Winning with Standard Deviation

If I play perfect blackjack and have an adequate bankroll (100 times average bet), standard deviation tells me that
sometime before my bankroll is depleted, I will ahead by 50%. If I quit with a 25% profit. I am a sure winner.

The question is: do the laws of standard deviation continue into my next session where they left off in this one?

If I cash out and go to another table with my original bankroll, do the law of chance rewind and start over with me?

Cal

No, the statistical conditions don't start over. Your results were close to completely random at the first table, and they'll be close to completely random at the second table as well. No matter how much time or distance is between your playing sessions, you're adding to the same set of results and not starting a new set.

Quote: cals5839

If I play perfect blackjack and have an adequate bankroll (100 times average bet), standard deviation tells me that
sometime before my bankroll is depleted, I will ahead by 50%. If I quit with a 25% profit. I am a sure winner.

The question is: do the laws of standard deviation continue into my next session where they left off in this one?

If I cash out and go to another table with my original bankroll, do the law of chance rewind and start over with me?

Cal

"Playing session" is an illusion. In reality, you only have one long playing session. What, as a practical matter, is the difference between your next hand being in five seconds, in three days, or in six months?

Thanks for the input. It is what I guessed. But it seems rather hazy to me. If the odds of a coin coming up heads is independent of the results of the last flip, why isn't every set of 100 flips independent of the last set of 100?

Cal.

Unless those sets of flips overlap (or you discover you are using a biased coin), they ARE independent.

Also, in the original post, you are never guaranteed to be ahead. It is quite possible that you lose your first hand, never get ahead for that session, and lose your session bankroll before ever seeing positive results.

People often confuse events and long-term probability.

Each event is independent of eachother, however when calculating probability and standard deviation, the calculations are based on long term string of events.

It seems like the reality is often forgotten when people gamble. The reality is you're flipping a coin over and over again with the casino. When the casino wins, you lose $10. When you win, you receive $9.85. Sometimes you'll win 10x in a row, other times you'll lose 10x in a row, however on average, you can expect that you'll win about as many times as you lose. However, notice that if you flip the coin 1000x and you win 50% of the time, you lose $5000 and you win $4925, with a loss of $75. This is why casino's are open 24/7 and they always make money.

Quote: cals5839

If I play perfect blackjack and have an adequate bankroll (100 times average bet), standard deviation tells me that
sometime before my bankroll is depleted, I will ahead by 50%. If I quit with a 25% profit. I am a sure winner.

This statement is totally untrue.

I can not totally agree. Let's we have a coin and flip it 100.000.000 times.

I no for sure, after 100.000.000 coin flips we don't see exactly 50.000.000 time tail. It will be close to 50.000.000 but because of the standard deviation the outcome is another number.

We can say the same for blackjack... looking at a player flat betting and using basic strategy.. doing 100.000.000 sessions and play.. let's say 1.000.000.000.000 hands.
The chance he has lost money at the end of that 1.000.000.000.000 is bigger then a win but still... because of the standard deviation he can be up and have a small win in the end.

Some people are just a but more lucky.. also in the long, long run.. just a bit more lucky.

But I agree, talking in 'sessions' means nothing.. because when you gamble.. the end of the session is when you die or quitte gambling.

Quote: mkl654321

"Playing session" is an illusion. In reality, you only have one long playing session. What, as a practical matter, is the difference between your next hand being in five seconds, in three days, or in six months?

Even the Internal Revenue Service is unable to respond logically on that one.

Quote: cals5839

The question is: do the laws of standard deviation continue into my next session where they left off in this one?

Think of it as a coin being automatically tossed by a machine with perhaps a dozen bettors all standing around making bets on it. Suddenly you decide to "end your session" and come back later. Would you really call out to the coin to "hold them standard deviations in memory, I'll be right back" What if an additional player walks up? Does he start at the next flip? If he has been watching but not betting, would you really ask if the standard deviation is held in abeyance for awhile?

The house edge is like the law of gravity: it always is applicable. There is no escape. There are expectations. You can get lucky. You can get unlucky. In other words, the emotionally relevant session may start with your making a bet but the statistically relevant session started long ago and will continue for a long time: each flip of the coin, each spin of the wheel, each roll of the dice ... are all alike. You may remember the last coin toss, but the coin does not.

Your next session at Blackjack can start whenever you want. The dealer may remember you, the waitress may remember you, surveillance may remember you, but them cards don't.

Standard Deviation says you will deviate. It does not guarantee in which direction. There is no guarantee that you will be ahead at any point... the Wizard has pointed out that no such certainty is true in a negative expectation game out to infinity.

PS: since this fallacy has come up before, maybe the WoO should put it in his FAQ's

Quote: odiousgambit

Standard Deviation says you will deviate. It does not guarantee in which direction.
PS: since this fallacy has come up before, maybe the WoO should put it in his FAQ's

I think it is a matter of my not wanting to acknowledge the fallacy.

Its a matter of expectations and desires. I go into the singles bar hoping for this stunning blond to walk right up to me, hand me a map to her home and say to me "My place, now... and don't still be there when I wake up". What happens is that sometimes a demented bag-lady is the only one who wants to extend any such invitations and sometimes I just guzzle booze until my chin bumps the foot rail. I keep waiting for that stunning blond though! Intellectually I understand it ain't gonna happen, but I have hope.

After four Reds in a row, ... I start to think well now in real life its still fifty-fifty on that next spin (oh, forget that darned green, will you!), yet I think that somehow FIVE reds in a row is less commonly encountered in real life so I should bet on Black because its a more realistic expectation. The trouble is that FIVE reds in a row still does indeed happen. We think our luck will change, we think that Stunning Blond will in fact appear and that tonight will be the night it happens.

I swear almost every time I hit 16, I lose. Yet, I continue to do so because it is right. I swear every time its a Tie in Baccarat all I have to do is wait one hand and then it will be a tie again. So I finally give in and make the massive Tie Bet but then have it turn out to be two hands before the next tie! Serves me right for believing in "trends" in Baccarat.

Well, the alcoholic fog of the Thanksgiving Wine is starting to wear off, time for me to find out: Is it stunning blond lying there or is it demented bag lady lying there... or am I alone in the bed and merely have a sore chin? ... Oh well, sore chin yet again!!! Why must Lady Luck always frown on me.

Think of it this way. When the standard deviation is zero, you have an absolute. For example, the money under your matress will always be there. You know how much is there, and the standard deviation of that is zero.

Martigaling is a great example of "trying to beat the standard deviation" by always doubling your bet. The problem is that you will always run into the situation where you lose your entire session before the martingale "recovers". That said, standard deviation tells you how LIKELY it is to be within a certain range of expected values (note, not how LIKELY you are). Where you land on that graph is effectively the contribution of your sample. You can land on the right side of expected value and be "lucky" or you can land on the far left of the graph (broke).

The problem with this which is the great thing for casinos is that people are very much limited on the left side (the losing side) to their session limits while there is no limit on the right side of the graph. This (and alcohol) allows for the casino to take back your money. Most players, after experiencing positive standard deviation, will just keep playing until they approach the middle of the graph and lose their money back. Yes, it's possible to get another royal flush right after you hit the first one, but you've got to realize that you've just been lucky and that the likelihood of getting the next one has nothing to do with the last one.

Good gamblers (those with excellent money management skills and realize when they are experiencing "positive variance") will recognize these events and manage their sessions carefully. I would say that the top skills at the casinos are knowing the strategy for your game and sticking to it, and money management.

Quote: boymimbo

Think of it this way. When the standard deviation is zero, you have an absolute. For example, the money under your matress will always be there. You know how much is there, and the standard deviation of that is zero.

Martigaling is a great example of "trying to beat the standard deviation" by always doubling your bet. The problem is that you will always run into the situation where you lose your entire session before the martingale "recovers". That said, standard deviation tells you how LIKELY it is to be within a certain range of expected values (note, not how LIKELY you are). Where you land on that graph is effectively the contribution of your sample. You can land on the right side of expected value and be "lucky" or you can land on the far left of the graph (broke).

The problem with this which is the great thing for casinos is that people are very much limited on the left side (the losing side) to their session limits while there is no limit on the right side of the graph. This (and alcohol) allows for the casino to take back your money. Most players, after experiencing positive standard deviation, will just keep playing until they approach the middle of the graph and lose their money back. Yes, it's possible to get another royal flush right after you hit the first one, but you've got to realize that you've just been lucky and that the likelihood of getting the next one has nothing to do with the last one.

Good gamblers (those with excellent money management skills and realize when they are experiencing "positive variance") will recognize these events and manage their sessions carefully. I would say that the top skills at the casinos are knowing the strategy for your game and sticking to it, and money management.

Unless you are playing a game with a positive expected value, I don't think money management changes much. Sure, your artificially created 'sessions' will tend to have more frequent wins but in the end you are really playing one big session that includes every smaller sessions you every played. Probabilities don't take a break the moment you leave the table.

Quote: HKrandom

Unless you are playing a game with a positive expected value, I don't think money management changes much. Sure, your artificially created 'sessions' will tend to have more frequent wins but in the end you are really playing one big session that includes every smaller sessions you every played. Probabilities don't take a break the moment you leave the table.

I've been continually amazed by how many people, including on this board, don't realize this. You lose $3,000 in a weekend--and you rationalize that by breaking it up into fifty-three "sessions", thirty-four of which you "won". Or you play blackjack for forty minutes, but every time you stop to take a sip from your drink, that's a new "session". Sessions don't mean a thing--only the bottom line.

I have a 10% session goal an it works for me, and my system is backed up by CV Data Sim simulation software.

And to answer your question I have to reluctantly disagree with the math professionals who have responded to the post.

If you play with a session goal in mind you are greatly reducing any high negative and high positive variance swings. Although you are forfeiting some high positive variance swings you might encounter as well as dreaded negative variance . But when I look at session goals I see the words better safe than sorry. And if you get all your session profits in a cashiers check and send them to yourself you can never really go bust can you...

And your question about law of chance rewinding... no the law of chance is always the same however leaving in the middle of the deck and starting over at a new casino and new deck does start the variance at zero again.

Now I know I am probably going to get heat from this but I don't care. I post what I think....

Quote: blackjackgolden

... starting over at a new casino and new deck does start the variance at zero again ... I post what I think....

... better to stay quiet and be thought a fool than to open your mouth (post) and remove all doubt ...

Variance does not start over. A constant is a constant. Variance is a constant, defined based on the probabilities of the various outcomes, the outcomes themselves, and the overall expected value of the game.

17 starts over ... when you walk into a new casino
The speed of light starts over ... when you walk into a new casino
The number of senators starts over ... when you walk into a new casino
The radius of the earth starts over ... when you walk into a new casino

It doesn't even make sense ...

--Ms [Happy F&^%'n Holidays] D.

Really so If I get my session goal in one casino and stopped when the variance wasy high positive, when I walk into another casino it is going to high positive again instead of slightly negative... Is that what your saying so your saying if I leave a casino with high variance I should start my bet at out at the next casino big because the casino I just left the variance was high positive...

Quote: blackjackgolden

Really so If I get my session goal in one casino and stopped when the variance wasy high positive, when I walk into another casino it is going to high positive again instead of slightly negative... Is that what your saying so your saying if I leave a casino with high variance I should start my bet at out at the next casino big because the casino I just left the variance was high positive...

You have no idea what "variance" means ... go take a high school course in statistics ... or read a little bit ... just educate yourself instead of glorifying your ignorance on these pages...

A CONSTANT is not something that gets high or positive or anything else, it's just a f&&k'n constant value defined for a game ... Do you think the numbers 1,2,3,4,5,6 on the dice change when you go from one casino to the next? No, they're constants. Get it? Variance is a CONSTANT. Moreover, it is a constant that is NEVER NEGATIVE.

For example, the variance for playing the Banker in baccarat is 0.86. The variance for one hand of Let it Ride is 26.73. The variance for betting on one number, straight up, in roulette is 33.21. These numbers don't change ... they don't get high positive, or negative, or start over. They are just CONSTANTS.

I have no idea what you are talking about, and neither do you.

Read about Variance on Wikipedia, demonstrate to yourself that you understand it by computing the variance for a few casino games, then return and let's see what you have to say ...

Wikipedia article on variance

--Ms. D.

DorothyGale, what does it mean that the variance for strait up in roulette is 33.21? French(singlezero) or American roulette?

Sorry, I read wikipedia but it is hard to catch some formulaes.

Is the variance calculated for a certain trials? 33.21 is for 1 trial?

I know that 1 standard deviation is the square root of the variance, but in standard deviation you measure a group of numbers along a sample to check for a abnormal deviaton.

Most statistics is based on sampling. However, in Roulette you know the whole population (0, 00, 1, 2, ... 36) and each outcome's probability so you can compute the population mean and variance rather than the sample mean and variance. The formulas are similar; computing the true (population) variance requires dividing by n, not n-1, and you measure the deviates from the population mean rather than the sample mean.

Quote: ybot

DorothyGale, what does it mean that the variance for strait up in roulette is 33.21? French(singlezero) or American roulette?

Sorry, I read wikipedia but it is hard to catch some formulaes.

Is the variance calculated for a certain trials? 33.21 is for 1 trial?

I know that 1 standard deviation is the square root of the variance, but in standard deviation you measure a group of numbers along a sample to check for a abnormal deviaton.

Your post shows your level of understanding. DG's variance is for 1 trial and 1 unit wager. The variance of the wager. Not the sample variance of a population or even the binomial standard deviation.

You should understand these concepts.
expected value
the law of large numbers
the central limit theorem

They are free to study on the web.
But you can still ask questions, it helps us in the learning.