13.5% ror question?
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in cvcx help it says:
"Bankroll Growth - This is the default method of bet optimization. Bets are calculated to maximize bankroll growth. This is the same as calculating bets for the highest desirability index with a risk of ruin at about 13.5%.
......
Set Kelly Factor - With this method, you can set your own desired Kelly Factor on the Bankroll tab. The bets will be calculated to maximize the Desirability Index based on your desired Kelly Betting. A Kelly Factor of 1.0 equates to a risk of 13.5%. A factor of 0.5 means that you will be betting with double the bankroll required for a risk of 13.5%. In a perfect world, this would mean that yours bets would be half as much. But, this is not quite true because of bet simplification and the inability to bet fractions of a dollar."
now still the question of how come a 13.5% ROR is the (i guess one would call it) standard, i wonder as well.
there's more on this sort of stuff in the link below:
http://www.bjrnet.com/articles/kellyfaq.htm
"Bankroll Growth - This is the default method of bet optimization. Bets are calculated to maximize bankroll growth. This is the same as calculating bets for the highest desirability index with a risk of ruin at about 13.5%.
......
Set Kelly Factor - With this method, you can set your own desired Kelly Factor on the Bankroll tab. The bets will be calculated to maximize the Desirability Index based on your desired Kelly Betting. A Kelly Factor of 1.0 equates to a risk of 13.5%. A factor of 0.5 means that you will be betting with double the bankroll required for a risk of 13.5%. In a perfect world, this would mean that yours bets would be half as much. But, this is not quite true because of bet simplification and the inability to bet fractions of a dollar."
now still the question of how come a 13.5% ROR is the (i guess one would call it) standard, i wonder as well.
there's more on this sort of stuff in the link below:
http://www.bjrnet.com/articles/kellyfaq.htm
I do too lol.
All I know is plug "=EXP(-2/1)" into an Excel cell and 0.13534 is the result.
The "1" means "Full-Kelly" factor.
Change it to "=EXP(-2/0.5)" and the risk is now 0.13534*.13534=1.83%.
Kelly maximizes the logarythmic growth of your roll - it does not maximize EV.
It takes both risk and reward into consideration.
Take a $10K roll betting "Full-Kelly". It should have an ROR of about 13.53%.
Double roll to $20K and your ROR will go down but how much you make per round, how much your SD per round is, will not change since you are still betting, say, $10 as a unit.
So you are not really "underbetting" in any way because win rate and SD per round have not changed. All you have done is lessen the %logarhythmic growth of your roll which isn't surprising because you now have twice as much roll.
Or. like you say, you could halve your $unit from say $10 to $5k and keep total $roll the same (say $10K) and your risk will go down to the same 1.83% but of course now, while your W/L% remains the same, your SD/rd and EV/rd will halve. But youi still have twice as many units in roll that way.
"EXP" and "LN" might be functions in Excel that are just the opposite sides of the same coin lol.
Basically, I'm not really sure because, like maybe many, I have no real understanding of all this, but I'm not sure if there is anything better than "exponential growth".
Take any sheet of mine and double $roll. The new ROR will become "original ROR*original ROR" and EV and SD/rd will be the same.
Halve the $unit while keeping total roll the same, the new ROR will also be "original ROR*original ROR" but now EV and SD/rd will halve.
Moral: Take a Full-Kelly $roll and double it and you are fine lol. Risk should now be around 2% or less lol.
All I know is plug "=EXP(-2/1)" into an Excel cell and 0.13534 is the result.
The "1" means "Full-Kelly" factor.
Change it to "=EXP(-2/0.5)" and the risk is now 0.13534*.13534=1.83%.
Kelly maximizes the logarythmic growth of your roll - it does not maximize EV.
It takes both risk and reward into consideration.
Take a $10K roll betting "Full-Kelly". It should have an ROR of about 13.53%.
Double roll to $20K and your ROR will go down but how much you make per round, how much your SD per round is, will not change since you are still betting, say, $10 as a unit.
So you are not really "underbetting" in any way because win rate and SD per round have not changed. All you have done is lessen the %logarhythmic growth of your roll which isn't surprising because you now have twice as much roll.
Or. like you say, you could halve your $unit from say $10 to $5k and keep total $roll the same (say $10K) and your risk will go down to the same 1.83% but of course now, while your W/L% remains the same, your SD/rd and EV/rd will halve. But youi still have twice as many units in roll that way.
"EXP" and "LN" might be functions in Excel that are just the opposite sides of the same coin lol.
Basically, I'm not really sure because, like maybe many, I have no real understanding of all this, but I'm not sure if there is anything better than "exponential growth".
Take any sheet of mine and double $roll. The new ROR will become "original ROR*original ROR" and EV and SD/rd will be the same.
Halve the $unit while keeping total roll the same, the new ROR will also be "original ROR*original ROR" but now EV and SD/rd will halve.
Moral: Take a Full-Kelly $roll and double it and you are fine lol. Risk should now be around 2% or less lol.
No.
It's a square root function, not a linear function.
But I know what you say sounds "logical" lol.
EV is linear but SD isn't.
Make 10 cents/rd with an SD of 34$rd.
In 100 rounds EV will equal $10. That's linear.
In 100 rounds SD will equal $34/round*square-root of 100 rounds=$340.
Doubling roll will have no effect on how much you make per round or it's variance.
Doubling roll just means you will still have won $10 100 rounds later and you still will have an SD of $340 100 rounds later but having that $340 SD 100 rounds later is a lot smaller percentage of your original $10K roll than if you had had a $20K original roll.
Understanding that EV increases alot faster per round than SD does is one of those keys to the kingdom lol.
Above, EV has increased 100X in 100 rounds but SD has only increased 10X.
Make any sense?
It's a square root function, not a linear function.
But I know what you say sounds "logical" lol.
EV is linear but SD isn't.
Make 10 cents/rd with an SD of 34$rd.
In 100 rounds EV will equal $10. That's linear.
In 100 rounds SD will equal $34/round*square-root of 100 rounds=$340.
Doubling roll will have no effect on how much you make per round or it's variance.
Doubling roll just means you will still have won $10 100 rounds later and you still will have an SD of $340 100 rounds later but having that $340 SD 100 rounds later is a lot smaller percentage of your original $10K roll than if you had had a $20K original roll.
Understanding that EV increases alot faster per round than SD does is one of those keys to the kingdom lol.
Above, EV has increased 100X in 100 rounds but SD has only increased 10X.
Make any sense?
i get the part where what your saying is right and everything.
just one thing that throws me besides mostly being confused by it all, lol.
that being using terms like sd/round or standard deviation per round.
maybe it's just me but from a technical writing perspective it seems misleading. like for instance if i'm writing about the speed something is traveling then i can say such and such was going Xmiles/hr. that tells the person reading that ok if 100 hours goes by then such and such went 100*Xmiles, sort of thing.
but if some one writes sd/rnd, the same type of maths and units canceling rules don't follow. makes me think that sd/rnd is a misnomer.
no big deal, just as confused as i can be i guess that sort of thing can make me even more confused. like, i dunno i guess i'd want to see the term sd/rnd written in a different way. i mean heck, like for Xmiles/hr we know that miles is a physical something and hours is a physical some thing. but for sd/rnd far as i know a round is a physical something but a standard deviation maybe isn't a physical something. well i guess even the term round can be fairly nefarious, where one round might mean who knows how many hands or cards.
but the term standard deviation is even more abstract or convoluted. it's like, i think where you gotta take the square root of the variance to even get it. and variance is convoluted enough cause what do you got to do to get it? square the differences from the mean or ev or something like that.
so i dunno what does std/rnd mean? does it mean some range of the chances of some result happening with respect to ev for a given round?
just one thing that throws me besides mostly being confused by it all, lol.
that being using terms like sd/round or standard deviation per round.
maybe it's just me but from a technical writing perspective it seems misleading. like for instance if i'm writing about the speed something is traveling then i can say such and such was going Xmiles/hr. that tells the person reading that ok if 100 hours goes by then such and such went 100*Xmiles, sort of thing.
but if some one writes sd/rnd, the same type of maths and units canceling rules don't follow. makes me think that sd/rnd is a misnomer.
no big deal, just as confused as i can be i guess that sort of thing can make me even more confused. like, i dunno i guess i'd want to see the term sd/rnd written in a different way. i mean heck, like for Xmiles/hr we know that miles is a physical something and hours is a physical some thing. but for sd/rnd far as i know a round is a physical something but a standard deviation maybe isn't a physical something. well i guess even the term round can be fairly nefarious, where one round might mean who knows how many hands or cards.
but the term standard deviation is even more abstract or convoluted. it's like, i think where you gotta take the square root of the variance to even get it. and variance is convoluted enough cause what do you got to do to get it? square the differences from the mean or ev or something like that.
so i dunno what does std/rnd mean? does it mean some range of the chances of some result happening with respect to ev for a given round?
sagefr0g said:
i get the part where what your saying is right and everything.
just one thing that throws me besides mostly being confused by it all, lol.
that being using terms like sd/round or standard deviation per round.
maybe it's just me but from a technical writing perspective it seems misleading. like for instance if i'm writing about the speed something is traveling then i can say such and such was going Xmiles/hr. that tells the person reading that ok if 100 hours goes by then such and such went 100*Xmiles, sort of thing.
but if some one writes sd/rnd, the same type of maths and units canceling rules don't follow. makes me think that sd/rnd is a misnomer.
no big deal, just as confused as i can be i guess that sort of thing can make me even more confused. like, i dunno i guess i'd want to see the term sd/rnd written in a different way. i mean heck, like for Xmiles/hr we know that miles is a physical something and hours is a physical some thing. but for sd/rnd far as i know a round is a physical something but a standard deviation maybe isn't a physical something. well i guess even the term round can be fairly nefarious, where one round might mean who knows how many hands or cards.
but the term standard deviation is even more abstract or convoluted. it's like, i think where you gotta take the square root of the variance to even get it. and variance is convoluted enough cause what do you got to do to get it? square the differences from the mean or ev or something like that.
so i dunno what does std/rnd mean? does it mean some range of the chances of some result happening with respect to ev for a given round?
just one thing that throws me besides mostly being confused by it all, lol.
that being using terms like sd/round or standard deviation per round.
maybe it's just me but from a technical writing perspective it seems misleading. like for instance if i'm writing about the speed something is traveling then i can say such and such was going Xmiles/hr. that tells the person reading that ok if 100 hours goes by then such and such went 100*Xmiles, sort of thing.
but if some one writes sd/rnd, the same type of maths and units canceling rules don't follow. makes me think that sd/rnd is a misnomer.
no big deal, just as confused as i can be i guess that sort of thing can make me even more confused. like, i dunno i guess i'd want to see the term sd/rnd written in a different way. i mean heck, like for Xmiles/hr we know that miles is a physical something and hours is a physical some thing. but for sd/rnd far as i know a round is a physical something but a standard deviation maybe isn't a physical something. well i guess even the term round can be fairly nefarious, where one round might mean who knows how many hands or cards.
but the term standard deviation is even more abstract or convoluted. it's like, i think where you gotta take the square root of the variance to even get it. and variance is convoluted enough cause what do you got to do to get it? square the differences from the mean or ev or something like that.
so i dunno what does std/rnd mean? does it mean some range of the chances of some result happening with respect to ev for a given round?
Can you see "time" or "distance"? Will a plane travelling 100 mph every hour of every day in 2003 travel the same distance in 2004? If I asked you how far that plane would travel in a year, you'd have to ask me in what year lol.
If you measured each "day" by the sun and earth's orbit, a "day" no longer would have exactly 24 hours in it lol.
Is wind a physical thing? What if that plane encountered wind traveling east and west? It's still travelling 100 mph but will travel farther in an hour if downwind.
Now you have to ask me both what year is it and what's the wind :grin:
Can you see EV?
If you like 100 mph*8 hours=800 miles traveled, then just use variance instead of SD. 100 rounds with a variance of $8/per round=$800 total variance.
A "round" is not nefarious lol. When you have played versus 1 dealer upcard you have played a round.
House advantage is always expressed as a % of initial bet on one spot. EV is always expressed the same way. One splits to 4 hands, doubles each, one has played one round. If the HA is 0.5% and you initially bet $10, even though on that "round" you played 4 "hands" and had $80 bet in total, your EV is $10*-0.5. Not -0.5*$80.
Man do I digress lol.
So "does SD mean some range of the chances of some result happening with respect to ev for a given round?".
Yes lol.
Why are you asking stuff I know you already know the answer to lmao.
In sims, think of the "avearge bet" as a "flat-bet" - it's as if one bet that amount every round as one's initial bet.
So "SD/round" just means, as always, one's results will be within that amount from "EV/round" 68% of the time etc.
lol, i dunno it's alien stuff to me. your explainations i dotted out really do help and make sense.
i just have a problem with the terminology std/rnd where when you multiply the term by some number of rounds you don't get the number of standard deviations for that many rounds sort of thing. i guess it's just implicit when dealing with standard deviation that one has to multiply by the square root of the number of rounds instead of just the number of rounds.:whip:
wouldn't the units of the term then end up (std/rnd)* [square root (rnd)] = (std)*[square root (rnd)/(rnd)]?
factor out the std unit and you end up with square root rnd = (square root rnd)/rnd or rearanging you get rnd* square root (rnd) = square root (rnd).
i just have a problem with the terminology std/rnd where when you multiply the term by some number of rounds you don't get the number of standard deviations for that many rounds sort of thing. i guess it's just implicit when dealing with standard deviation that one has to multiply by the square root of the number of rounds instead of just the number of rounds.
:whip:wouldn't the units of the term then end up (std/rnd)* [square root (rnd)] = (std)*[square root (rnd)/(rnd)]?
factor out the std unit and you end up with square root rnd = (square root rnd)/rnd or rearanging you get rnd* square root (rnd) = square root (rnd).
Yep.
That's basically where my "faith" begins lol.
Believe me, as little as I understand, it is an act of faith to me too :grin:
I have alot of fath lol - you think I understand why I am supposed to double 11 vs Ace in S17 1D and 2D games but not 4D games :grin:? Trust me, I don't really know why.
If I invented this stuff, I'd actually maybe understand why. I'm not Newton sitting under a tree watching an apple fall and discovering gravity or something.
I'm not Archimedes sitting in a bathtup discovering my body displaces the same volume of water as my body when it's submerged and exclaiming "Eureka" and realizing its implications for density etc. I'm fascinated my farts still smell when the bubbles reach the surface :grin:
You and your "whys" lol. Like you, I ask "why" for as long as I can understand the answer, at least a little bit anyway lol.
When I no longer understand it, which always happens eventually, I just do it anyway.
I'm a regurgitator. A copy-cat. A charade.
I can recite 100 lines of "Odysseus" in Greek but it doesn't mean I know what I'm saying. I could write them in Greek too but I still wouldn't know what I'm writing lol.
So, if 1SD is 4 units/round, just know in 100 rounds it's 40 units, and in 10,000 rounds its 400 units.
Unless maybe you're back-counting lmao.
And forget about your last paragraph as an act of faith lmao.
That's basically where my "faith" begins lol.
Believe me, as little as I understand, it is an act of faith to me too :grin:
I have alot of fath lol - you think I understand why I am supposed to double 11 vs Ace in S17 1D and 2D games but not 4D games :grin:? Trust me, I don't really know why.
If I invented this stuff, I'd actually maybe understand why. I'm not Newton sitting under a tree watching an apple fall and discovering gravity or something.
I'm not Archimedes sitting in a bathtup discovering my body displaces the same volume of water as my body when it's submerged and exclaiming "Eureka" and realizing its implications for density etc. I'm fascinated my farts still smell when the bubbles reach the surface :grin:
You and your "whys" lol. Like you, I ask "why" for as long as I can understand the answer, at least a little bit anyway lol.
When I no longer understand it, which always happens eventually, I just do it anyway.
I'm a regurgitator. A copy-cat. A charade.
I can recite 100 lines of "Odysseus" in Greek but it doesn't mean I know what I'm saying. I could write them in Greek too but I still wouldn't know what I'm writing lol.
So, if 1SD is 4 units/round, just know in 100 rounds it's 40 units, and in 10,000 rounds its 400 units.
Unless maybe you're back-counting lmao.
And forget about your last paragraph as an act of faith lmao.
i think i see my mistake where i was askin, wouldn't the units of the term then end up (std/rnd)* [square root (rnd)] = (std)*[square root (rnd)/(rnd)]?
i think what it is, is that when you do the mathematical operation that the math only operates on the numbers not the units. duh
so really in my question it would be (1std)/(1rnd)* square root(1)rnd = 1(std/rnd)*1(rnd) = 1sd = sd .
edit:
but i'm still confused on this units conversion thing cause i know there is stuff like square feet and meters^2....
like isn't 2M * 2M = 4M^2 (ie four meters squared)
i think what it is, is that when you do the mathematical operation that the math only operates on the numbers not the units. duh
so really in my question it would be (1std)/(1rnd)* square root(1)rnd = 1(std/rnd)*1(rnd) = 1sd = sd .
edit:
but i'm still confused on this units conversion thing cause i know there is stuff like square feet and meters^2....
like isn't 2M * 2M = 4M^2 (ie four meters squared)
Last edited:
sagefr0g said:
i think i see my mistake where i was askin, wouldn't the units of the term then end up (std/rnd)* [square root (rnd)] = (std)*[square root (rnd)/(rnd)]?
i think what it is, is that when you do the mathematical operation that the math only operates on the numbers not the units. duh
so really in my question it would be (1std)/(1rnd)* square root(1)rnd = 1(std/rnd)*1(rnd) = 1sd = sd .
edit:
but i'm still confused on this units conversion thing cause i know there is stuff like square feet and meters^2....
like isn't 2M * 2M = 4M^2 (ie four meters squared)
i think what it is, is that when you do the mathematical operation that the math only operates on the numbers not the units. duh
so really in my question it would be (1std)/(1rnd)* square root(1)rnd = 1(std/rnd)*1(rnd) = 1sd = sd .
edit:
but i'm still confused on this units conversion thing cause i know there is stuff like square feet and meters^2....
like isn't 2M * 2M = 4M^2 (ie four meters squared)
I've never had a head for variables anyway lol. All those x's and y's. I need 2's and 4's lol.
So maybe it might make sense lol.
Whether SD/rd is in $'s or units, the math is the same as far as I know.
But, I was thinking of what you said when I got up today, for some reason, when you said " variance is convoluted enough cause what do you got to do to get it? square the differences from the mean or ev or something like that."
summed up so perfectly my understanding of the subject lmao.
However, I sort of think, all that squaring stuff doesn't really relate to geometry and the area of a square. Although I would call a square 2M on each side has an area of 4 square meters rather than 4 meters squared lol.
I think that squaring stuff is just, maybe, some kind of convenience so one doesn't have to deal with a negative number when it is left of expected.
So, maybe with a mean of 6 and one result at 4, it's obvious it varies by "-2" from the mean, just as a result of 8 would also vary by "+2" from the mean.
So, both are 2 things away from the mean - they "vary", the total variance in both cases is "2", 8 is as far away from 6 as 4 is far away from 6, the same distance from the mean.
So if you square "-2" or "+2", you still get 4. You can't take the square root of a negative number becasue two negative numbers when multiplied together always produces a positive number. (Another act of faith on my part lol.).
So, in this case, whether the result is "4" or "8", the SD is square root of 2 since the variance is "2" in either case.
And, before you ask, I have no idea why 1SD always means a result, either that far left or right from expected, will fall within that range from expected 68%ish of the time lol. Maybe something to do with a bell-shaped curve wherein it is assumed all results are equally likely to occur. Or something.
PS. I did really, really bad at geometry. And even worse at probability. God how I hated probabilty. 40 years later and that's all I remember about it. I hated it. Still do. Never took a statistics course.
Which is, of course, the ultimate irony here. I can add, subtract, multiply and divide. I much prefer whole numbers but I can divide by fractions if I have to lol. I couldn't take the square root of 2, manually, if you paid me.
That's pretty much it.
just confused is all
the part that's throwing me is what i'm calling units.
unfortunately in blackjack we call units what we bet with and
on the other hand when your doing unit conversion stuff you
might be talking about other kinds of units. so in this case
i'm tryin to figure out how to convert units that are standard
deviation and units that are rounds. namely sd/rnd . especially the rnd or rounds part.
like the stuff in link:
http://www.unitconversion.org/
like if you look at aceleration you'll notice seconds are
squared, sort of thing.
makes me wonder if you take the square root of a round do you
gotta take the square root of that unit? ie. square root (rnd)
or would it just be square root of the number of rounds but you
don't mess with the rnd unit?
that's where i'm lost, lol.
i'm thinking it must be you only take the square root of the number and not the unit (ie. rnd), which is what sort of makes me think sd/rnd is sort of a misnomer.
yeah lmao, it's this standard deviation stuff is derived from
variance which is derived from results and how they differ from
the average result.
http://www.mathsisfun.com/data/standard-deviation.html
yeah, yeah a matter of convenience sort of thing. so when you
know standard deviation stuff you can talk about blackjack
stuff more in the abstract to where you have a abstract
standard that relates 'across the board' sort of thing. you can
say such and such game has this standard deviation and such and
such other game has this standard deviation, so then you got
like a yard stick to compare games with. i guess with variance
it would be more difficult to talk about it all and make
comparisons and stuff.
excepting for that imaginary stuff, right?
http://en.wikipedia.org/wiki/Imaginary_unit
what ever, lol, just thought i'd throw that nonsense in there,
confuse the issue, lmao.
lmao, i think i already ask that and i think i forgot the
answer. maybe those numbers, 68.27%, 95.45% & 99.73% are just
arbitrary numbers some genius picked out far as i know. more
convienienc maybe, lol. at this point those numbers are as much
a mystery to me as the ROR 13.5% number is. but i think the
13.5% number has something to do with the stuff in this link:
http://www.bjrnet.com/articles/kellyfaq.htm
where they talk about, certainty equivalents and utility stuff
"Q4: How can certainty equivalents be used in a practical
setting?
A4: The need for the use of logarithms and exponentiation makes
the calculations quite difficult when analyzing a complex game
such as blackjack. A formula for approximating the certainty
equivalent (that is very accurate when your advantage or
disadvantage is 10% or less) is
CE = E - V/2kB
where CE is the certainty equivalent, E is the expected
winnings, V is the variance of those winnings (i.e. the square
of the standard deviation), B is your bankroll and k is your
Kelly Number, a measure of the amount of risk you wish to take.
The Kelly criterion corresponds to k = 1.0 and in this
situation this formula closely approximates calculations based
upon the log(x) utility function. When k is not 1, the utility
function that you are approximating is x^(1-1/k) / (1-1/k).
For the $200 coin flip above which has E = $20 and V = $$39600
(the standard deviation is $198.997) the formula gives a CE =
$13.40 which is quite close to the exact value of $13.38
derived above."
what ever, lol.
but maybe the 68% stuff could be gotten from integrating the
bell curve sort of thing where you get the area under the curve
or what ever: http://en.wikipedia.org/wiki/Integral
lmao, i did really, really good in geometry but never took
probabilty cause i dropped out of high school. but the worst
geometry i ever messed with was called analytic geometry. geesh
that stuff is hairy. never could fathom trigonomety either. so
but then in university they were kind enough to try and teach
me schrodinger's equation with out me having a clue what
probability was. go figure, lmao.
hey but i can add, subtract, multiply and divide if i got a
calculator and even divide by fractions if i go back and look
up the rule.
i got the chance now cause i'm almost sixty and the local
university lets sixty year olds take free courses to take a
free probability course. i might just do it for laughs, only
thing is they make you interview with the professor first.
lmao, what am i gonna tell him when he asks why i want to take
the course? interested in gambling, lmao.
maybe in the interview i should instead tell him so i can get
the answer to the question, if you take the square root of some
number of rounds do you have to take the square root of that
unit (ie square root of round).
probably he'll kick me out and say no class for you, lol.
the part that's throwing me is what i'm calling units.
unfortunately in blackjack we call units what we bet with and
on the other hand when your doing unit conversion stuff you
might be talking about other kinds of units. so in this case
i'm tryin to figure out how to convert units that are standard
deviation and units that are rounds. namely sd/rnd . especially the rnd or rounds part.
like the stuff in link:
http://www.unitconversion.org/
like if you look at aceleration you'll notice seconds are
squared, sort of thing.
makes me wonder if you take the square root of a round do you
gotta take the square root of that unit? ie. square root (rnd)
or would it just be square root of the number of rounds but you
don't mess with the rnd unit?
that's where i'm lost, lol.
i'm thinking it must be you only take the square root of the number and not the unit (ie. rnd), which is what sort of makes me think sd/rnd is sort of a misnomer.
yeah lmao, it's this standard deviation stuff is derived from
variance which is derived from results and how they differ from
the average result.
http://www.mathsisfun.com/data/standard-deviation.html
yeah, yeah a matter of convenience sort of thing. so when you
know standard deviation stuff you can talk about blackjack
stuff more in the abstract to where you have a abstract
standard that relates 'across the board' sort of thing. you can
say such and such game has this standard deviation and such and
such other game has this standard deviation, so then you got
like a yard stick to compare games with. i guess with variance
it would be more difficult to talk about it all and make
comparisons and stuff.
excepting for that imaginary stuff, right?
http://en.wikipedia.org/wiki/Imaginary_unit
what ever, lol, just thought i'd throw that nonsense in there,
confuse the issue, lmao.
lmao, i think i already ask that and i think i forgot the
answer.
maybe those numbers, 68.27%, 95.45% & 99.73% are just arbitrary numbers some genius picked out far as i know. more
convienienc maybe, lol. at this point those numbers are as much
a mystery to me as the ROR 13.5% number is. but i think the
13.5% number has something to do with the stuff in this link:
http://www.bjrnet.com/articles/kellyfaq.htm
where they talk about, certainty equivalents and utility stuff
"Q4: How can certainty equivalents be used in a practical
setting?
A4: The need for the use of logarithms and exponentiation makes
the calculations quite difficult when analyzing a complex game
such as blackjack. A formula for approximating the certainty
equivalent (that is very accurate when your advantage or
disadvantage is 10% or less) is
CE = E - V/2kB
where CE is the certainty equivalent, E is the expected
winnings, V is the variance of those winnings (i.e. the square
of the standard deviation), B is your bankroll and k is your
Kelly Number, a measure of the amount of risk you wish to take.
The Kelly criterion corresponds to k = 1.0 and in this
situation this formula closely approximates calculations based
upon the log(x) utility function. When k is not 1, the utility
function that you are approximating is x^(1-1/k) / (1-1/k).
For the $200 coin flip above which has E = $20 and V = $$39600
(the standard deviation is $198.997) the formula gives a CE =
$13.40 which is quite close to the exact value of $13.38
derived above."
what ever, lol.
but maybe the 68% stuff could be gotten from integrating the
bell curve sort of thing where you get the area under the curve
or what ever: http://en.wikipedia.org/wiki/Integral
lmao, i did really, really good in geometry but never took
probabilty cause i dropped out of high school. but the worst
geometry i ever messed with was called analytic geometry. geesh
that stuff is hairy. never could fathom trigonomety either. so
but then in university they were kind enough to try and teach
me schrodinger's equation with out me having a clue what
probability was. go figure, lmao.
hey but i can add, subtract, multiply and divide if i got a
calculator and even divide by fractions if i go back and look
up the rule.
i got the chance now cause i'm almost sixty and the local
university lets sixty year olds take free courses to take a
free probability course. i might just do it for laughs, only
thing is they make you interview with the professor first.
lmao, what am i gonna tell him when he asks why i want to take
the course? interested in gambling, lmao.
maybe in the interview i should instead tell him so i can get
the answer to the question, if you take the square root of some
number of rounds do you have to take the square root of that
unit (ie square root of round).
probably he'll kick me out and say no class for you, lol.