Help with Multiple Kelly

[OnlyMe]

Hi,

I can work out Kelly for a single bet in a race, but am unsure how it pans out with more than one selection in a race.

For example, say I am betting fixed Kelly and using European style odds we have:

Odds=4/1, Estimation=3/1 Kelly = 0.0625

But say I have this artificial example
Odds Estimation Kelly
6/1 3/1 0.125
4/1 3/1 0.0978
4/1 3/1 0.1406

Is this correct? I have two selections with the same odds and estimation but with different Kelly's

If I add a fourth at 4/1 and 3/1 I get yet another Kelly at 0.25!

Is this correct? If so could someone provide an explanation, if not could some one provide the correct Kelly's?

Thanks

PS Of course I can supply my workings if needed.

[Dave Schwartz]

The safe way:

Suppose you are playing 2 races. The first race calls for a Kelly of 6% and the second for a Kelly of 8%.

If you started with $1000, made the first bet and lost, you'd bet $60 and wind up with $940. Of that you should bet 8%.

Another way to say it:

If you lose both bets you should wind up with 94% * 92% or 86%. Thus, if you have to make both bets at once, the total of the two bets should be 14%. Bet them proportionately (i.e. 6/14's on the 1st and the balance on the 2nd.)


Hope this helps.

Regards,
Dave Schwartz

[Overlay]

Based on my understanding of Kelly, if you have two horses in the same race, and both their estimated/fair odds and their actual odds are identical, you would bet the same percentage of bankroll on each of them. I would need to see your information in more detail. (You can send me a private message if you wish.)

[OnlyMe]

Dave,

That may be the safe way but it isn't the right way is it?images/UBGX/E1.gif

If I bet 6/14 on one then 8/14 on the next then all I am doing is just making two independent single Kelly bets aren't I?

[Dave Schwartz]

My math is relatively weak.

There is a long (and correct) way to do this - Actually, Mike Pascuale wrote a book about it years ago - He (and the book) have faded into the woodwork.

In fact, if anyone knows where he is, I need him for a project.


Dave

[OnlyMe]

Here is a page that purports to do it.

However, there are mistakes in it, so I don't trust it.

http://www.racing.saratoga.ny.us/kelly.html

So if I duplicate the method I have no idea if its right or wrong!

[OnlyMe]

Don't worry I'v got it working :jump:- though if it makes any sense it anyones guess

[Overlay]

I believe the text by Mike Pascual that Dave is referring to is Bankroll Control (although I have no idea where Mike is now). The most interesting piece of information that I recall from it was discussion of a group overlay method where you could include horses with a high true probability of winning as part of a group wager (even if the high-probability horses were slightly underlaid in comparison to their toteboard odds when considered as individual bets), and yet realize a greater return on investment than if the underlaid horses had been excluded from the group wager.

[Dan Montilion]

I dated Multiple Kelly. Best 6 months of my life. However, needed another 6 months to recover.

Dan Montilion

[Dave Schwartz]

Dan,

Just kind of like from another planet, huh? <G>


Dave

[DJofSD]

This is an old program I wrote way back. I believe I used the "Bankrole Control" manual to write it.

DIM odds(8)
DIM bet(8)
null$ = ""
hdr1$ = "* * * * * Optimal Multiple Horse Betting * * * * *"
hdr2$ = "Version 25 Oct 93"
lhdr1 = LEN(hdr1$)
lhdr2 = LEN(hdr2$)
hdrtop$ = SPACE$((79 - lhdr1) / 2) + hdr1$
hdrtop2$ = SPACE$((79 - lhdr2) / 2) + hdr2$
answer$ = null$
totbet = 0
endbank = 1000
profit = 0
DO WHILE answer$ = null$
totbet = 0
FOR j% = 1 TO 8
odds(j%) = 0
bet(j%) = 0
NEXT j%
CLS
PRINT hdrtop$
PRINT hdrtop2$
PRINT null$
INPUT "Win percent "; p
IF p > 1! THEN p = p / 100!
INPUT "Percent of Kelly desired "; pk
IF pk > 1! THEN pk = pk / 100!
INPUT "Number of wagers "; numbets%
IF numbets% > 8 THEN PRINT "Limited to 8 bets": numbets% = 8
s# = 0
FOR j% = 1 TO numbets%
INPUT "Odds of horse "; odds(j%)
s# = s# + (1 + odds(j%)) ^ -1
NEXT j%
'
s# = 10 ^ 4 * s#
s# = 10 ^ -4 * INT(s#)
'PRINT "Break even % = "; s#
IF p > s# THEN
PRINT "Previous Bankroll = "; USING "$$#####.##"; endbank
INPUT "Enter new bankroll or <ENTER> for previous "; b
IF b = 0 THEN b = endbank
CLS
PRINT hdrtop$
PRINT hdrtop2$
PRINT null$
z# = (p - s#) / (1 - s#)
c# = (1 - s#) / s#
e = (1 - z#) ^ (1 - p) * (1 + c# * z#) ^ p
z# = z# * 10 ^ 4
z# = 10 ^ -4 * INT(z#)
l# = z# * pk
PRINT " Win "; " Kelly "; " Break "; " Starting "; " Optimal "; " Risk"
PRINT " Pct "; " Pct "; " Even "; " Bankroll "; " Risk "; " Limit"
PRINT USING " .## .### .#### $$#####.## .##### .####"; p; pk; s#; b; z#; l#
IF z# < l# THEN l# = z#
e = (1 - l#) ^ (1 - p) * (1 + c# * l#) ^ p
PRINT null$
PRINT "On selection Odds Bet"
FOR i% = 1 TO numbets%
bet(i%) = b * l# / (s# * (1 + odds(i%)))
ip = INT(bet(i%))
fp = bet(i%) - ip
IF fp > .499999 THEN bet(i%) = ip + 1 ELSE bet(i%) = ip
IF bet(i%) < 2 THEN bet(i%) = 2
totbet = totbet + bet(i%)
PRINT USING " # ##.# $$#### "; i%; odds(i%); bet(i%)
NEXT i%
PRINT SPACE$(27); "_____"
PRINT USING " $$#### &"; totbet; " Total bets"
PRINT null$
PRINT "Expotential Growth Factor = "; e
INPUT "Win payoff (for a $2.00 bet) "; w
INPUT "Number of winner in group "; n%
profit = (bet(n%) * w / 2!) - totbet
endbank = profit + b
PRINT "Ending bankroll = "; USING "$$#####.##"; endbank
PRINT null$
ELSE
PRINT "No play"
END IF
INPUT "Do another (--Y--| N ) "; answer$
IF UCASE$(answer$) = "Y" OR answer$ = null$ THEN answer$ = null$ ELSE answer$ = "N"
LOOP
'
END

[JackS]

The way I understand it, each bet at 4/1 has a probability of 20%. Your expectation before making the first bet that both bets will be successful is 4% or 24/1 (.20x.20). After the successful conclusion of the first bet, the second bet returns to 20%.

[OnlyMe]

Regarding "Bankrole Control" method thats interesting, though I can't quite work out why backing underlays makes you more money.

I suppose if they are favourites then although you lose on a race if it wins you don't lose your whole stake.

Of course it must be a tradeoff.

Thanks for the code I'll give it a walkthrough.

Does it work? ie did you make money with it?

(I suppose not or you'd still be using it :) )