i can't make sense of variance or standard deviation
yeah well thanks a lot Weezely Cat one, now you have me realizing that i don't think i even know what the heck any of that stuff is, ie. standard deviation and variance. 
i think i know what expected value is. it's kind of abstract but i think i get what it is.
what's easy for me to understand is results. something that actually happened. and those results when you record them you can see how they present in some kind of distribution of differing results but where a distribution of those results lots of those differing results are identical to one another and repeated when they present sort of thing.
when you run a simulation you get a whole bunch of results data. and what i think happens is the expected value results is gonna be represented by the biggest pile of data realized that has identical numerical values, where it would be in terms of win rate say dollars per hand or units per hand or dollars per round or units per round, or dollar per hour or units per hour. since that pile of results is the biggest pile we say that represents expected value, EV. the tricky thing being is this EV pile is related to the advantage that you enjoy or don't enjoy as the case may be. reason being is that advantage, that ever present (over time) influence drives the probability of that result happening to the greatest extent for all of the silly reasons makes that event the most likely thing to happen while other events are less likely to happen by various degrees.
then you got a bunch of other groups of data, where within each of those groups the numerical values are identical. but those groups make smaller piles than the big daddy expected value pile. and as it turns out i guess by decree of the blackjack god's these lesser piles are if you line them up by size of the pile and place them on the left of the EV pile if their numerical value is less than the EV pile and if you put them on the right of the EV pile if their numerical value is more than the EV pile then you get this really nifty bell curve looking thing.
but if your gonna say the big pile is the most expected result then your gonna want to classify these pesky lesser piles some way. to me they are just lesser expected results but results that happen none the less.
their probability of happening is lower but they go ahead and happen anyway. they are deviations from the norm, the norm being the expected value pile. in shuffled and fully dealt blackjack games the true count presents in a normal distribution and since true counts is mainly what we know influences advantage it tends to be that the win rate presents in a normal distribution as well. and how we bet consistently taking into consideration those true counts as they present is gonna shape our results bell curve.
but what ever it's those pesky lesser sized piles that don't fall into the expected value pile is where we come up with this variance and standard deviation stuff.
and maths nerd's makes us follow certain rules for figuring variance and standard deviation. i think what it is, they want to be able to have a standardized way of manipulating the results data stuff. then they can take this standardized variance and standard deviation stuff and further fool with it. but really it's just stuff that happens or should happen and then fiddled around with mathematically. the rules are according to the encyclopedia of blackjack as follows:
expectation. The theoretical outcome per wager and a measure of how much the player (or casino) can expect to lose (or win) in a particular game based on the handle. This measure (generally expressed in dollars or percent) is based on the player's statistical advantage or disadvantage. An example of expectation for a fixed game such as American roulette would be -5.26% for a 1-unit wager on black or red.
variance. In statistics, the mean of the squares of the variations from the mean of a frequency distribution.
standard deviation. (SD). Also called fluctuation or luck. This statistical index is often used in technical blackjack texts as a measure of how much individual wins and losses can differ from the average. In statistics, the SD is the square root of its variance and is used as a measure of dispersion in a distribution. In an even game, the SD is often approximated as the square root of the total number of hands or bets divided by 2 as shown below:
SD = (Square Root of N) / 2
where N = number of hands.
For all practical purposes (99.7% of the time), you will be within 3 SDs of your expectation. 95.4% of the time you will be within 2 SDs and 68.3% of the time you will be within 1 SD.
In blackjack, where one side enjoys an advantage, it is more appropriate to express SD as a percentage. The percentage of the SD can be expressed as:
% SD = (1.1 / (Square Root of N)) x 100
Katweezel said:
Here is Bootlegger's definition of variance:
Variance. "This can be determined by subtracting the expected value from each possible outcome in a game or hand, squaring the differences and multiplying each square by its probability of occurring and then summing the total of the product."
Sage, In your recent, excellent Synopsis on Luck, you failed to mention the dreaded word, variance. Congratulations.
Variance. "This can be determined by subtracting the expected value from each possible outcome in a game or hand, squaring the differences and multiplying each square by its probability of occurring and then summing the total of the product."
Sage, In your recent, excellent Synopsis on Luck, you failed to mention the dreaded word, variance. Congratulations.
i think i know what expected value is. it's kind of abstract but i think i get what it is.
what's easy for me to understand is results. something that actually happened. and those results when you record them you can see how they present in some kind of distribution of differing results but where a distribution of those results lots of those differing results are identical to one another and repeated when they present sort of thing.
when you run a simulation you get a whole bunch of results data. and what i think happens is the expected value results is gonna be represented by the biggest pile of data realized that has identical numerical values, where it would be in terms of win rate say dollars per hand or units per hand or dollars per round or units per round, or dollar per hour or units per hour. since that pile of results is the biggest pile we say that represents expected value, EV. the tricky thing being is this EV pile is related to the advantage that you enjoy or don't enjoy as the case may be. reason being is that advantage, that ever present (over time) influence drives the probability of that result happening to the greatest extent for all of the silly reasons makes that event the most likely thing to happen while other events are less likely to happen by various degrees.
then you got a bunch of other groups of data, where within each of those groups the numerical values are identical. but those groups make smaller piles than the big daddy expected value pile. and as it turns out i guess by decree of the blackjack god's these lesser piles are if you line them up by size of the pile and place them on the left of the EV pile if their numerical value is less than the EV pile and if you put them on the right of the EV pile if their numerical value is more than the EV pile then you get this really nifty bell curve looking thing.
but if your gonna say the big pile is the most expected result then your gonna want to classify these pesky lesser piles some way. to me they are just lesser expected results but results that happen none the less.
their probability of happening is lower but they go ahead and happen anyway. they are deviations from the norm, the norm being the expected value pile. in shuffled and fully dealt blackjack games the true count presents in a normal distribution and since true counts is mainly what we know influences advantage it tends to be that the win rate presents in a normal distribution as well. and how we bet consistently taking into consideration those true counts as they present is gonna shape our results bell curve.
but what ever it's those pesky lesser sized piles that don't fall into the expected value pile is where we come up with this variance and standard deviation stuff.
and maths nerd's makes us follow certain rules for figuring variance and standard deviation. i think what it is, they want to be able to have a standardized way of manipulating the results data stuff. then they can take this standardized variance and standard deviation stuff and further fool with it. but really it's just stuff that happens or should happen and then fiddled around with mathematically. the rules are according to the encyclopedia of blackjack as follows:
expectation. The theoretical outcome per wager and a measure of how much the player (or casino) can expect to lose (or win) in a particular game based on the handle. This measure (generally expressed in dollars or percent) is based on the player's statistical advantage or disadvantage. An example of expectation for a fixed game such as American roulette would be -5.26% for a 1-unit wager on black or red.
variance. In statistics, the mean of the squares of the variations from the mean of a frequency distribution.
standard deviation. (SD). Also called fluctuation or luck. This statistical index is often used in technical blackjack texts as a measure of how much individual wins and losses can differ from the average. In statistics, the SD is the square root of its variance and is used as a measure of dispersion in a distribution. In an even game, the SD is often approximated as the square root of the total number of hands or bets divided by 2 as shown below:
SD = (Square Root of N) / 2
where N = number of hands.
For all practical purposes (99.7% of the time), you will be within 3 SDs of your expectation. 95.4% of the time you will be within 2 SDs and 68.3% of the time you will be within 1 SD.
In blackjack, where one side enjoys an advantage, it is more appropriate to express SD as a percentage. The percentage of the SD can be expressed as:
% SD = (1.1 / (Square Root of N)) x 100
