Calculating variance w/spread

[NewbieCC]

I was wondering how to calculate variance when using a bet spread. My gut feeling is that it is NOT just the variance of the average of the bets, but that the higher bets contribute more to the variance then the smaller bets. How do I go about calculating this? Thanks in advance.

NewbieCC

 

[The Mayor]

Amazing question

I have to tell you, this is one of the best questions I ever remember seeing on this site.

What contributes to an increase in variance? It is not spread, it is an improper bet ramp!

Optimal ramps, betting the proper amount at the proper count, and not under or over-betting. If you bet too much at a low count, that increases variance. If you bet too little at a high count, that increases variance! IN fact, any improper bet size (relative to a kelley system) increases variance.

Assuming your cannot control the game you are playing, or the counting system you are using, the only other control you have is your bet size. That is a critical variable in the equation, and your ramp, betting the right amount at the count, is the only other variable you have control over!

Again, great question.

--Mayor

 

[Alexander Mundy]

Good answer also.

 

[Adam N. Subtractum]

funny you should ask...

I have been doing some research on this subject recently, and have found a few useful equations. Mason Malmuth has some excellent writings and equations useful in calculating variance and standard deviation, and some old school rec.gamblers even attempted to modify those methods, and I think in at least one case, someone succeeded. Not that Mason's equation wasn't correct in the first place (though there was much debate on this at the time), it was, it was just for larger samples (around 30 or more). I believe the modified version was better suited for smaller samples, but I'm just getting into it so I can't really say yet.

Of course all of the Mayor's comments were on point, error in any way, shape, or form will almost always contribute to increased variance.

ANS

 

[NewbieCC]

Re: Like all good questions . .

. . it seems to raise more questions than answers! (grin) Thanks for the info. I guess it is back to the books.

NewbieCC

 

[T-Hopper]

I think you mean RISK and not variance

 

[The Mayor]

Correct, of course

Risk is computed by looking at Variance, EV, and BR. Risk combines these, and each can be considered separately, but you are certainly correct in your statement as well.

 

[Rob McGarvey]

I think that you are doing well enough to understand this concept, rather than have the exact computations for it. Think of a high wind, and I mean above the ground. At ground zero it is calm. 100 feet up it's a breeze, 200 it's enough to get your coat moving, etc. Because you need a wild spread in multi deck, you have to fly high and take chances. By having a good "wing spread" of two or three hands, you can stabilize yourself. Single deck is like going in under the radar. Doing it online is like attacking the biggest vault in the world with tunnel warfare. ;>

Why would you like to know the numbers?

 

[Adam N. Subtractum]

How to calculate it...

The thoughts I brought up in my prior post pertain to approximation methods that help to simplify the estimation of standard deviation and variance over a period of time. If one has the time and necessity to do so, it can be calculated rather accurately.

A few weeks ago someone asked about figuring standard deviation without a simulation. I responded with the notion of executing a method utilizing the knowledge of frequency of advantage, or more ideally, true count, to determine the overall standard deviation for any spread. There's no reason this wouldn't work (assuming I was correct;-) for the variance, as variance itself is simply the square of the standard deviation.

Further research on this matter has uncovered that this methodology has been utilized by Michael Hall, as well as George C., so I'm pretty confident I was on the right track.

The following is an excerpt from Michael Hall's 1991 RoR article.

--------------------------------------------------

III. George C. on the Ruin Formula

From "The Ruin Formula", by George C., Blackjack Forum, September 1988...

George shows how to compute variance, like so:

6 Decks Strip Rules w/DDAS, 75% Penetration

Advantage__Hands/Hour_______Bet Squared $__Product $
------------- --------------- ------------------ ---------------
__-3.4%_______1.0_______________10000______10000
__-2.9%_______2.0_______________10000______20000
__-2.4%_______3.0_______________10000______30000
__-1.9%_______4.0_______________10000______40000
__-1.4%_______8.0_______________10000______80000
__-0.9%______13.0_______________10000_____130000
__-0.4%______35.5_______________10000_____355000
___0.1%______13.0_______________40000_____520000
___0.6%_______8.0______________250000____2000000
___1.1%_______4.0______________562500____2250000
___1.6%_______3.0_____________2250000____6750000
___2.1%_______2.0_____________2250000____4500000
___2.6%_______2.0_____________2250000____4500000
___3.1%_______1.0_____________2250000____2250000
___3.6%_______0.5_____________2250000____1125000

Sum of Products = 24560000
Sq Root of Products = 4956
Times 1.1 = 5451 = Hourly standard deviation in $

[snip]

This is consistent with what I posted the other day about
computing variance from frequency distributions, so it
looks like I was probably right. -MH

-------------------------------------------

It's clear to see that we can derive other figures from the given info, such as advantage and win rate, and much more. The main factor is accuracy of the input, which will consequently result in corresponding accuracy in calculations.

ANS

 

[Cyrano]

I've been wrestling with something and I would like to hear some opinions on this: what if we take a modified version of the Sharpe Ratio and apply it to various bet ramps, as opposed to "optimal bet ramps". Is it possible to come up with a "clearer picture" of what the new risk-adjusted returns would be? Is this comparing apples to oranges?

 

[Adam N. Subtractum]

A modified Sharp Ratio...

...is what you should be using, wether it's SCORE, or my preference, ROI. Also, the reason optimal spreads are usually used in comparisons, as far as I know, is so the effect of rounding doesn't alter results.

ANS