Variance: A Non-Math Explanation, Please
July 21st, 2013 at 9:20:14 PM
permalink
Here's what I understand re: variance. Pure math lays out a sequence of rolls according to the expected outcomes, based on the 36 possible combinations of numbers by 2 dice, each w/ 6 faces, 1-6 over an infinite series of rolls. I'll call this the Grand Sequence. However, grand as that sequence may be, there are slices of sequences within it that "vary" from what the Grand Sequence is all about. IOW, there are sequences where the 7 shows more times than others, and less times than others. Craps players define these sequences as "cold" and "hot" tables. However, both "hot" and "cold" tables show a high variance from the Grand Sequence, for both vary greatly from the Grand Sequence.
What I'm really getting at is an explanation of "high" and "low" variation BETS. I see a high variation bet as one made on a number that is less likely than the 7 to show up in the Grand Sequence: the 2, 3, 4, 5, 9, 10, 11, 12. Consequently, bets on these numbers, mainly the prop bets, have higher odds/payouts. Low variation bets would be the 6/8 & all that attaches. Consequently, these bets pay lower. (I also know that the 4,5,9,10 are not prop bets per se. Let's just forget that discussion.)
All I'm asking is whether or not I'm correct in my understanding of variance from a non-math standpoint. This question is important to me because I've seen variance used in so many different contexts in which the writer attaches whatever meaning he wants to it. This confuses me. And, please. Don't flood me w/ a lot of numbers/tables, numbers out to the 5th & 6th decimal points like the Wizard does. All I want is confirmation/correction of what I've just said, w/o the math.
Wizard: Don't bother to refer me to one of your explanations. They do not work for me. If you can explain variance w/o all the numbers & tables, I'd appreciate it. You do not explain a math concept to me by using other "simpler" math concepts. I am math illiterate & not proud of it.
What I'm really getting at is an explanation of "high" and "low" variation BETS. I see a high variation bet as one made on a number that is less likely than the 7 to show up in the Grand Sequence: the 2, 3, 4, 5, 9, 10, 11, 12. Consequently, bets on these numbers, mainly the prop bets, have higher odds/payouts. Low variation bets would be the 6/8 & all that attaches. Consequently, these bets pay lower. (I also know that the 4,5,9,10 are not prop bets per se. Let's just forget that discussion.)
All I'm asking is whether or not I'm correct in my understanding of variance from a non-math standpoint. This question is important to me because I've seen variance used in so many different contexts in which the writer attaches whatever meaning he wants to it. This confuses me. And, please. Don't flood me w/ a lot of numbers/tables, numbers out to the 5th & 6th decimal points like the Wizard does. All I want is confirmation/correction of what I've just said, w/o the math.
Wizard: Don't bother to refer me to one of your explanations. They do not work for me. If you can explain variance w/o all the numbers & tables, I'd appreciate it. You do not explain a math concept to me by using other "simpler" math concepts. I am math illiterate & not proud of it.
July 21st, 2013 at 11:28:02 PM
permalink
Variance means that if you roll the dice 36 times you will NOT get:
one 2 and one 12
two 3s and two 11s
three 4s and three 10s
four 5s and four 9s
five 6s and five 8s
and six 7s.
...except on rare occasions
one 2 and one 12
two 3s and two 11s
three 4s and three 10s
four 5s and four 9s
five 6s and five 8s
and six 7s.
...except on rare occasions
July 21st, 2013 at 11:36:43 PM
permalink
Quote: Sonny44If you can explain variance w/o all the numbers & tables, I'd appreciate it.
S**t happens.
July 21st, 2013 at 11:58:17 PM
permalink
Quote: Sonny44What I'm really getting at is an explanation of "high" and "low" variation BETS..
Are you referring to the particular quality of dice (or die)
1+6, 2+5, 3+4, all = 7
6+6= 12 only one way to make 12 with two dice.
Whereas, if you had one of these, you would only roll one, but all equal opportunity?
Sanitized for Your Protection
July 22nd, 2013 at 12:58:15 AM
permalink
I too would enjoy a textual explanation rather than a mathematical one, no matter how simple and elegant the mathematical proof may be.
I think you are on the right track and your use of the term Grand Sequence is just fine: it is stately, venerated, beautiful, pure, elegant and could be likened to a stunningly beautiful woman descending a Grand Staircase. An ideal yet one most definitely from real life.
Variance is that which we notice while awaiting her descent of the staircase. That which takes away a bit of the grandeur, some extra years, some extra pounds, some tattered hemline. Imperfections, jewelry that is not so valuable ... until we notice that the woman is somewhat unattractive and the staircase is the one on the RMS TITANIC.
The Titanic was indeed real life but it was unexpected and unlikely. Only four men had died crossing the North Atlantic on steamships. Collisions at sea always had sufficient lifeboats contributed by the ship that was foundering as well as by nearby ships that came to her aid.
In an ideal world we see various sequences that while not identical to this exalted Grand Sequence are sufficiently close to it that we accept the results. Atsome point we turn and wish to reject the results and get off the sinking ship. This is the point where Lady Variance has let us down and in abandoning us has left us with the real world.
The Dice Table gives us the pure result. The samplings from the real world that are sufficiently close to the Dice Table's pure result are just fine. Its those rather few samples that we doubt and rage against our fate. The SnakeEyes is part of the Dice Table, but when SnakeEyes appears eight times in a row we consider it to be alien and apart from purity. The Seven can appear that many times, but Snake Eyes can't.
I think you are on the right track and your use of the term Grand Sequence is just fine: it is stately, venerated, beautiful, pure, elegant and could be likened to a stunningly beautiful woman descending a Grand Staircase. An ideal yet one most definitely from real life.
Variance is that which we notice while awaiting her descent of the staircase. That which takes away a bit of the grandeur, some extra years, some extra pounds, some tattered hemline. Imperfections, jewelry that is not so valuable ... until we notice that the woman is somewhat unattractive and the staircase is the one on the RMS TITANIC.
The Titanic was indeed real life but it was unexpected and unlikely. Only four men had died crossing the North Atlantic on steamships. Collisions at sea always had sufficient lifeboats contributed by the ship that was foundering as well as by nearby ships that came to her aid.
In an ideal world we see various sequences that while not identical to this exalted Grand Sequence are sufficiently close to it that we accept the results. Atsome point we turn and wish to reject the results and get off the sinking ship. This is the point where Lady Variance has let us down and in abandoning us has left us with the real world.
The Dice Table gives us the pure result. The samplings from the real world that are sufficiently close to the Dice Table's pure result are just fine. Its those rather few samples that we doubt and rage against our fate. The SnakeEyes is part of the Dice Table, but when SnakeEyes appears eight times in a row we consider it to be alien and apart from purity. The Seven can appear that many times, but Snake Eyes can't.
July 22nd, 2013 at 4:40:06 AM
permalink
Quote: Sonny44
What I'm really getting at is an explanation of "high" and "low" variation BETS. I see a high variation bet as one made on a number that is less likely than the 7 to show up in the Grand Sequence: the 2, 3, 4, 5, 9, 10, 11, 12. Consequently, bets on these numbers, mainly the prop bets, have higher odds/payouts. Low variation bets would be the 6/8 & all that attaches. Consequently, these bets pay lower. (I also know that the 4,5,9,10 are not prop bets per se. Let's just forget that discussion.)
The explanation you give for understanding how variance works in a gambling enviroment (from a non-mathematical way) sound about right.
The lower the probability of an succesful outcome of a bet (which usually means higher odds) also means higher variance.
Variance of 1 is for a bet that pays even money (or lose 1 bet only): example beting Red in Roulette.
Blackjack has variance of around 1.3: It is higher than the Even money Variance of 1 but close to it, because most of the time you win or lose 1 but a few times you also have BJ which you het paid 1.5 and Doubles, Splits where you can win/lose 2 or more units.
Variance of 0 means the Result is Certain. An example is Surrender in BJ where you lose 0.5 units.
July 22nd, 2013 at 5:25:25 AM
permalink
I think the theme song for Full House hints at the meaning.
https://www.youtube.com/watch?v=m23OOfPOGMA
https://www.youtube.com/watch?v=m23OOfPOGMA
I am a robot.
July 23rd, 2013 at 5:04:28 PM
permalink
An easy way to think of variance is to consider roulette bets and sitting at a roulette table, while say waiting a long time for a friend, and compare two possible methods (assuming the same number of total bets).
(1) You only bet on ONE number: then occasionally you will win £35 and normally lose £1. If it's your lucky day you'll get more than average hits and come out ahead.
(2) You only bet on TWELVE numbers: then quite often you'll win £2 and more often lose £1.
Statistically both methods lose the same on average but the big difference is you can win big (i.e. when it's your lucky day) betting on ONE number but can also lose by getting very few any payouts. On the second method you stand to win less but also lose less - the range of results is narrower.
(1) You only bet on ONE number: then occasionally you will win £35 and normally lose £1. If it's your lucky day you'll get more than average hits and come out ahead.
(2) You only bet on TWELVE numbers: then quite often you'll win £2 and more often lose £1.
Statistically both methods lose the same on average but the big difference is you can win big (i.e. when it's your lucky day) betting on ONE number but can also lose by getting very few any payouts. On the second method you stand to win less but also lose less - the range of results is narrower.
