August 4th, 2012 at 2:24:46 PM
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Is there any way to lower variance besides the following?

1. Lower bet size

2. Less bets

3. Less juice

4. Better winning %

1. Lower bet size

2. Less bets

3. Less juice

4. Better winning %

August 4th, 2012 at 2:30:30 PM
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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.

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

August 4th, 2012 at 2:37:44 PM
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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.

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

August 4th, 2012 at 2:48:43 PM
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#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.Quote:bigpete88Is there any way to lower variance besides the following?

1. Lower bet size

2. Less bets

3. Less juice

4. Better winning %

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)

August 4th, 2012 at 3:27:22 PM
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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).

August 4th, 2012 at 3:31:59 PM
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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)

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)

August 4th, 2012 at 4:30:22 PM
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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).

August 5th, 2012 at 11:55:57 AM
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7craps,

Thanks for correcting my number 2. I fully understand.

Thanks for correcting my number 2. I fully understand.

September 16th, 2012 at 2:43:22 PM
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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!!!

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!!!