Twice in one night

[coppinpr]

No, you're wrong, probability and odds are not the same, and every time the double six does not come up the probabilities of it coming up do increase. This not a fallacy, it's a used fact in mathematics.

An example of odds and probabilities changing (albeit for a totally different reason) is dealing four hands of cards. The odds of the same four hands being dealt is so high that it is almost certain that it has never happened, ever, anywhere since cards have been played, but every time a hand of cards is dealt the odds of that hand being dealt again somewhere in the future go down, because one of the millions of options has been used up, and the probabilities go up for the same reason.

End of subject for me... it's boring

[pennymachines]

Paul, as a non-mathematician, I'd agree if you said probability was difficult or complex but I'm amazed, particularly as a bandit enthusiast, you find it boring! It lies at the very heart of our wonderful mechanical games of chance and, to my mind, gives them much of their magic.

Statistics and probability can be counter-intuitive, even to professional mathematicians (see De Méré's Paradox on throwing double sixes with two dice). This can lead to more serious errors of judgement than the gambler's fallacy. However, the gambler's (or Monte Carlo) fallacy is particularly germane to our hobby and it does have consequences in the real world, especially for those who adhere to it.

On August 18, 1913, at the casino in Monte Carlo, black came up a record twenty-six times in succession [in roulette]. … [There] was a near-panicky rush to bet on red, beginning about the time black had come up a phenomenal fifteen times. In application of the maturity [of the chances] doctrine, players doubled and tripled their stakes, this doctrine leading them to believe after black came up the twentieth time that there was not a chance in a million of another repeat. In the end the unusual run enriched the Casino by some millions of francs.

The Gambler's Fallacy and its sibling, the Hot Hand Fallacy, have two distinctions that can be claimed of no other fallacies:

They have built a city in the desert: Las Vegas.
They are the economic mainstay of Monaco, an entire, albeit tiny, country, from which we get the alias "Monte Carlo" fallacy.

http://www.fallacyfiles.org/gamblers.html

Paul, can you explain how you think odds and probability are different?
To realize they're the same, consider the fact that one can be converted into the other with a bit of maths. The chances of getting two sixes when you throw two dice can be expressed as a probability of 0.0279 (3%) or as odds of 35 to 1 against.

Things could only work as you suggest in your examples if there was a magical force acting to conserve or enforce probability. This would produce some curious and absurd effects. For example, when the first reel landed on 'plumb', the magic force would quickly try to push the next reel away from plumbs, because its improbability had just increased! It would also make Garp's decision to buy a house a moment after a small plane crashes into it, "because the chances of another plane hitting it have just dropped", perfectly rational.

The fundamental thing to bear in mind is that, as JC says, each spin of the reels is completely independent and unconditioned by the outcome of previous spins. So, the probability of Hutto winning the jackpot on his Aristocrat two times on the trot is twice as improbable as winning it once. However, after he has won it once, the odds for doing so again remain 7999 to 1 against.

[john t peterson]

All these number theories make my head spin!

I stand by the olde saying: "Once a King, always a King, but once a night is enough."

J Peterson
Night-night

[coppinpr]

I can't explain why they are different but I know they are. One of my very best friends is a mathematician and he and the guy he worked with at the university where they taught at once tried to explain it to me. I'm too dumb to explain it but they spent ages trying to show me why it was obvious.
This was in the days prior to personal computers, they were both working on maths with regard to computers which were just emerging and were way out of my league.
It came about because we played a lot of role playing games (before computers took over the donkey work) so we were using multi sided dice. I had designed a game which involved the sudden death of a character if a throw of 30 came up on a pair of dice (1* 20 sided dice and 1*10 sided). Because the odds of that happening were so high, I expected it to either never happen or at least have the same very slight chance of coming up every time. They spent all evening trying to show me that every time it didn't happen, the probabilities of it happening next time went up.

Like I said, I'm no expert - just passing on the wisdom of those who are.

[jimmy55]

There is a subtle difference, at least they are a different way of expressing events. Best explanation I could find on Google ....
Probability vs. odds

Chance can be expressed either as a probability or as odds. In most contexts, there is no particular reason to prefer one over the other. Most scientists tend to feel more comfortable thinking about probabilities than odds, but that is a matter of training and custom, not logic.
The distinction is simple:
The probability that an event will occur is the fraction of times you expect to see that event in many trials. Probabilities always range between 0 and 1.
The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.
A probability of 0 is the same as odds of 0. Probabilities between 0 and 0.5 equal odds less than 1.0. A probability of 0.5 is the same as odds of 1.0. Think of it this way: The probability of flipping a coin to heads is 50%. The odds are “fifty: fifty,” which equals 1.0.
As the probability goes up from 0.5 to 1.0, the odds increase from 1.0 to approach infinity. For example, if the probability is 0.75, then the odds are 75:25, three to one, or 3.0.
If the odds are high (million to one), the probability is almost 1.00. If the odds are tiny (one to a million), the probability is tiny, almost zero.
Converting between odds and probability is straightforward:
To convert from a probability to odds, divide the probability by one minus that probability. So if the probability is 10% or 0.10 , then the odds are 0.1/0.9 or ‘1 to 9’ or 0.111.
To convert from odds to a probability, divide the odds by one plus the odds. So to convert odds of 1/9 to a probability, divide 1/9 by 10/9 to obtain the probability of 0.10.

Now I remember why I gave up on A level pure maths and statistics half way through back in 1971 (depressing or what!)

[coppinpr]

Well here it is guys, the reason why odds and probabilities are different, explained in classroom manner on youtube:



Can we end this now, my brain hurts

[pennymachines]

The exercises in that video show how you can convert back and forth between probabilities expressed as fractions and odds expressed as ratios. Just as Fahrenheit and Centigrade are different methods of indicating temperature, probability and odds are different methods of indicating the chances that specific events will occur. As I said, they're the same thing expressed differently.

...they spent all evening trying to show me that every time it didn't happen, the probabilities of it happening next time went up.

They may have said, "the more times you throw it, the greater the probability of it happening", but I'm sure they didn't say, "every time it didn't happen, the probabilities of it happening next time went up". If they did, they were winding you up. No mathematician would make that claim.

Can we end this now, my brain hurts

Sure we can - but come on Paul, it's not too late to 'repent thy sins' and forswear the Gambler's Fallacy once and for all. You'll feel better for it, and it might save you money.
My nephew's next door - a graduate in Mathematics and Computer Science, just embarking on an MA in Statistics, Probability and Operational Research (whatever that is). Let's not drag him into it.

[coppinpr]

No, I'm not going to repent, the video above clearly states that odds and probabilities are similar BUT NOT THE SAME and goes on to show why. My original comment was, "odds and probabilities are not the same" QED

"the more times you throw it, the greater the probability of it happening", but I'm sure they didn't say, "every time it didn't happen, the probabilities of it happening next time went up

I can concede that point because it was long ago. I could be wrong on their wording, but your very comment implies that odds and probabilities are different as the odds of it happening would remain the same while the probabilities change.

Enough now, I need my comfort blanket
Good discussion though, and no one got mad, which is how it should be.

[pennymachines]

Good discussion though, and no one got mad, which is how it should be.

Absolutely! I find it an intriguing subject. Thanks for not taking offence Paul - I know I can be a bit relentless... I'm going to see if I can get a triple jackpot now.

[andydotp]

I find it an intriguing subject.

Me too but I when you two & jimmy55 took the discussion to Stratospheric levels - wot I'm not goodly enuff at..
Well done all.

Oh, but we never considered this From Yahoo!7News this morning.

MOSCOW/VIENNA (Reuters) - What can man do to prevent Earth being hit by meteorites and asteroids?

Russia has found, to its cost, that it has no answers. But U.S. and European experts may be able to help with a few ideas that at first glance seem straight out of science fiction, including smashing spacecraft into asteroids, using the sun's rays to vaporize them, or blasting them with nuclear bombs.

That should come as some relief to the many worried Russians who want something done immediately, even though scientists say the explosion of a meteor over central Russia on Friday was a once-in-a-lifetime event.

,,,,,,,,,,, "the-once-in-a-lifetime event". Who's lifetime FGS.. Ooooooh

I'm going to see if I can get a triple jackpot now.

As we've now learned,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
let us know if it was a Unique Event David
a.p