Gambler's Fallacy and million bet simulations

This topic can relate to any casino game, but naturally I am going to reference craps.

The gambler's fallacy basically says that when I know an event has a 50-50 chance of happening, say a coin flip, and if I have just seen 5 heads in a row, then I am expecting a tail to show up, since I know there should be an equal number of heads and tails over an infinite number of coin flips.

In craps threads, we are constantly discussing EV, House Edge, and millions of rolls over a lifetime. We talk about taking bets down, about leaving when we have a winning session, keeping sessions short, and of course, that all of your life is just one giant session, so none of it matters. Playing one bet every Saturday for 52 weeks is the same as playing 52 straight bets today.

We then expound upon how the games are not beatable. That over your lifetime the HE and the EV is going to win out. The math says so. The million roll simulations say so.

So here comes the argument.......

I played craps this weekend, and had my best craps trip ever. I have played on hotter tables before, I have been on longer rolls, but I have never brought home as much money. Has my strategy gotten better, or did I just happen to have the right bets at the right times?
This event is over. I beat the game. I experienced Positive Variance for a change. Let's say I won $10,000 (I didn't, but it works nicely for this).

If I move forward from here and analyze my future craps play, what will my lifetime expectancy be for my craps bankroll outcome?

If next week Joe was to begin playing craps for the first time, we would determine Joe is going to lose, over his lifetime, the House Edge % times the amount of money he bets at that HE. He is most likely to end up a loser. We'll pretend the expected loss is calculated to be $5,000

I decide to play the EXACT same times and bets as Joe. Therefore, I would expect to lose $5,000, BUT, I won $10,000 already, so, Can I expect to end up an overall winner at craps ($5,000), OR is my lifetime still expected to come out losing my total bets x HE of the bets?

Please explain your reasoning.

Quote: RaleighCraps

This topic can relate to any casino game, but naturally I am going to reference craps.

Please explain your reasoning.

Your future life time expected value is total bets * house edge. Your past is no indicator of the future, and expected value has become an actual value. In this case the actual value > expected value. That doesn't change the future expected value of all the bets.

If that's the last time you play craps, your expected lifetime winnings will indeed be $5000. I don't need to explain the reasoning behind this, since you just did.

Think of it this way - let's say you're playing hold 'em. You pretty much know you're not going to get a royal flush. You get QJs. Now it's more likely, but still pretty unlikely. Now the flop comes up - you get your king and ten. Now your chances (let's say for the sake of argument that someone's all in and you've got your straight, so there's little chance of this hand ending early) are about one in twenty-four. Of a royal flush. An absurdly unlikely outcome, which now has a chance of one in 24. And the next hand it's no less likely.

The longer you play, absent any other information, the lower your chances of staying ahead will be. Any information changes this, just like any other proposition, so knowing the first part is a winner increases that chance in any given window. However, if you do stay ahead beyond a certain threshold, you should recognize that you're at the far end of the bell curve, just like any bridge hand has the same astronomically low chance.

Quote: RaleighCraps

In craps threads, we are constantly discussing EV, House Edge, and millions of rolls over a lifetime. We talk about taking bets down, about leaving when we have a winning session, keeping sessions short, and of course, that all of your life is just one giant session, so none of it matters. Playing one bet every Saturday for 52 weeks is the same as playing 52 straight bets today.

Not ALL talk about just HE and EV and millions of rolls over a lifetime.
The ones that KNOW the total truth
talk about HE, EV, Variance, standard deviation and the lifetime of bets.

No one wants to listen to all that, it is too much they all say,
so most just say EV and HE and can never win in the long run.

Quote: RaleighCraps

We then expound upon how the games are not beatable.
That over your lifetime the HE and the EV is going to win out.

That is just one part of the formula.
As pointed out, the more bets one makes in their lifetime, the chances keep going down of showing a net profit from gambling.
Not impossible by any means.

Quote: RaleighCraps

The math says so.
The million roll simulations say so.

The math also says so when it comes to the variance and standard deviation of a number of lifetime bets also.
Most just do not understand variance or those that do can't explain it to others very well for understanding.

Learn how to calculate the variance and use it.
https://wizardofvegas.com/forum/gambling/tables/1213-variance-in-craps/


The HE is NOT a set in stone value.

Example:
1000 pass line bets at $5, no odds.
Total action $5000
yeah, everyone says you WILL lose 1.41% of $5000. not much more or less.

BS, all that jazz
EV: -$70.71
SD: $158.10 >>>>>>>> so what the hell IS this value good for???
This tells the range from the EV. This is more valuable than just EV by itself, IMO.
and EV/SD can tell one, after X number of bets, what the chances are of coming out even or ahead.

Take the SD for all those bets ($158) and divide by the $5000 (total action)
0.031619614*100 = 3.1619614% >>>> This is the standard deviation for the HE.
1.41% +/- 3.16% (feel free to use 4SD)
(also the unitSD/square root of the number of trials works too)

I think most do not push variance and standard deviation is because it is more difficult to work with.
Especially when multiple bets are combined that resolve at different times, average bets and rates.
More math is involved and sometimes just easier to run large simulations to find the variance.

The next time someone pushes HE and EV only for a number of bets,
session or lifetime, ask what the variance is.

Now you can get a range around that EV that one can fall into from random play.

There are general rules of thumb at play with HE and EV.
The higher the HE is, the less chance of overcoming it over many many bets,
some HE only needs a few thousand lifetime bets to be almost impossible (1 in a million) to be beaten,
many other bets (low to 0% HE) can easily go 10,000 to 50,000 and higher lifetime bets
and still have a decent chance of beating the EV, with just a bit of good luck,
thanks to variance, and beating the casinos over that lifetime of play.

That is why some bets are way better than others.
But the popular opinion is no one can beat the casinos, blah, blah, blah... broken record

Back to Laura Nyro concert and South Park

Quote: RaleighCraps

The gambler's fallacy basically says that when I know an event has a 50-50 chance of happening, say a coin flip, and if I have just seen 5 heads in a row, then I am expecting a tail to show up,
since I know there should be an equal number of heads and tails over an infinite number of coin flips.

This is where most do not understand the Law of Large Numbers.

There will not be an equal NUMBER,

but the percentages, or ratios will be closer to expectation, being 50% as the actual number of trials increase.

The actual numbers of heads (or tails) can and many times are far away from the EV, just use variance to determine how far.

Quote: 7craps

There are general rules of thumb at play with HE and EV.
The higher the HE is, the less chance of overcoming it over many many bets,
some HE only needs a few thousand lifetime bets to be almost impossible (1 in a million) to be beaten,
many other bets (low to 0% HE) can easily go 10,000 to 50,000 and higher lifetime bets
and still have a decent chance of beating the EV, with just a bit of good luck,
thanks to variance, and beating the casinos over that lifetime of play.

That is why some bets are way better than others.
But the popular opinion is no one can beat the casinos, blah, blah, blah... broken record

One's chance of being ahead flat-betting will always be less than 50%, and will come to minuscule amount over a typical "lifetime" of gambling, even with an SD/EV in the thousands. Pressing one's wins, as most gamblers do, will decrease this.

In fact, this line of thinking, taken to its logical conclusion, I can only see as an endorsement of chasing one's losses.

These are two different questions:

1) What is my lifetime expectancy if I start playing craps tomorrow?

2) What is my lifetime expectancy if I start with an initial win of $10000?


Same thing with jackpots in slots. People conflate "What are the odds of hitting jackpots back to back?" with "What are the odds of hitting jackpots back to back, after I've already hit the first one?"

Quote: Mosca

These are two different questions:

1) What is my lifetime expectancy if I start playing craps tomorrow?

2) What is my lifetime expectancy if I start with an initial win of $10000?

Good questions that most all gamblers can never accurately answer those because they do not track their actual sessions played,
action per wager, especially Craps players.
They go by their memory and stop there.

Also, they do not even want to project into the future of the possible number of bets and the average $bet to even see a picture of what they can expect.
Plus, most all gamble at every session play with way too small of a bankroll,
this has to be the biggest nail in the coffin for most all Craps players.

If they all would just track their play and the bets made, and resolved,
many answers would be presented in full living color.

But it is too much work for everyone, and the casino will not let you have a computer by the table to track your bets.
They really do not want the average player to know what really goes on.

Now, everyone wants the easy way out.
Want to lose weight, do not go to your doctor, just go here, take these pills and the pounds and inches will fall off.
Want to always win playing Craps for hours and never lose you $100 bankroll, play this way. A{6,8}>?@bet{1,2,d,e,f}

Results shown are not typical
Your actual results will vary

My understanding is that statistics is less useful in examining the past than the future in this case. Right now you are up $10,000. At the end of your life your expected result is $10,000 minus (total amount bet) times (house edge).

Whether your 10k initial win will help your lifetime EV strongly depends on your "lifetime money management".

Um.... since you've already won $10000 (for sake of argument)

Quote: RaleighCraps

Can I expect to end up an overall winner at craps ($5,000), OR is my lifetime still expected to come out losing my total bets x HE of the bets?

this is the same thing. There is no OR. If you play enough craps in your lifetime to have a -$5000 EV over all FUTURE bets, then your expected bankroll at the end of your life is $5000.

If you are actually asking whether the past bets you have made matter toward the EV calculation, well, that's just preposterous. Do you think the next craps table knows you went on a bender last time, and intends to take your money to make everything right with the universe?

Quote: bigfoot66

My understanding is that statistics is less useful in examining the past than the future in this case. Right now you are up $10,000. At the end of your life your expected result is $10,000 minus (total amount bet) times (house edge).

Less useful? Not useful at all, except to marvel and say "huh, what a stroke of good/bad luck," or "oh, I guess that wasn't significantly far out after all," or in very rare cases "WTF HAX." The past is past.

Quote: 7craps

Good questions that most all gamblers can never accurately answer those because they do not track their actual sessions played,
action per wager, especially Craps players.
They go by their memory and stop there.

Also, they do not even want to project into the future of the possible number of bets and the average $bet to even see a picture of what they can expect.
Plus, most all gamble at every session play with way too small of a bankroll,
this has to be the biggest nail in the coffin for most all Craps players.

I can not say what other players do, but I agree that I go by memory. For 2012. I decided to blog about my trips, as soon as I get back home. I do keep some items vague, because I don't think people really want to know I won exactly $1,410 for the trip. I put in enough detail to paint the picture, and to try and convey how the craps games were trending. And the excitement or disappointment that all craps players can understand.

I tried keeping some accurate records during my craps play a couple of years ago. Not each number rolled, but some meaningful stats like amount won for a shooter, amount lost at 7 out, and the predominant betting pattern (Pass, CB, Place, DC, etc)
Outcome of Come bets, vs Place/Buy bets.
But even minimal stats were impossible to keep while trying to play the game (at least with as much action as I am putting on the table).
It is either play and remember, or just watch and keep stats. If I am going to do that, might as well stay home and use WinCraps.

It's not that I don't want to look into the future, because I really do. I believe you think a lot of us are choosing to ignore 'reality'. Instead, in my case, I do not have the understanding I need to totally grasp the concepts that many people here take for granted. There is a huge difference between being ignorant and being indifferent.

I agree 1000% that I gamble with way too small of a session bankroll. The risk of ruin threads pointed that out to me. And I had stumbled into it when I was playing with WinCraps and noticed I had a better mean when I ran one autobet with a higher starting bankroll. Again, I do not understand everything that goes into the calculations, and I cannot begin to explain it, but I got enough to know I play too big for my Buy in. But why play at $5 Pass line, with max odds and perhaps one $5 Come bet with max odds, hoping to avoid losing a lot of money? Is that fun? Certainly not to me!

Quote: RaleighCraps

I tried keeping some accurate records during my craps play a couple of years ago. Not each number rolled, but some meaningful stats like amount won for a shooter, amount lost at 7 out, and the predominant betting pattern (Pass, CB, Place, DC, etc)
Outcome of Come bets, vs Place/Buy bets.
But even minimal stats were impossible to keep while trying to play the game (at least with as much action as I am putting on the table).
It is either play and remember, or just watch and keep stats. If I am going to do that, might as well stay home and use WinCraps.

The only things you need to track of your play at the Craps table, real easy to do,
to see how many sessions played this way is the type of bet, the actual $ made and the resolved bets.
$6 Place6 - W
$30Place 6 - no (I chickened out and pulled it down)
$6P6 - L
$12P8 - L (f**k)
$5 pass, w
$10podds6 - w

etc

You can play that or enter into WinCraps, not any actual roll is really needed except to resolve the bet,
each session and it, as you know, will show you all sorts of data.

The most important is the mean and standard deviation.

You could break down every bet to get the average bet resolved and the average HE, but that requires some math.
Using WC is a no-brainer.

But if you go that far, just program your betting style in WC. I think you know how to do that.
problem solved.
Run many simulations, the more the better, to get your EV and SD.
You are now done.
You have all the values to tell you your chances of winning a session or multiple sessions
and how much you can win
or how much you could lose per session or a lifetime of sessions.

Still, where you fall in the "curve' is mostly due to luck of many random events,
unless you can predict better than the average player the bets that will win more times than lose and bet for them.

Almost every "goatcabin" post had sim data and results. He did a great job on this stuff.
He did even a better job IMO of explaining what he was doing.

There is so much that can be learned from average bets, HE, EV, variance, it IS not funny no more.
Like spitting into the wind.

Keep up the good work.
Make sure you always compare apples to apples
Have a nice day

If I was flat betting, I agree, records could be kept. I don't. I press, but not in a consistent pattern.
I play mostly by feel. If 6's are hitting a lot (and I know if they are by the size of my pressed bets), I may start pressing even harder.
If I have bet the Buy 4/10 and twice in a row I have not hit either one of them, I may not make the bet for a while.
There is ABSOLUTELY no math that backs up this play, but I don't wish to play like a program.
There is NO reason I should have bet $500 after the 10 had already hit 5 times. And I CERTAINLY should not have bet $1000 after the 6th hit. But it worked.

I can't program any of this feel stuff into WinCraps. But I am trying to figure out how much my 'emotional' betting plays could be costing me.
Many people post stats, most of which I do not understand, that they have gotten from Xcel sheets or custom programs. And that data coincidentally agrees with stats posted from WinCraps. No shocker there. And I have a pretty good idea what WinCraps is going to tell me when I roll a 1M roll simulation.

What got my attention was when I changed my WinCraps hyperdrive to end after 100 shooters. And I would run that 100 times, analyzing the data after each run. That I could understand. The different means and outer band results was educational. I am sure it is the same data that you are able to extract from your 1M roll sim, but I got to see it in pictures....... ;-)

I do not disagree with the law of large numbers. I just don't believe I will ever play enough for it to be the determining factor in my final outcome. Many people will disagree with that statement, and that is fine. I am not seeking to convert the world, nor am I selling The Winning Craps System. For the casino, the Law of Large numbers is certainly a reality, but my play is going to be just a random walk. I have NO PROOF or math to back up this comment. I think some very knowledgeable people may be able to construct some arguments to help support my thoughts, but I am not one of them.

I agree, Goatcabin was a great resource, and it was too bad that he stopped participating. He had the ability to take the math topics and explain them in a way that us non-math people could understand. I am sure many of you are saying the same things goatcabin would have been saying, but I think I just understood him better. Then again, I think our topics now are quite a bit more complex than they were, so maybe he could not have gotten through to me either.

Quote: RaleighCraps

If I was flat betting, I agree, records could be kept. I don't. I press, but not in a consistent pattern.
I play mostly by feel. If 6's are hitting a lot (and I know if they are by the size of my pressed bets), I may start pressing even harder.
If I have bet the Buy 4/10 and twice in a row I have not hit either one of them, I may not make the bet for a while.

I agree.
There are many things that can not be programmed into a computer, like feeings and hunches...

but you can easily still write down your bets, the $ bet and the result after each win or a loss.
This all is valuable info.
Most think it is not.
Good for them.

You can still get a weighted average for each bet from many bets. Every bet does not have to be a flat bet.

There is no good reason NOT to track your bets.

Then use WC to crunch the numbers. or Excel or your local high school math class.
Just do it.

What you will find from that, on average,
is most are making too may of the worse bets available for whatever reason,
too many hardway bets, too many hardway parlay bets... for example, every player is different.
and not making more of the better long term bets. or having more money resolved on the better bets, the lower resolved HE bets, like odds at 0%,
line bets at 1.41% or 1.40%
and place6&8 at 1.52%, just to name a few.

Actual data from actual sessions played are eye openers.
But you can't look at that unless you track it.
It is not that hard.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
AS to the Law of Large Numbers, learn BOTH EV and SD.
BOTH, not just EV.

EV may be -$150 after X number different bets and of different average bets made but if the SD is $400,
now one can fall into a 1SD range (68% of the time)
between -$550 to +$250.
NOT ALWAYS LOSING $150!
as EV pushers want everyone to believe

One needs to know what to expect in any session
and by looking at just EV is like looking at the world through Stevie Wonder's eyes.
But SW knows about variance.

more reading
http://krigman.casinocitytimes.com/article/the-law-of-large-numbers-and-the-anarchy-of-small-samples-61001

If your lifetime number of bets are less than about 200, be happy and play to the wind.
If not, you make more bets, try placing more money on the better low HE per decision type bets.
You will enjoy counting more money in your pocket
when you are not playing.

Quote: 7craps

I agree.
There are many things that can not be programmed into a computer, like feeings and hunches...

but you can easily still write down your bets, the $ bet and the result after each win or a loss.
This all is valuable info.
Most think it is not.
Good for them.

You can still get a weighted average for each bet from many bets. Every bet does not have to be a flat bet.

There is no good reason NOT to track your bets.

Then use WC to crunch the numbers. or Excel or your local high school math class.
Just do it.

What you will find from that, on average,
is most are making too may of the worse bets available for whatever reason,
too many hardway bets, too many hardway parlay bets... for example, every player is different.
and not making more of the better long term bets. or having more money resolved on the better bets, the lower resolved HE bets, like odds at 0%,
line bets at 1.41% or 1.40%
and place6&8 at 1.52%, just to name a few.

Actual data from actual sessions played are eye openers.
But you can't look at that unless you track it.
It is not that hard.

This is sound advice. I had never really considered the value of looking at my results, AFTER the play, and then running the numbers to see where I fell in relation to the expected results.
Thanks for Krigman's link. I am getting ready to read it now.

Quote: 7craps

more reading
http://krigman.casinocitytimes.com/article/the-law-of-large-numbers-and-the-anarchy-of-small-samples-61001

Thanks for the link. I read a number of articles on his site. He had some fascinating numbers. However, he, like many others, does not even begin to try and explain where the number came from. I'm just supposed to believe that his 1.414% is correct. Of course, thanks to the Wiz, who does show how he arrives at his answers I know how that is derived. It's not that I doubt Al's numbers, I would just like more of an indication as to how he arrived at that result.

He does do a good job though, at explaining what the numbers mean. And I really like his concluding statement in the linked article,

"...And, if they’re like most players, they’d like to know their prospects for breaking even or emerging with a profit. Adding the probabilities of all such results shows that Vinnie’s chance is over 56 percent while Winnie’s is greater than 63 percent. Despite the house’s edge, in the short run, bettors have a decent shot at bringing home the bacon...."

Frequently my worst session results are 20 to 30 times negative expectation. That requires maxing on free odds to get that kind of variance.

I believe a reasonable proportion of folks could be down 20 times expectations in a lifetime. Something to bear in mind.

Quote: odiousgambit

Frequently my worst session results are 20 to 30 times negative expectation. That requires maxing on free odds to get that kind of variance.

I believe a reasonable proportion of folks could be down 20 times expectations in a lifetime. Something to bear in mind.

This is a good point. I forget that some people gamble with money they cannot afford to lose, so for those people, having a realistic expectation of the ALL of the possible outcomes is crucial.
Just another of the hidden elements of a game like craps. Lots of ways to play the game, and what is the best way to play for person A, may be a horrible way for person B to play.

Quote: odiousgambit

Frequently my worst session results are 20 to 30 times negative expectation.
That requires maxing on free odds to get that kind of variance.

Not really. If you only understand EV (expected loss) and have no clue what standard deviation is or what use it is, here are numbers based on EV and SD (standard deviation)

$5 pass bets
100 pass line bets NO odds:
ev: -$7.07
sd: $50.00 (most use +/- 3 or 4 sd)
range +/- $200
about 28 EVs.
In line with your figures.

$5 pass bets
100 pass line bets 2X odds:
ev: -$7.07
sd: $142.89 (most use +/- 3 or 4 sd)
range +/- $571 (4sd)
about 82 EVs. NOT In line with your figures, but with the 4sd range.
range +/- $428.67 (3sd)
about 61 EVs. NOT In line with your figures, but with the 3sd range.

conclusion:
learn to use standard deviation instead of just using the EV.
Not that hard to learn
The results will be more in line with reality.

Quote: odiousgambit

I believe a reasonable proportion of folks could be down 20 times expectations in a lifetime.
Something to bear in mind.

By just going off of expectation (EV) one gets only a one dimensional view of the possible range on can fall into after a lifetime of play.

This is really not how it should be done, using expectation only,
cuz now everyone thinks they are doing something worse than expectation, while in all reality, they are right within expectation.

Learn about standard deviation.
It aint hard, no, no.

The Wizard has helped a little with his house edge page

Quote: 7craps

most use +/- 3 or 4 sd

Thanks for the input, but help me out here. My understanding has been that results can be expected to "lie within" 3 standard deviations [haven't seen 4] with a very good degree of certainty [there's never absolute certainty].

But I am not familiar with the way you are using this. To find that your results have been a variation by as much as 3 standard deviations is to say that you have had extraordinarily bad luck, I thought. 99.73% of the time your session would not be as bad as that, right? Yet you state "about 28 EVs. In line with your figures." I'm happy to see I'm in line with something [g] but I'm interpreting this to say 28 EVs is "just what you should expect" instead of "you should only expect this 0.27% of the time"

Quote: 7craps

Now everyone thinks they are doing something worse than expectation, while in all reality, they are right within expectation.

Certainly we see new posters constantly with a thread about "what are the odds this could have happened", and the Wizard has dealt with that to exhaustion for decades... when actually the luck was merely bad, but not unheard of in the least.

Yes, bad results will be within expectation of some kind.

http://en.wikipedia.org/wiki/68-95-99.7_rule

But I am not quite buying your examples overall.

To "be among the unfortunate few who, statistically speaking, will be located in the far left tail of the Gaussian curve." is to have bad luck. No? Although "someone has to be there" and sometimes "it will be you", I still think it is odd to tell someone located there, hey, Pal, that's within expectation like there was nothing remarkable. That's not to say we need a new thread about "what are the odds of this happening?" from every guy with a bad session.

So, help me out here with what you are trying to say with your examples.

Above quotes are from Arnold Snyder's article below. Thanks again to EvenBob for finding that one.

http://www.blackjackforumonline.com/content/wontwin.html

PS: my point being, I still think free odds are what likely would get you into 20-30-40 times EV, but perhaps I stated it badly.

It is interesting. I sometimes run 1 million bet simulations with my video poker software. (I have the free, crappy old FVP suite). Usually it hits almost exactly the projected E.V., but the last one I did just had a ton of royals and just kept going up, and up, and up. You know, ended up with like 100,000 units to the good.

Is it too much to ask to be THAT person? :)

On the other hand, it's terrifying to imagine the other side of that bell curve...

Quote: teddys

It is interesting. I sometimes run 1 million bet simulations with my video poker software. (I have the free, crappy old FVP suite). Usually it hits almost exactly the projected E.V., but the last one I did just had a ton of royals and just kept going up, and up, and up. You know, ended up with like 100,000 units to the good.

Is it too much to ask to be THAT person? :)

On the other hand, it's terrifying to imagine the other side of that bell curve...

That was how I discovered the Risk of Ruin, although I did not know it as such.
I have WinCraps, registered version, and had created a high risk press strategy.
I would run 10,000 games, ending with either 100 shooters or bust, and a $2K starting BR each game.
It would bust out a lot!
But it would also have a few wins in the $10,000 range.

I then found that if I increased the starting BR to $4k, I did not have as many bust outs. But a $4K game loss was way out of my league.

That was when I decided that running 1M simulations wasn't really what I was looking for. Now, I am learning on here about Standard Deviations, and that is a big part about those 1M simulations that I was missing.

In the meantime, I now run a simulation that is closer to my typical craps session. And I run that 100 times. Look at the data, and repeat. I guess you could say I am looking at pictures, until I learn how to read data.

Quote: odiousgambit

Thanks for the input, but help me out here. My understanding has been that results can be expected to "lie within" 3 standard deviations [haven't seen 4] with a very good degree of certainty [there's never absolute certainty]

I have seen 4SD and higher many many times in actual casino play and simulations even for small samples.
You are under the impression that such "bad luck' or a rare event just does not happen that often, but they can and they do.

#1) For one, it would be rare and even more rare to have a 4SD happen back to back in a small sample size, but it does happen.

But many still argue that anything outside of 3SD is a freak and is not to be expected.
Total BS, IMO.

#2) But for many with many trials, the rare events that many point to,
close to 3SD or higher
becomes even a less rare event by observers because of the frequency (how many times) of a rare event.

#3) And for one player playing many trials, it is to be expected that rare events will and do happen.
They key is knowing what the EV and SD
IS
for any number of trials.

You use EV and EV in place of SD.
Where did that come from?

Quote: odiousgambit

But I am not familiar with the way you are using this.
To find that your results have been a variation by as much as 3 standard deviations is to say that you have had extraordinarily bad luck, I thought. 99.73% of the time your session would not be as bad as that, right? Yet you state "about 28 EVs. In line with your figures." I'm happy to see I'm in line with something [g] but I'm interpreting this to say 28 EVs is "just what you should expect" instead of "you should only expect this 0.27% of the time"

You are unique in your use of EV and number of EVs to explain the possible range that the standard deviation shows.
I, Never seen it done this way.
My examples show why one should not use EV in place of standard deviation.

Quote: odiousgambit

Certainly we see new posters constantly with a thread about "what are the odds this could have happened", and the Wizard has dealt with that to exhaustion for decades... when actually the luck was merely bad, but not unheard of in the least.

Yes, bad results will be within expectation of some kind.

http://en.wikipedia.org/wiki/68-95-99.7_rule

That page implies to the average reader that anything outside of 3SD is a very rare event over life.
Ain't so.
The number of trials is also important in the calculation.

Quote: odiousgambit

But I am not quite buying your examples overall.

They are not for sale.
I was pointing out how you use EV in place of SD and
just a simple pass line odds throws your EV standard right out the window since you claim to always see 20 to 30 times EV.

Quote: odiousgambit

To "be among the unfortunate few who, statistically speaking, will be located in the far left tail of the Gaussian curve." is to have bad luck. No? Although "someone has to be there" and sometimes "it will be you", I still think it is odd to tell someone located there, hey, Pal, that's within expectation like there was nothing remarkable. That's not to say we need a new thread about "what are the odds of this happening?" from every guy with a bad session. [edit]

So, help me out here with what you are trying to say with your examples.

Again, you are using EV and EV instead of EV and SD.

I tried it both ways with very simple examples and your EV/EV method needs to be tossed into the trash.

Quote: odiousgambit

PS: my point being, I still think free odds are what likely would get you into 20-30-40 times EV, but perhaps I stated it badly.

Again, you are using EV in place of standard deviation.

Let us find others that can do that successfully.

Or maybe you can show under what assumptions EV and EV will show better and more accurate results than EV and SD.

try with a simple example of coin flips for 20 flips.
IF Mary flipped 16 out of 20 Heads, 2 times in a row, many would question that coin.
Something MUST be wrong with it.
and then Jane come along and flips 20 out of 20 Heads,
people would freak out and demand to see the coins used saying they are rigged.

Use your EV and EV method to see how rare these events are.
Can they just not happen for 3 trials or 1 million trials equally??

Quote: RaleighCraps

In the meantime, I now run a simulation that is closer to my typical craps session.
And I run that 100 times. Look at the data, and repeat. I guess you could say I am looking at pictures, until I learn how to read data.

RC, it is good to try to simulate the exact way you might play at a Craps table.
But just having 100 sims (or 100 other players) to show the data results in data that is not very accurate.
It will have a very high margin of error.

For simulations, the more times run, the more accurate the results will be.
The rule is a sample size 100 times larger will give a better estimate of the true probability by just a factor of 10.

Flip a coin just 100 times and get 44 heads leads one to conclude that the probability of Heads is just 44%,
based from the very small sample size.
Flip a coin 1,000,000 times and we see the % converges to the true probability (50% with a smaller margin of error)
way easier than the 100 sample or even the 10,000 sample, but not exactly.
The average or percentages get closer but the not necessarily the absolute numbers, they can get further away from each other.

here is a site to see this
Coin Toss Computer Simulation
http://www.tinafad.com/coin.php

Lean what to expect from your play over time and that will take away the many surprises of real bad sessions, because we should expect them, Craps is a game of random dice rolls.

one of the things I have learned here is that 1,000, or even 10,000 trials is usually not enough; and there is nothing excessive about 100 million trials or more.