More Weird Stats @AQU !!!

[Wizard of Odds]

Originally Posted by TheOracle

Hey Wiz

You bring up a good point I don’t have any statistical data regarding casino games but I do have a healthy amount of results data from NYC tracks

As far as I can know, a Chi Squared test checks to see if two variables are related in some population so education levels and incarceration or education levels and marital status so I’m not sure how that would apply to my data.

However, I do remember that there is some test that measures randomness I forget which one that is, I could perform a randomness test against my data and see what I get from the data.

Let me look into that.

Chi-Squared is one correct test.

If, over a week, a fair coin is flipped 100 times, is it more likely or less likely that you would find a run of 6 heads in a row? If the 6 heads in a row happened on a Tuesday, would that mean Tuesday's are highly correlated with throwing heads?

[TheOracle]

Originally Posted by Wizard of Odds

Chi-Squared is one correct test.

If, over a week, a fair coin is flipped 100 times, is it more likely or less likely that you would find a run of 6 heads in a row? If the 6 heads in a row happened on a Tuesday, would that mean Tuesday's are highly correlated with throwing heads?

Hey Wiz

The number of heads in a row is no more or less likely than the number of tails they both have the same probability of happening also if 6 heads appeared on Tuesday there's no correlation that you can draw to say it would happen on that day or any other day of the week.

However, let's say that coin is not a fair coin. Let's say it is heavily weighted on one side every Tuesday then you can make some correlations about outcomes on Tuesdays

[Wizard of Odds]

But, in 100 consecutive fair die throws, do you think it is more or less likely there will be at least one instance of 6 heads in a row?

[TheOracle]

Originally Posted by Wizard of Odds

But, in 100 consecutive fair die throws, do you think it is more or less likely there will be at least one instance of 6 heads in a row?

Hey Wiz,

Both heads and tails have the same probability so you can't say that one is more or less likely than the other to happen no matter how many consecutive fair die throws.

[Wizard of Odds]

Originally Posted by TheOracle

Hey Wiz,

Both heads and tails have the same probability so you can't say that one is more or less likely than the other to happen no matter how many consecutive fair die throws.

I believe you may be missing my point.

In 100 consecutive throws of a fair coin, it is more likely than not that there will be a run of 6 (or more) consecutive heads. This is entirely due to randomness and follows from basic probability calculations. Although the run of 6 heads in a row would be purely a consequence of randomness, there is a danger that someone (you, perhaps?) might attribute the run of 6 consecutive heads to something else (e.g., the coin was not actually a fair coin during the run of 6 heads in a row).

This is a common behavioral economic bias/misconception and is what I mean by "fooled by randomness".

[ReplayRandall]

Originally Posted by Wizard of Odds

I believe you may be missing my point.

In 100 consecutive throws of a fair coin, it is more likely than not that there will be a run of 6 (or more) consecutive heads. This is entirely due to randomness and follows from basic probability calculations. Although the run of 6 heads in a row would be purely a consequence of randomness, there is a danger that someone (you, perhaps?) might attribute the run of 6 consecutive heads to something else (e.g., the coin was not actually a fair coin during the run of 6 heads in a row).

This is a common behavioral economic bias/misconception and is what I mean by "fooled by randomness".

I just realized who you are....Greetings Michael Shackleford! I've been to your website umpteen times over the last 20 years, you're a trusted resource for me....Thanks for keeping that website interesting...

[Wizard of Odds]

Originally Posted by ReplayRandall

I just realized who you are....Greetings Michael Shackleford! I've been to your website umpteen times over the last 20 years, you're a trusted resource for me....Thanks for keeping that website interesting...

Not who I am... but very flattering to think so

[ReplayRandall]

Originally Posted by Wizard of Odds

Not who I am... but very flattering to think so

Are you brothers?....Re-read some of your previous posts, you sure fooled me.

Guess that's easy to do...


Edit- In your bio, you state you're an Actuary...

Here's Michael Shackleford bio from his website:

The Wizard of Odds is Michael Shackleford, a former professional actuary who has made a career of analyzing casino games. He runs the numbers on new games for casinos and game developers and has helped design many of the popular slot machines on the Internet. He has twice served as an Adjunct Professor of Casino Math at the University of Nevada, Las Vegas, a former contributing editor to Casino Player magazine, and the author of the book Gambling 102, recently published by Huntington Press. The Wizard's landmark research into the actual returns of slot machines on the Las Vegas strip garnered international attention in 2002, and he has appeared numerous times on national television as a recognized expert on gambling strategy.

[Wizard of Odds]

I'm a different actuary

[Dave Schwartz]

Originally Posted by Wizard of Odds

I believe you may be missing my point.

In 100 consecutive throws of a fair coin, it is more likely than not that there will be a run of 6 (or more) consecutive heads. This is entirely due to randomness and follows from basic probability calculations. Although the run of 6 heads in a row would be purely a consequence of randomness, there is a danger that someone (you, perhaps?) might attribute the run of 6 consecutive heads to something else (e.g., the coin was not actually a fair coin during the run of 6 heads in a row).

This is a common behavioral economic bias/misconception and is what I mean by "fooled by randomness".

Oracle, this is really good stuff and he's right: you are missing his point.

What he's saying is that strange things happen. The question is, "Are they a pattern that can be expected to repeat?" or is it just a normal part of the experience.

Now, back to your regularly scheduled expert.


Dave
PS: Please continue, Wiz. And please jump to examples as quickly as possible.

[castaway01]

I'm just jealous that I pointed out these kinds of errors by The Oracle and got all kinds of nasty messages and negative reputation points from him and his followers, yet he's willing to take it from you. Must be nice to be charming...

[Wizard of Odds]

Originally Posted by Dave Schwartz

Oracle, this is really good stuff and he's right: you are missing his point.

What he's saying is that strange things happen. .

I believe what I'm saying may be something a little stronger.... that a run of 6 heads in a row in a string of 100 tosses IS NOT A STRANGE THING AT ALL.

[Wizard of Odds]

Originally Posted by castaway01

I'm just jealous that I pointed out these kinds of errors by The Oracle and got all kinds of nasty messages and negative reputation points from him and his followers, yet he's willing to take it from you. Must be nice to be charming...

We must be forgiving because this is a common misconception and may be built into the software of our brains. It takes cold logic and objectivity to overcome such biases and errant intuition.

[ReplayRandall]

Originally Posted by Wizard of Odds

I believe what I'm saying may be something a little stronger.... that a run of 6 heads in a row in a string of 100 tosses IS NOT A STRANGE THING AT ALL.

A run of 6 tails in a row in a string of 100 tosses will appear as well with the string of heads.....Normal randomness.

[Wizard of Odds]

Originally Posted by ReplayRandall

A run of 6 tails in a row in a string of 100 tosses will appear as well with the string of heads.....Normal randomness.

Yes, of course. Not will appear, but is likely (more than 50% chance) to appear than not.