A Kelly Conundrum

Dopple

Well-Known Member
#1
Kelly says 1% of BR, adjusted for SD, is the optimum bet. I read in BJA3 a suggested ramp is 1,2,4,6,66@TC1 to 5 on pg 4. How can an exponentially increasing ramp be in accordance with Kelly. Your edge at T5 is not 12x your edge at T1. There is some SD difference but not of such magnitude. This suggested ramp is clearly strongly exponential as opposed to the roughly linear Kelly dictated ramp from my perspective. I have the Bible in my hand and I am already off on the wrong foot. Help! My math is rough but my hands are clean.
 

gronbog

Well-Known Member
#2
For blackjack, full Kelly is ADVANTAGE x BR / VARIANCE. Where did you get the flat 1% figure. If you think about it, if you used a flat percentage of BR, you would never raise your bet unless your bankroll grew.
 

DSchles

Well-Known Member
#3
"Kelly says 1% of BR, adjusted for SD, is the optimum bet."

Have no idea where you got this from. It says no such thing.

"I read in BJA3 a suggested ramp is 1,2,4,6,66@TC1 to 5 on pg 4."

You might want to wait and read a little further. See Chapter 10 in particular.

"How can an exponentially increasing ramp be in accordance with Kelly."

It isn't increasing exponentially; it's increasing in proportion to the edge you have at each TC.

"Your edge at T5 is not 12x your edge at T1."

A bet of 2 x 6 is not the same as one bet of 12. It's more like a bet of 8. And the edge at +5 is very close to eight times the edge at +1.

"There is some SD difference but not of such magnitude. This suggested ramp is clearly strongly exponential as opposed to the roughly linear Kelly dictated ramp from my perspective."

No it isn't at all.

"I have the Bible in my hand and I am already off on the wrong foot. Help! My math is rough but my hands are clean."

Be patient; read slowly.

Don
 
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Dopple

Well-Known Member
#4
Thanks, regarding Kelly I was not saying it was from your book. Money management on this site is where I got my interpretation of Kelly. I can see what your saying and appreciate the correction.
 

Meistro

Well-Known Member
#5
. I read in BJA3 a suggested ramp is 1,2,4,6,66@TC1 to 5 on pg 4. How can an exponentially increasing ramp be in accordance with Kelly. Your edge at T5 is not 12x your edge at T1.
Because you are making two separate but connected wagers 2x6 is more like 1 x 8.5 than 1 x 12.

Also your edge at TC +5 could easily be 12 x your edge AT tc +1, although it all depends on the rules. You could have a .2% edge at TC +1 and at 2.4% (or higher) edge at TC +5 with some rules.
 

Dummy

Well-Known Member
#6
Look up covariance for understanding betting two spots. As said, the edge at TC +1 could be anywhere from almost nothing to a nice little edge depending on the rules. Things can't scale from an unrelated, seemingly random starting point.
 
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