bigpete88
bigpete88
Joined: Mar 8, 2011
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August 4th, 2012 at 2:24:46 PM permalink
Is there any way to lower variance besides the following?

1. Lower bet size

2. Less bets

3. Less juice

4. Better winning %
EvenBob
EvenBob
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August 4th, 2012 at 2:30:30 PM permalink
Some people think using more than one handicapper
lowers the variance. That way your variance isn't
tied to that of just one guy. All handicappers have
winning streaks, finding one and then finding
another after that can work wonders.
"It's not enough to succeed, your friends must fail." Gore Vidal
EvenBob
EvenBob
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August 4th, 2012 at 2:37:44 PM permalink
For instance, here's the guy I follow for baseball..
He's got a 61% hit rate going this summer, though
he's starting to falter. The same thing happened to
him last year at this time.
"It's not enough to succeed, your friends must fail." Gore Vidal
7craps
7craps
Joined: Jan 23, 2010
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Thanks for this post from:
onenickelmiracle
August 4th, 2012 at 2:48:43 PM permalink
Quote: bigpete88

Is there any way to lower variance besides the following?

1. Lower bet size

2. Less bets

3. Less juice

4. Better winning %

#2 is not correct IF you do have an edge, you want as many bets as you can possibly make, with the largest possible bankroll to RoR.

That way EV (positive in your case) will quickly swamp variance as the number of bets INCREASE, not decrease.

Even the Wizard has said this.
I do not have a link at the moment.

"The longer you play, the ratio of money lost to money bet will get closer to the expectation for that game."

So IF you have an edge "the ratio of money won to money bet will get closer to the expectation for that game"
So lots of bets and lots of money bet (they go hand in hand) is what the +EV player should strive for.
winsome johnny (not Win some johnny)
MangoJ
MangoJ
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August 4th, 2012 at 3:27:22 PM permalink
Quote: 7craps

#2 is not correct IF you do have an edge, you want as many bets as you can possibly make

[...]

"The longer you play, the ratio of money lost to money bet will get closer to the expectation for that game."



You need to distinguish between "total variance" and the "ratio of your net wins (or losses) with your net stakes".

Your expected wins (or losses) increase linear with the number of bets when playing with positive (or negative) EV.
Whereas the total variance always *increases* - but much slower. It increases with the square root of the number of bets (all for constant betsize and EV).

Hence the contradictory discussion whether variance increases or decreases.
However there is no contradiction: the total variance always *increases*, while the ratio always *decreases*, since the variance growths slower than your expected wins (or losses).

Short example:
If your very first bet is $100 win or lose bet on even odds, then the total variance is roughly $100 around whatever your EV is. Say if you lose, since nothing will ever bring back your initial $100, your lifetime total variance must always be larger than those lost $100 - around any EV. In fact a second $100 bet will increase the total variance to about $144 around EV.

Once you get over the point where your EV is larger than your total variance, you are getting into the "closer to expectation" zone. The number of bets needed is called N0. If you make those N0 bets, you have a ~67% chance of being ahead (if EV is positive).
7craps
7craps
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August 4th, 2012 at 3:31:59 PM permalink
Using your 2500 bets example at 2% edge
http://wizardofvegas.com/forum/gambling/sports/10840-another-math-question/#post169697

This is using the normal distribution.
(When I have more time I can put more math and the formulas)
EV = 0.02*2500*110 = $5500
SD = $5237.6426 ( formula can be found here. I am lazy tody
http://wizardofvegas.com/forum/gambling/tables/1213-variance-in-craps/)

EV and SD about the same
1,2,3 SD
10737.64
15975.29
21212.93

-1,-2,-3SD
262.36
-4975.29
-10212.93

You have the same chance of being UP 15975.29 as you do being DOWN -4975.29


Now 12,500 bets
EV: $27499.99925
SD: $11711.72489

1,2,3 SD
39211.72414
50923.44904
62635.17393
-1,-2,-3SD
15788.27436
4076.54946
-7635.175434
You have the same chance of being UP 50923 as you do being UP 4076.

The 3SD value can still kill.

Cant make 12,500 bets with a 2% edge???
Very possible.
So cappers bet more when their edge is higher.
Just as Kelly says to do, IF you believe in Kelly betting in Sports.

More bets with a hgher average bet.
Solves the problem to a certain degree but the variance does go up when the bet increases.
The win rate must also.
But I already spelled that out.


25,000 bets
Hey look, No negative values for the -3SD.
EV: $54999.9985
SD: $16562.88018 way LESS than the EV.

1,2,3 SD
71562.87868
88125.75887
104688.6391
-1,-2,-3SD
38437.11832
21874.23813
5311.357945


Casinos can easily book 25,000 bets in one day.
Can one player?

So one player needs many days and many bets to over come the variance.
(and the proper bankroll to ride out the downswings)
winsome johnny (not Win some johnny)
MangoJ
MangoJ
Joined: Mar 12, 2011
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August 4th, 2012 at 4:30:22 PM permalink
Thanks for your data. For a 2% advantage even bet one would calculate N0 to sqrt(N0) = 2% * N0, or N0 = 2500 - which agrees perfectly with your numbers (EV=$5500 and SD=$5238 for 2500 bets).
bigpete88
bigpete88
Joined: Mar 8, 2011
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August 5th, 2012 at 11:55:57 AM permalink
7craps,

Thanks for correcting my number 2. I fully understand.
bigpete88
bigpete88
Joined: Mar 8, 2011
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September 16th, 2012 at 2:43:22 PM permalink
Can anyone answer the following?

What is the variance difference of 3% ROI vs 9% ROI in sports betting. I am guesssing that it is a huge difference.

Also, using a 2% bet size of bankroll if that matters.

Thanks MustangSally and 7Craps!!! Thanks again!!!
MangoJ
MangoJ
Joined: Mar 12, 2011
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September 16th, 2012 at 2:54:20 PM permalink
Could you be more clear, variance of your bet ? variance of your bankroll ? ROI at what odds ?

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