[vpFREE] Re: how to tell if your machine is fair?

Hi.

Sorry for the triple post.

I found an interesting 2010 paper about "mean time" and "waiting time"
and using it to detect changes in underlying behavior (e.g. a gaffed
game).
http://ff.im/USw3M

So what are the "mean time" and "waiting time" to see a bad streak of
23/200 flushes?
How many hands?

If we have seen 23/200 flushes way too soon, maybe the underlying
machine is "gaffed".

Mitchell

The authors of the papers say "The statistics of waiting time may not
justify the prediction by the gambler's fallacy, but paying
attention to streaks in the hot hand belief appears to be meaningful
in detecting the changes in the underlying process."

The debate over the statistical validity of the hot hand belief has
lasted more than twenty years (e.g., Bar-Eli et al., 2006), and it
is not likely to be ended by simply introducing a new set of
statistics. However, pattern time statistics do seem to support some
of the existing theories.

In particular, it has been suggested that the hot hand belief arises
when people are evaluating human performance, and people pay
particular attention to streak patterns in order to detect a change in
the performance, for example, fluctuations in
the shooting accuracy of basketball players (e.g., Ayton & Fischer,
2004; Burns, 2004; Burns & Corpus, 2004; Sun, 2004).

By such account, the prediction to continue a streak is actually valid
on the basis of a higher probability
of a single outcome (e.g., a higher shooting accuracy, a higher
probability of heads in case of a biased coin).

It can be shown that by the measure of either mean time or waiting
time, streak patterns are indeed a good indicator
for detecting the changes in the probability of single outcomes.

------------------------------------

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Re: [vpFREE] Re: how to tell if your machine is fair?

 

> On Apr 18, 2012, at 8:59 AM, matt20482002 wrote:
>> OK, you converted 23 of 200 flushes.
>>

Shorter version of my previous message.

It would be cool to know, if I played 5,000 or 10,000 flush draws, how
likely I am to have a bad streak where only 23/200 flushes connect.
Or...What is the number of flush draws I need to play (e.g. 1,000,
10,000), before I have 50% chance of seeing a bad streak of 23/200 or
worse.

Mitchell

Here's a link I found:

Recently I've come across a task to calculate the probability that a
run of at least K successes occurs in a series of N (K≤N) Bernoulli
trials (weighted coin flips), i.e. "what's the probability that in
50 coin tosses one has a streak of 20 heads?"
http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/

It's messy.

Does any know any links to "bad streaks of 23/200" as opposed to "runs
of 23"?

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Re: [vpFREE] Re: how to tell if your machine is fair?

 


On Apr 18, 2012, at 8:59 AM, matt20482002 wrote:
> OK, you converted 23 of 200 flushes. That's 11.5%. Whenever you have
> 4 cards to a flush, there are 9 cards left in the deck that can make
> the hand and 48 cards total. So, that is 18.75% you should expect to
> make or 37.5 hands of 200. Was what you experienced bad luck?
> Consult the binomial distribution. http://en.wikipedia.org/wiki/Binomial_distribution
>
> Your n=200 and p=.1875, np=37.5 and the variance is np(1-p)=30.5.
> The square root of that is the standard deviation = 5.5. So, what
> happened to you was (37.5-23)/5.5 = 2.6 standard deviations below
> the mean.
>

Thanks for the refresher on binomial distributions. I haven't seen
the np(1-p) variance thing in so many years.
P.S. 47 cards left for the draw (not 48).

What would be interesting is for x hands, what is the expected best/
worst streak of certain types of hands (and what's the std dev on
those streaks).
My mind is just too lazy to sit down & figure out the equations, but
the result would be something like...

If you have 1,000 flush draws, your best & worst 50-hand flush streaks
will probably be 3/50 (+/- 2) and 20/50 (+/- 5).
Any mathematicians out there handy with this stuff?

Streaks often have some really non-intuitive behaviors.

-----
Here's another quirky streak thing.

If we play a 50-50 game, in the *long run* we will be highly likely
close to even.

Guess how often we will flip from "losing" to "winning" (or vice-versa)?
I think in 100,000 trials (or 1,000,000 trials), the expected number
of crossings is 5-6. (I haven't seen the result in decades, so I
could be a little off here).

or have a bad losing streak.
This matches our real-world experience, that we tend to either "get
lucky" and have a long winning streak.

------
To translate to the flush draw issue. Once you are on a bad streak of
flush draws, the streak will probably go for quite a while before
rebalancing.

e.g. If you converted 23 of 200 flushes, what is the expected number
of flush draws you will need before you are statistically even?
I don't know, but my raw guess would be that you might need
1,000-2,000 flushes before you draw even.

Mitchell

P.S. I have seen some analysis along these lines for "Risk of Ruin"
and "How much do you expect to lose before going permanently positive
when playing blackjack?"
e.g. When playing $5 blackjack (with $5-25 spread), you might expect
to lose $600 before going permanently positive ($600 is totally made
up).

[Non-text portions of this message have been removed]

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Re: [vpFREE] 24/7 private vaults burglarized

 

One of my favorite movies is "The Bank Job," which is supposedly a
true story about the same kind of thing in Great Britain in 1971 or
so. Towards the end, the main character, one of the thieves, is asked
where he'll keep his share of the loot and he says "it sure won't be
in a safe deposit box."

seedub49 wrote:

>Not sure if you heard (since the news has seemed strangely quiet about this), but 24/7 Private Vaults was broken into over the weekend. If you google it, you'll find news articles on it, but I think it strange that the first articles didn't show up until 3 or 4 days after the fact.
>
>I went in and was told that only the VIP vault was broken into so if your box was in the main vault, you got lucky. If you had a box in the VIP vault, I feel for you and hope yours didn't get hit.
>
>You can stop by or call between 10 am and 4 pm to see if your items were stolen. Strangely if you call after 4 pm they won't tell you whether you are a victim or not. Makes for a miserable night sans sleep if you don't hear about the burglary until after 4.
>
>While the video they show you to sell a box says that there are two security guards on duty at all times (and supposedly stationed in different monitoring rooms), it seems evident from the news articles that there was only one. Sadly, it seems the place was a good idea poorly executed.
>
>Speaking of execution. I wonder how long before the thieves are caught by some of the less-forgiving victims. Honestly I think you would have to be an idiot to steal what is likely eight figures from people who have that kind of money and need it stored anonymously. Even if one of them doesn't track you down, you've certainly made yourself a target of other criminals who might have access to that grapevine and wouldn't mind getting a piece of that heist.
>
>I hope no one here was affected, but I think there undoubtably are a few.

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[vpFREE] 24/7 private vaults burglarized

 

Not sure if you heard (since the news has seemed strangely quiet about this), but 24/7 Private Vaults was broken into over the weekend. If you google it, you'll find news articles on it, but I think it strange that the first articles didn't show up until 3 or 4 days after the fact.

I went in and was told that only the VIP vault was broken into so if your box was in the main vault, you got lucky. If you had a box in the VIP vault, I feel for you and hope yours didn't get hit.

You can stop by or call between 10 am and 4 pm to see if your items were stolen. Strangely if you call after 4 pm they won't tell you whether you are a victim or not. Makes for a miserable night sans sleep if you don't hear about the burglary until after 4.

While the video they show you to sell a box says that there are two security guards on duty at all times (and supposedly stationed in different monitoring rooms), it seems evident from the news articles that there was only one. Sadly, it seems the place was a good idea poorly executed.

Speaking of execution. I wonder how long before the thieves are caught by some of the less-forgiving victims. Honestly I think you would have to be an idiot to steal what is likely eight figures from people who have that kind of money and need it stored anonymously. Even if one of them doesn't track you down, you've certainly made yourself a target of other criminals who might have access to that grapevine and wouldn't mind getting a piece of that heist.

I hope no one here was affected, but I think there undoubtably are a few.

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[vpFREE] 7 Star Event in Vegas

 

Hi Gang:
We found out today that the 2nd Caesars/Harrah's Seven Stars Signature
Event in 2012 will be in Las Vegas Sept. 20-23. Does anybody have any further
details on this? Thanks in advance for any help.
Regards,
CoachVee & Hedy

[Non-text portions of this message have been removed]

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[vpFREE] Re: how to tell if your machine is fair?

 


OK, you converted 23 of 200 flushes. That's 11.5%. Whenever you have 4 cards to a flush, there are 9 cards left in the deck that can make the hand and 48 cards total. So, that is 18.75% you should expect to make or 37.5 hands of 200. Was what you experienced bad luck? Consult the binomial distribution. http://en.wikipedia.org/wiki/Binomial_distribution

Your n=200 and p=.1875, np=37.5 and the variance is np(1-p)=30.5. The square root of that is the standard deviation = 5.5. So, what happened to you was (37.5-23)/5.5 = 2.6 standard deviations below the mean.

In general, you had a bad day. What happened to you (the down swing) happens less than 0.5% of the time (just under 0.4%). 4 out of every 1,000 times. You should be pissed, but not ready to take legal action. Try it again randomly (without the "selection bias" that the other poster refers to, you may have only remembered this bad time) and if the same thing happens, then something might be wrong. Since you had a large expected value of number of hands (18.75) you can approximate all this stuff with the normal distribution too via some online calculator.

--- In vpFREE@yahoogroups.com, "armchairpresident" <smellypuppy@...> wrote:
>
> I like the analogy; This immediately brought another question to mind - can people (not the machine) be gaffed? I don't mean this in a bad way, just that in the big picture almost every study I have seen, people are distributed along a probability curve. I didn't look at the data, but I even remember a study about lightning and that certain people were more or less predisposed to being struck and that those once struck were more predisposed to a second strike.
>
> My point is, what if everyone's baseline varied from the expected for every VP hand when examined on many different machines for a large N value of hands? For example, I thought I was not converting 4 to a flush near the expected frequency regardless of what machine I played. I then kept count over several sessions on 9/6 job and several different machines. I only kept count for 200 consecutive events 23 converted out of this lot. Perhaps I am gaffed in a negative manner for this hand?
>
>
>
>
>
>
> --- In vpFREE@yahoogroups.com, "Frank" <frank@> wrote:
> >
> > OK. You completely misunderstood what I was saying. It will completely invalidate the testing utility I'm making if people use their currently existing data. Why? Imagine this.
> >
> > You post in the newspaper that you'd like to do a study into how likely it is to be hit by lighting. Not surprisingly, the people that answer your add are those most concerned about this issue (AKA people that have been hit). After looking at all your volunteer test subjects you conclude that the chances of being hit by lighting are 1 in 1.
> >
> > Problem: All the people that weren't hit by lighting, didn't volunteer.
> >
> > Solution: Take the volunteers, but toss out all that has happened to them in their lives before they signed up for your study. Dismiss their preexisting data, and collect new data from this point on.
> >
> > The rule of thumb with statistical tests is never to use the data that made you want to do the test. Test forward from the point in time you decide to do the test and dismiss what's gone before.
> >
> > All data by definition is past data. The past I'm talking about here, that should be ignored, is what's happened before you decided to do the test.
> >
> > ~FK
> >
> > --- In vpFREE@yahoogroups.com, "cdfsrule" <cdfsrule@> wrote:
> > >
> > > I know I am taking this quote out of context (sorry FK), but your statement:
> > >
> > > --- In vpFREE@yahoogroups.com, "Frank" <frank@> wrote:
> > > >
> > > >Statistical test cannot be used on anything that's already happened, or else one opens the door for selective recruitment and confirmation bias.
> > > >
> > > > ~FK
> > > >
> > >
> > > is absolutely not true. In fact, statistical tests can only be used on "data"-- that is on stuff that already has been observed, computed, recorded, etc. In fact, statistical tests are used in determining (in the sense of ascribing a probability to) if there is or was bias, selective recruitment, etc. of events (and associated data) that has already occured.
> > >
> > > Take a look at: http://en.wikipedia.org/wiki/Statistical_hypothesis_testing
> > >
> >
>

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