kelly adjusted for a finite world

[formula_2002]

Per , http://en.wikipedia.org/wiki/Kelly_criterion
For simple bets with two outcomes, one involving losing the entire amount bet, and the other involving winning the bet amount multiplied by the payoff odds, the Kelly bet is:

seehttp://en.wikipedia.org/wiki/Kelly_criterion


where
• f* is the fraction of the current bankroll to wager;
• b is the net odds received on the wager (that is, odds are usually quoted as "b to 1")
• p is the probability of winning;
• q is the probability of losing, which is 1 − p.
that may work in an infinite world enviorment (that is you will live to infinity)
so let me try to adjust the formula for we (irish) that will live but a little while (say 50 years of betting life) .
enter the standard deviation!!
Can someone please pick it up from there??
Else, i'll continue :)

[HUSKER55]

please continue. i always thought the criterian was reset everytime you hit.

But I am not a math major.

[Overlay]

please continue. i always thought the criterian was reset everytime you hit.

But I am not a math major.

As applied to horse racing, I've always understood true Kelly to be a constant amount that did not change from race to race, and that was calculated according to the equation in the article that formula_2002 cited, based on the bettor's long-term handicapping performance (the probabilities corresponding to the bettor's long-term win percentage, and to the long-term average odds of the bettor's winning selections).

I've also heard of "hyper-Kelly" (or a fixed percentage thereof), that applied the equation to each individual race based on the disparity between the bettor's personal "fair odds" on a horse, and the actual odds established on the horse by the public. In that case, the optimal amount to wager could/would vary from race to race.

[formula_2002]

As applied to horse racing, I've always understood true Kelly to be a constant amount that did not change from race to race, and that was calculated according to the equation in the article that formula_2002 cited, based on the bettor's long-term handicapping performance (the probabilities corresponding to the bettor's long-term win percentage, and to the long-term average odds of the bettor's winning selections).

I've also heard of "hyper-Kelly" (or a fixed percentage thereof), that applied the equation to each individual race based on the disparity between the bettor's personal "fair odds" on a horse, and the actual odds established on the horse by the public. In that case, the optimal amount to wager could/would vary from race to race.

the key is "long term"

I'm going to define long term
as the set size that yields the minimum change in the roi standard deviation.

say you have developed a system that generated 1000 plays.
example:take 10 plays at a time and determine the a/e roi
(actual wins/expected wins) ,where expected wins =1/(odds+1).

now determine the roi standard deviation for each set of 10 plays.

keep increasing the set size,10,20,30 etc.
when standard deviation in each set size shows little or no change I expect two thing happen.
one is, the set size has determined you minimum number of plays to test.
the second is...I'm stilling working on it. :)

I expect it to develope into something that will determine the bet size vs risk.

[HUSKER55]

I would think in a 1000 race block your base set of wins had better be over 250 to show a positive ROI. The exception is if you only play horses that are long shots in which case I have no idea how to calculate those figs.

I think using 10 race intervals is basically going track to track or day to day depending on your betting habits. For what you are trying to do aren't you going to need annual figs?

Perhaps I missed the point. Aren't we putting the your strike against the odds offered?

Thanks

[formula_2002]

here are some results for 1000 picks, most of which i posted in the "selections" forum.
1000 win bet play block had a .94 a/e roi.

in sets of 100 plays it looked like this

0.86
0.87
0.89
0.89
0.89
0.92
0.92
0.95
1.03
1.1
0.077 stdev


in sets of 200
1.07
.90
.91
.87
.89
.081 stdev

two sets of 500
.98
.90

[formula_2002]

THE ATTACHED IS 20 SET OF 50 PLAYS SHOWING THE FLAT BET WPS PLAYS.

THE OVERALL PLACE BET ROI IS .985

11 OF THE 20 PLACE SET ROI'S ARE >1 (A POSITIVE)

WITH A 7% REBATE, 3 MORE SETS ARE POSITIVE.

LIKE WISE, 15 OF THE 20 SHOW SETS ARE POSITIVE.

[formula_2002]

IN 55 SET OF 10 PLAYS, THE PLACE ROI WAS POSITIVE.
ADD A 7% REBATE, THEN 64 SETS ARE POSITIVE..

THATS A 64% CHANCE OF BING POSITIVE IN SETS OF 10 PLAYS.

WITH A 7% REBATE, THE OVERALL SYSTEM IS POSITIVE

[formula_2002]

IN 55 SET OF 10 PLAYS, THE PLACE ROI WAS POSITIVE.
ADD A 7% REBATE, THEN 64 SETS ARE POSITIVE..

THATS A 64% CHANCE OF BEING POSITIVE IN SETS OF 10 PLAYS.

WITH A 7% REBATE, THE OVERALL SYSTEM IS POSITIVE

IN THE CASE ABOVE , A 6% KELLY BET IN THE PLACE POOL RETURNED OVER $7000 IN 1000+ PLAYS. STARTING BANKROLL WAS $1000

(ASSUMING THE PLACE POOL COULD HANDLE A $500 BET W/O IMPACTING THE RETURN :)