Oops... If that means what I think it means, I hope you didn't lose too much...


not at all. I came UP $150. As in, I won.
quote:

For my part, I don't completely comprehend your system as described above, but I must say that I agree with all the others: there is no system to beat an honest roulette wheel, and probability events (such as the spin of that wheel) have no "memory." The oddes of RRRRRRR are exactly the same as the odds of RRRRRRB.

That is true, and I do not deny that. But think of it like this...

Would you bet that sometime in the next 10 spins a red will come up, or would you bet that none will come up?

quote:

For what it's worth...if you ever demonstrate otherwise in practice...you'll have done what a million preachers have failed to do: put gamblers out of business!

Silas

Ive done well so far!
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Silas Sparkhammer
I Saw V-Chips Come Sailing In


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quote:
Originally posted by vtsquire:
Would you bet that sometime in the next 10 spins a red will come up, or would you bet that none will come up?

Obviously, it is quite likely that a red will come up in a ten-spin experiment. But...ah... what does that gain you? You can't know when, or how many times; it might happen early, or late, or a whole bunch of times in the middle... and it just *might* not happen at all. There isn't any information that is applicable to any single spin, and Las Vegas won't let me bet on ten-spin sequences.

Are you familiar with "conditional probability?" It's a measure of the probability of one event, given that another event has happened.

i.e., what are the odds that you can correctly guess Joe Smith's home (U.S.) state? Well, one in 50, naturally. But let's give away the fact that he lives in a state whose name begins with a "T." Well, now the odds are one in two. The "conditional probability" of picking the correct state, given the condition that the state is Texas or Tennessee is different than the probability without the condition.

The "gambler's fallacy" is thinking that the conditional probability of red, given that a red has previously come up, is different than the probability of red without the condition. But...it ain't, since the events are independent.

Still, I'm glad for you that you didn't lose your shirt, farm, family, legs, birthright, and/or repro' organs!

(I've been in Las Vegas twice in my life, and both times, I did only one thing: used the bathroom.)

Silas (and the first time, I didn't even use a bathroom to use the bathroom!)

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vtsquire
I Saw Three Shipments


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quote:
Obviously, it is quite likely that a red will come up in a ten-spin experiment. But...ah... what does that gain you?
a 47% chance of profiting on the first spin, about 10% chance of profiting on the second (if I play sections of 12) incorporated with the odds that I would have to be sitting down at the table when a rare occurance happens (bout 1:4,500 if played right)
quote:

Are you familiar with "conditional probability?" It's a measure of the probability of one event, given that another event has happened.

absolutely. if I flip a coin twice and at least one is heads... the odds that both are heads is 1 in 3 instead of 1 in 4.

quote:
The "gambler's fallacy" is thinking that the conditional probability of red, given that a red has previously come up, is different than the probability of red without the condition. But...it ain't, since the events are independent.
they are independant, I do not refute that at all. I do acknowledge, however, that certain odds are rarely acheived or displayed. (i.e., a single number has never come up 10 times in a row, because the odds of that happening are ****ing astronomical)
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erwins
Deck the Malls


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Good luck Silas. Vtsquire, you say that you don't deny that the spins are independent, but you must not understand what that means.

It's true that the odds any particular result (whether it's red, the number 9, or the digits of pi) over n number of spins becomes astronomical as you increase n.

BUT that does not affect the odds of that result happening on any given spin.

Maybe this will work:
Imagine that there are two roulette wheels. One has just come up with 9 red results in a row. One has just had rrbbbrrb on the last 9 spins. The odds of the next spin being red (or black) is exactly the same on both wheels. There is NO advantage to betting on the 1st wheel.

The nine previous results have already happened. So the chance of having 10 in a row is just the base odds (about 47% if I remember correctly) on a single spin.

If you are comparing that to the odds of 10 red in a row it doesn't work because the odds include all of the cases in which the string of red would be broken before getting to 9. Once you're already at 9 (or 99, or 1, or 1 million) the previous results don't matter. The odds of the only spin you can bet on -- the one that is about to happen -- are always the same.

erwins

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BeachLife
The Bills of St. Mary's


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The fact still remains though, if you have a system that is guaranteed to pay well, as vtsquire maintains he does, you aught to take a a week vacation and give it a try. That should give you enough time to prove it out. At that point, knowing that you can be a millionarie with a few months of hard gambling seems to be a no brainer career move, eh?

Though, if you're just blowing smoke about the whole thing, it's easier to brag about how your system works while remaining a working stiff.

--------------------
Wisdom comes with age, but sometimes age comes alone.
Jack Dragon, On Being a Dragon
Confessions of a Dragon's scribe
Diary of my Heart Surgery

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vtsquire
I Saw Three Shipments


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quote:
If you are comparing that to the odds of 10 red in a row it doesn't work because the odds include all of the cases in which the string of red would be broken before getting to 9. Once you're already at 9 (or 99, or 1, or 1 million) the previous results don't matter. The odds of the only spin you can bet on -- the one that is about to happen -- are always the same.

erwins [/QB]

...except that I do not just bet on one spin.
say theres 7 red/greens in a row... (something that happens about once every 160 spins) then I bet on black.

while my odds to win are 47% (on the FIRST spin)

...what are the odds that I happened to sit down when it will miss another 9 times? (as I can martingale).

for me to lose I have to reach my max bet, otherwise I recoop losses. So the table has to (in total) miss black 16 times in a row... something that happens once every 25,000 spins.

if I sit down for 200 spins... my odds are (200/25k) 1/125 that I will ever see this happen while I am playing.

so what's the more logical choice... assume you sat down during that 1/125th of the time that you would max out and go broke... or that you didnt?

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F minor
I'll Be Home for After Christmas Sales


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This relates to something I was thinking about the other day. You know there are ways of playing the lottery that make you more likely to be the only winner if you win - playing consecutive numbers, or numbers that can't be birthdays, and so on.

I had the idea that the best thing to do would be to play, each week, the numbers that came up last week. After all, anyone that plays the same numbers every week is unlikely to play on after winning, and although it seems completely absurd that the same numbers would come up twice consecutively, there's no reason probability-wise why they shouldn't. I found the idea entertainingly counter-intuitive, anyway. Shame I don't play the lottery really...

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Troberg
Angels Wii Have Heard on High


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quote:
...except that I do not just bet on one spin.
And this is where your thinking is wrong. You always bet on one spin. That bet has nothing to do with what has come before, and it will have nothing to do with what comes after.

quote:
for me to lose I have to reach my max bet, otherwise I recoop losses. So the table has to (in total) miss black 16 times in a row... something that happens once every 25,000 spins.
Sure, the odds of losing are tiny, but the stakes are gigantic and the potential for win is minimal. You risk a big heap of money, albeit at a small risk of loss, to win a tiny sum.

It does not matter in which order you place your bets, how large they are or what you place them on, in the long run, things will even out and you will end up with roughly the same odds. This is of course assuming no major discoveries in the field of mathematics is made, such as, for instance, the discover of a new integer between 7 and 8.

--------------------
/Troberg

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Silas Sparkhammer
I Saw V-Chips Come Sailing In


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quote:
Originally posted by F minor:
This relates to something I was thinking about the other day. You know there are ways of playing the lottery that make you more likely to be the only winner if you win - playing consecutive numbers, or numbers that can't be birthdays, and so on.

I had the idea that the best thing to do would be to play, each week, the numbers that came up last week. After all, anyone that plays the same numbers every week is unlikely to play on after winning, and although it seems completely absurd that the same numbers would come up twice consecutively, there's no reason probability-wise why they shouldn't. I found the idea entertainingly counter-intuitive, anyway. Shame I don't play the lottery really...

Excellent point, in contrast with the main thread here: if one hopes to share lottery winnings with as few others as possible, one should choose "unpopular" numbers. 13, for instance, is usually on my list, since a lot of people shun it out of superstition.

My question: if a group of numbers wins this week, might there be some people who would bet those numbers again, imagining that they are somehow "lucky" numbers? (Or that, if they were picked once, maybe the system of choosing has a built-in bias toward them?)

This is, obviously, more of a psychological issue than a mathematical one. I would bet, for instance, that more people choose odd numbers than even ones, and thus even numbers have a (slightly!) higher expected payout.

Silas

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Silas Sparkhammer
I Saw V-Chips Come Sailing In


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quote:
Originally posted by vtsquire:
...except that I do not just bet on one spin.


Please name for me a casino where the management will allow you to bet money on sequences of spins.

quote:
say theres 7 red/greens in a row... (something that happens about once every 160 spins) then I bet on black.

while my odds to win are 47% (on the FIRST spin)


Exactly the same as they were, and will be, on every other spin.

quote:

...what are the odds that I happened to sit down when it will miss another 9 times? (as I can martingale).


Exactly the same as they were, and will be, on every other sequence of nine spins.

Listen, it's really simple: either the events are independent, or not. There is *NO* third choice.

If they are not independent, then the wheel must have some form of "memory." (i.e., if you coat the ball with oil -- or glue -- then each spin will change the wheel, altering the probabilities for the next spin.)

You appear to have in your mind the notion that the wheel has some form of memory, and that it doesn't "like" to repeat numbers. Until you clear this fallacy from your thinking, you will be subject to two forms of disappointment:

1) No one here is going to agree with you;
2) You probably aren't going to get rich in Las Vegas, and you certainly aren't going to get rich by dint of your method. (You might, however, simply get lucky; that happens fairly often, to a small number of people.)

I admire your persistence...but I'm putting my money in small cap mutual funds instead.

Silas

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Giant Communist Robot
I Saw Three Shipments


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Silas wrote:

quote:
Exactly the same as they were, and will be, on every other sequence of nine spins.


an' I don't think someone gets it. I pointed out earlier roulette is a random game with a negative expectation and he thinks his money management can overcome this.
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Jay Temple
It Came Upon a Midnight Clearance


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quote:
Originally posted by Silas Sparkhammer:
This is, obviously, more of a psychological issue than a mathematical one. I would bet, for instance, that more people choose odd numbers than even ones, and thus even numbers have a (slightly!) higher expected payout.

Silas

I know what would make a good crude estimate: For a given lottery, look at the winning numbers each week and whether there was a winning ticket. If you see significantly more winners when it's lopsided to even numbers than when it's lopsided to odd, you're onto something.

--------------------
"Well, it looks we're on our own ... again."--Rev. Lovejoy

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nicky
I Saw Three Shipments


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quote:
Originally posted by vtsquire:
...except that I do not just bet on one spin.
say theres 7 red/greens in a row... (something that happens about once every 160 spins) then I bet on black.

while my odds to win are 47% (on the FIRST spin)

...what are the odds that I happened to sit down when it will miss another 9 times? (as I can martingale).

for me to lose I have to reach my max bet, otherwise I recoop losses. So the table has to (in total) miss black 16 times in a row... something that happens once every 25,000 spins.

No, the chance of getting 16 non-blacks in a row once 7 non-blacks on a row have already happened, is the chance of getting 9 non-blacks in a row - 1 in 512.
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Troberg
Angels Wii Have Heard on High


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quote:
This relates to something I was thinking about the other day. You know there are ways of playing the lottery that make you more likely to be the only winner if you win - playing consecutive numbers, or numbers that can't be birthdays, and so on.

I had the idea that the best thing to do would be to play, each week, the numbers that came up last week. After all, anyone that plays the same numbers every week is unlikely to play on after winning, and although it seems completely absurd that the same numbers would come up twice consecutively, there's no reason probability-wise why they shouldn't. I found the idea entertainingly counter-intuitive, anyway. Shame I don't play the lottery really...

I think it wouldn't work, actaully it would probably lower the payout.

Why?

Because someone else is thinking the same way as you are. Remember, there is a huge bucket of possible combinations, and chances are that a random combination will be less likely to be taken than a combination that carries some kind of meaning or pattern. The random combinations are chosen, more or less, at random, while the patterns are chose because someone thinks it's a good idea, and most likely, he is not alone.

--------------------
/Troberg

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Silas Sparkhammer
I Saw V-Chips Come Sailing In


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quote:
Originally posted by Troberg:
I think it wouldn't work, actaully it would probably lower the payout.

Why?

Because someone else is thinking the same way as you are. Remember, there is a huge bucket of possible combinations, and chances are that a random combination will be less likely to be taken than a combination that carries some kind of meaning or pattern. The random combinations are chosen, more or less, at random, while the patterns are chose because someone thinks it's a good idea, and most likely, he is not alone.

Actually, as long as people can choose their numbers, randomness is not *quite* the best method. You can gain some small benefit by using "reverse psychology."

The obvious example is 13. Fewer people choose 13 than other numbers, because it is believed to be unlucky.

Now, yes, you're right in that if *enough* smart people chose 13, it would compensate for the susperstitious people not choosing it, thus negating the benefit. But...that's an awful lot of people! At this point in time, suspertitious people far outnumber game theorists, and 13 is a wise choice for a lottery number.

Silas

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Troberg
Angels Wii Have Heard on High


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I think that a "special" number such as 13 is always a bad idea. Not only statistics buffs choose it, I know several who consider it lucky (in fact, I would say that there is probably something like a 1/2 split between lucky/unlucky.

The less people think about a number, good or bad, the less it will be played.

That said, it probably evens out anyway with the huge number of players, so we are talking about a tiny ripple on the top of a deep ocean.

--------------------
/Troberg

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Ganzfeld
Let There Be PCs on Earth


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quote:
Originally posted by Silas Sparkhammer:
I think it wouldn't work, actaully it would probably lower the payout.

I don't understand. The payout changes depending on whether or not someone else has played or is playing the number? I didn't know that!

ETA Oh, you're talking about the lottery. Never mind.

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shifty rob
Jingle Bell Hock


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Ganzfield-
The quote you attributed to Silas should actually be from Troberg.

--------------------
"They got a name for the winners in the world; I want a name when I lose" -Steely Dan

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Silas Sparkhammer
I Saw V-Chips Come Sailing In


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Sorry to revive a semi-moribund thread, but I found a couple of amusing examples of the gambler's fallacy.

1) A casino owner decided to limit his losses. If any given customer lost money, well, that was just fine with him. But if a customer won money, the owner cut the customer off after $10,000 of winnings; at this point, the customer would be asked to leave the casino. What change would this make in his overall profits?

2) An eastern potentate, wanting more women for his harem, decreed the following: if a woman had a baby girl, she may have more children. But if a woman had a baby boy, she must immediately stop having any more children. This way, he reasoned, you would find families with one boy (at most) and one, two, three, maybe even eight girls! The future of his empire would be plentiful with young women! What is the actual effect of this decree on the sex ratio of the population?

Silas

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vtsquire
I Saw Three Shipments


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[QUOTE]An eastern potentate, wanting more women for his harem, decreed the following: if a woman had a baby girl, she may have more children. But if a woman had a baby boy, she must immediately stop having any more children. This way, he reasoned, you would find families with one boy (at most) and one, two, three, maybe even eight girls! The future of his empire would be plentiful with young women! What is the actual effect of this decree on the sex ratio of the population?

There would be more girls. This is because girls and boys to not make an exact 50/50 mark on the population. In fact, it's been shown that the XX-chromosomal sperm in humans is "more hearty" compared to xy-chromosomal sperm. more than 50% of the first borns are (and would be) women. It's also shown that once a women gives birth to a boy, she becomes more likely to have a boy than a girl during her next pregnancy. By taking those women out of the equation, there will be a steady lean in favor of more girls per boys, but not more than about 3%.

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Silas Sparkhammer
I Saw V-Chips Come Sailing In


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quote:
Originally posted by vtsquire:
There would be more girls. This is because girls and boys to not make an exact 50/50 mark on the population. In fact, it's been shown that the XX-chromosomal sperm in humans is "more hearty" compared to xy-chromosomal sperm. more than 50% of the first borns are (and would be) women. It's also shown that once a women gives birth to a boy, she becomes more likely to have a boy than a girl during her next pregnancy. By taking those women out of the equation, there will be a steady lean in favor of more girls per boys, but not more than about 3%.

Smarty pants! [Razz]

(In the first example, the casino owner would lose damn near all his customers due to negative publicity from his bone-headed policy, so his profits would plummet... But that ain't where these exercises were meant to go!)

Silas

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