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Chodempole
Chodempole
Joined: Oct 13, 2014
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May 13th, 2016 at 11:35:45 AM permalink
How can the Kelly criterion work, if for example, I have a bankroll of $1000. I bet a game for $50. Then, I bet another game before I know the outcome of the first game.. How is that calculated? In order for Kelly to be correct, I have to know my current bankroll. If I lose the first bet and the second bet was made based on $1000 bankroll and I lose the second, then I lost more than I should have. If I win, I win more than I should have. Same scenario if I win the first bet.. winning the second wins me less and loses me less.
odiousgambit
odiousgambit
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May 13th, 2016 at 12:03:27 PM permalink
Quote: Chodempole

How can the Kelly criterion work, if for example, I have a bankroll of $1000. I bet a game for $50. Then, I bet another game before I know the outcome of the first game.. How is that calculated? In order for Kelly to be correct, I have to know my current bankroll. If I lose the first bet and the second bet was made based on $1000 bankroll and I lose the second, then I lost more than I should have. If I win, I win more than I should have. Same scenario if I win the first bet.. winning the second wins me less and loses me less.



You do adjust for current bankroll, however, Kelly usually has you making a small bet vis a vis your bankroll, and the next bet change probably can be ignored for a while. If not, you are just going to have to guess where your bankroll will be.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
MathExtremist
MathExtremist
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May 13th, 2016 at 12:47:07 PM permalink
Since you have a sense of your EV on the first bet, you could use that as your theoretical bankroll to size your next one. If you have a $1000 bankroll and bet $50 (5%), you expect to win $2.50 (5% of $50). Size your next bet based on a bankroll of $1002.50 even though you only have $950 in hand.

I have no idea whether anyone's done that before but it seems correct to me.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
RS
RS
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May 13th, 2016 at 1:22:05 PM permalink
I don't know how much difference it would have, but perhaps calculate what your BR would be if your current bet wins and the chance it'll win, then do it again for if it loses.

Or you could figure out the variance / standard deviation for both bets being played out at the same time (concurrently), then should be able to determine the max amount you can bet on the second game, given the variance of the first.

ie: Maybe your bankroll allows a $10 bet on a 5-team parlay AND a $500 bet on a money line. As one shifts up, the other shifts down. Given a $10 and $500 bet are at jelly, you may be able to bet $5 on parlay and $750 on ML.....or $15 on parlay and $400 on ML.....etc. (I'm just using random numbers here btw). $10 correlates with $500, $15 correlates with $400, and $5 correlates with $750, for example.

Now, if your first bet was the ML bet, you could determine how much you can bet on the parlay.
mustangsally
mustangsally
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May 13th, 2016 at 3:35:01 PM permalink
Quote: Chodempole

"DOES THE KELLY CRITERION WORK ON SPORTS?"

answer = yes
but it might take time to “dominate” over other betting methods like flat betting

from:
THE KELLY CRITERION IN BLACKJACK SPORTS BETTING,
AND THE STOCK MARKET
EDWARD O. THORP
"One feature of sports betting which is of interest to Kelly users is the prospect of
betting on several games at once.
This also arises in blackjack when (a) a player bets
on multiple hands or (b) two or more players share a common bankroll.
The standard techniques readily solve such problems. We illustrate with:
Example 6.1.
"

the pdf is all over the internet
Quote: Chodempole

How can the Kelly criterion work

one must follow the rules
for Kelly betting to work properly

to start
know the winning probability of the event you wish to bet on and then calculate your advantage to see what bet size is correct.
easy to overbet.

of course
calculators can take the fun out of calculating for some, not all (like me - Sally pretty)

this one is highly spoken of
http://www.sportsbookreview.com/betting-tools/kelly-calculator/

Sally
I Heart Vi Hart
TomG
TomG
Joined: Sep 26, 2010
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May 13th, 2016 at 4:43:45 PM permalink
Quote: MathExtremist

Since you have a sense of your EV on the first bet, you could use that as your theoretical bankroll to size your next one.
I have no idea whether anyone's done that before but it seems correct to me.



Close, but can't be exact. A bet with an EV of $2.50 and a 10% chance of winning must be treated differently than a bet with an EV of $2.50 and an 80% chance of winning.

No one would ever bother with it for a lot of reasons. People who are betting enough games with enough of an edge to require large enough bets are already forced to bet fractional Kelly due to limits. Steam chasers have time constraints and need to get their bets down as soon as they can without bothering with exact formulas.
Chodempole
Chodempole
Joined: Oct 13, 2014
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May 16th, 2016 at 2:16:53 PM permalink
Quote: mustangsally


"One feature of sports betting which is of interest to Kelly users is the prospect of
betting on several games at once.
This also arises in blackjack when (a) a player bets
on multiple hands or (b) two or more players share a common bankroll.
The standard techniques readily solve such problems. We illustrate with:
Example 6.1.
"



If I read this correctly it would work if I knew how many games I would be playing. For instance, on a usual Sunday, I may bet a game and not know that i'm going to bet another game until 10 minutes later. And maybe another game 5 minutes later. If I know for sure i'm only going to bet 3 games then the math is easy. But for sporadic betting of an unknown number of games before knowing the result is what i'm after.

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