Long Run...how long is the long run.

[Marven]

I'm with Dr.Hubert here.

The "long run" in this particular context is neither infinity nor 10 million bets.

Anyone who plays fairly regularly (placed over a few thousand bets in his life) and yet thinks he's always in the "short run" is indeed misguided.

Learn about Standard Deviation calculation to be able to determine where you are in terms of "luck", "short run", "long run", etc.

The luck factor in a casino game is quantified using standard deviation (SD). The standard deviation of a simple game like Roulette can be calculated using the binomial distribution. In the binomial distribution, SD = sqrt (npq ), where n = number of rounds played, p = probability of winning, and q = probability of losing. The binomial distribution assumes a result of 1 unit for a win, and 0 units for a loss, rather than -1 units for a loss, which doubles the range of possible outcomes. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold. Therefore,

SD (Roulette, even-money bet) = 2b sqrt(npq ), where b = flat bet per round, n = number of rounds, p = 18/38, and q = 20/38.

For example, after 10 rounds at $1 per round, the standard deviation will be 2 x 1 x sqrt(10 x 18/38 x 20/38) = $3.16. After 10 rounds, the expected loss will be 10 x $1 x 5.26% = $0.53. As you can see, standard deviation is many times the magnitude of the expected loss.

The range is six times the standard deviation: three above the mean, and three below. Therefore, after 10 rounds betting $1 per round, your result will be somewhere between -$0.53 - 3 x $3.16 and -$0.53 + 3 x $3.16, I.e., between -$10.00 and $8.95. (There is still a 0.1% chance that your result will exceed a $8.95 profit) This demonstrates how luck can be quantified; we know that if we walk into a casino and bet $5 per round for a whole night, we are not going to walk out with $500.

The standard deviation for the even-money Roulette bet is the lowest out of all casinos games. Most games, particularly slots, have extremely high standard deviations. As the size of the potential payouts increase, so does the standard deviation.

As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is impossible for a gambler to win in the long term. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win.

The volatility index (VI) is defined as the standard deviation for one round, betting one unit. Therefore, the VI for the even-money American Roulette bet is sqrt(18/38 x 20/38) = 0.499. The variance (v) is defined as the square of the VI. Therefore, the variance of the even-money American Roulette bet is 0.249, which is extremely low for a casino game. The variance for Blackjack is 1.2, which is still low compared to the variances of electronic gaming machines (EGMs).

It is important for a casino to know both the house edge and volatility index for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the volatility index tells them how much they need in the way of cash reserves. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this field, so outsource their requirements to experts in the gaming analysis field, such as Mike Shackleford, the "Wizard of Odds".

Source: nolinks://en.wikipedia.org/wiki/Gaming_mathematics#Standard_deviation

A useful post by Laurence Scott:

Let's go through the methology in detail for both an even money (18 number bet) and a 5 number bet. In my earlier post, I did the math in terms of wins (which is an approximation when even money bets are involved), but in reality it needs to done in terms of Action vs. Return. And, after redoing my calculations the 400 figure was originally based on a 00 wheel. So, to be conservative, let's assume we are dealing with a 00 wheel.

For an even money bet, we need to find the number of spins where the house expectation = one standard deviation. In other words, by breaking even you are at one standard deviation (SD). I'm sure there must be a formula for this somewhere (contributors?), but I always do it by estimation and trial and error.

Even money:

Let's assume you bet $1 per number and cover 18 numbers. This would be the same as betting $18 on red/black/etc. Your total action over 400 spins would be 400 X 18 = $7,200.

The house edge is 5.26%. So, over 400 spins the house would expect to make $378.72 (7200 X .0526).

How many extra wins does it take to make this amount? Each win returns $36, so 379/36 = 10.5 wins.

The standard deviation over 400 even money bets is 10. SQRT(400 X .5 X .5).

If you were to just over come the house edge (I.e. break even) you would be 1 standard deviation over expectation.

You would then need to find some bet that is over 3 standard deviations. In other words, you would need to find an even money bet that had 30 net wins, for a profit of about $750. Quite an accomplishment, and a fairly rare event.

This bet then becomes your hypothesis. You then need to take an additional 400 spins to confirm the hypothesis.

Let's say that after 800 spins red does not perform as expected, but "odd" is now at 3 SD. Can you start betting odd? No. You would need another 800 spins to confirm the odd hypothesis.

Now, let's look at a 5 number sector:

2000 spins would be my initial threshold:

Action = 2000 X 5 = 10000
House expectation = 10000 X .0526 = $526 = 14.6 wins

N = 2000
P = 5/38
Q = 33/38

SQRT(N x P x Q) = 16.22

14.6 vs. 16.22. Close enough. 2000 is a nice round number for illustration purposes.

If I am looking for a 5 number event it would take at least 2000 spins to form my hypothesis. I would then need another 2000 spins to confirm my hypothesis.

The bottom line is that you need 4000 spins to confirm a 5 number bet.

*********************

How significant your orignial hypotheis should be is a matter of personal risk tolerance. 3 SD for an initial hypothesis is a pretty high bar. 2 SD will obviously qualify more wheels.

The proof is in the confiming indepent set. If you start out with a 2 SD event, and then it turns into a 3 SD event after the confirming set, you most likely have something real.

The bottom line is this: A 2000 spin initial set followed by another set of 2000 to confirm is NOT THE SAME as taking 8000 spins and then finding your event. This is a classic MISTAKE people make:

* I've taken 4000 spins
* I've found a 5 number sector that is @ 3 SD
* The sector performs in both the first 1/2 of the set and the second half of the set
* I've found my significant event! (WRONG)

The proper methodolgy is this:

* I've taken 2000 spins
* I've found a 5 number sector that is @ 3 SD
* I've taken another 2000 spins
* The 5 number sector is positive in my confirming set and is now over 3 SD.
* I've found my significant event! (RIGHT)

Source: nolinks://  nolinks.  advantageplayer  .com/roulette/forums/roulette-main/webbbs.cgi?noframes;read=1500

[Number Six]

Technically, surely you're always in the long run. The long run would be the entire population of decisions you've ever observed while playing for real cash-money, the gap in between sessions is irrelevant. When you stop, you're in the long run, when you start again you're in the long run. The characteristics of randomness will apply themselves to any sample or population, regardless of time, wheel, location. Someone mentioned "personal permeance"; everyone's long run is different, depending on how much you play, it can't be defined as 10 million decisions or 100 million. I'm not saying things don't happen in the short term, but everything is part of the long haul.

[seykid29]

So Maths has come into play to shed light.But in the end long run,short run what really matters is a good money management,good play strategies,discipline and walking out in profit everytime.

[Dr.Hubert]

Money management, gaming discipline won't make you a winner.   Strategy is everything.   Without the edge, you're not going to win in the long run.   

People should focus more attention on getting the edge before they worry about money management.

[Marven]

Indeed.

[seykid29]

Dr.Hubert you knew on Forum,but by the way you answer it feels you been playing for long.Concernin Strategy you right,and money management fits in,but i think discipline is key.Maybe you have read,or will read about some good players on Forum with good strategy who let them stray,as lack of discipline.

[hoper35]

"People should focus more attention on getting the edge before they worry about money management"


I don't agree.  Money management is critical.

[Proofreaders2000]

Strategy is all-important if you want consistent wins.  If your just playing for entertainment, money menagement is more important.

[sushie]

Good questions and responses are interessant.
Before when i read the term "long run", i was always thinking that it's playing everyday short sessions during some years and still winning until the dead. . .  ^^'

[iboba]

To me a long run means;
From the day I first start playing full time until now.
And only I know the results of that long run....W or L
It is like any company....if succ.you still running,if not you are out of buss......Iboba

[Danger Man]

Money management: another gambling misconception to thrown on the pile.  If you play for fun, you play with $50 you don't care about losing.  If you play for fun, it's pretty much guaranteed that you're going home with nothing.  People who play for "fun" don't know when to stop. 

The phrase "money management" should be banned from forums.  If you don't have an edge, money management simply means you're just looking for a way to lose as slowly as possible.  If you're obsessed with money management, stop playing because the red is going to get deeper.  The bet selection alone is everything. 

[hoper35]

Bet selection only makes a small difference.  Your bet selection only has to be average if you have good money management.

[Dr.Hubert]

Bet selection only makes a small difference.   Your bet selection only has to be average if you have good money management. 

That's absurd.    That's like saying you don't have to worry about how to make money.    You just need to worry about how to spend it. 

Get the edge first, then worry about money management/discipline. 

[Raider]

Using  data I collect to determine the SD with enough values to gain confidence, to validate that what I am doing is effect is naive?  Probability based on the physical properties of an object or objects is not dependant on those objects being in a "neutral state".  Having a person touch those objects does not effect the "neutral state".   A 3 + SD  for a method  based on 4000 bet decision will not change through out the course of 400K bet decisions.


So the answer to the question that started this thread is 4000 bet decision= long run and the long run is not just a set  totaling all the bet decisions with REAL MONEY that you make.   Cool

Get the edge before you have the discipline to use money management  must come from someone who lost money by having neither.

Just a thought

[Davey-Jones]

"People should focus more attention on getting the edge before they worry about money management"


I don't agree.  Money management is critical.

Bet selection only makes a small difference.  Your bet selection only has to be average if you have good money management.

[Davey-Jones]

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