Simultaneous Bet Kelly Staking

It does seem rather apparent that when placing bets sequentially, Kelly is the way to go.

But how to calculate proper Kelly stakes when we are sequentially placing sets of simultaneous bets?

[To further complicate matters, what if the sets of bets, while simultaneously decided, are not placed simultaneously, but rather are placed only with the knowledge that as naby as x more bets MIGHT still be placed?]

If you are following a proper Kelly strategy, at any point in time when you place a bet, assume that all undecided bets are sitting in your bankroll as cash valued at their current EV. If those other bets were also placed using Kelly, the overall performance of the system should still be optimal.

In other words, assuming all your bets are straight bets, simply ignore the other bets and assume the money is still in your bankroll. If you are talking about parlays, then I doubt you are using Kelly properly.

As an example, if your bankroll is 100 units and Kelly calls for betting 1 unit because of an assumed 1% advantage, there is no problem whatsoever in putting your whole bankroll down on 100 independent simultaneous bets of 1 unit each. After you have placed 99 of these, you are best off placing the entire remaining amount on the 100th one, and if yet another one arises you are still not violating the strategy if you borrow 1 unit, using your undecided bets as collateral, and betting that on a similar (but independent) proposition.

Your assumptions MUST be correct, however, ie. you MUST have a 1% edge and the bets MUST be independent (ie. non-correlated).

How the hell to figure that Kelly betting out?

Any place to find it? Is there a simpler modification you can use?

How do you put it into excel?

Darryl-

Your statement is incorrect, it is not optimal to place bets on simultaneous games as if they were simply sequential.. One of two things will happen. After the first game the remaining games will either win less than they should or lose more than they should. For example, if your expected winning percentage is 57% you would be betting 9.7% of your bankroll. If that first play wins your next wager should increase by this 9.7% and if it loses your bext wager would decrease by 9.7%. I know Northern Star is out of town until Monday but he wrote a paper on this exact subject and devised a way to use parlays to make simultaneous games mimic the results of sequential games a couple years back. I am in Chicago and don't have a copy of that paper with me, but maybe he will share some when he gets back to town.

Patriot-

In excel you can use the formula

=IF(D5="","",ROUNDUP(F5*(AA5-((1-AA5)/(1/AB5))),2))

F5=Bankroll
AA5=expected win %
AB5=Juice
D5 is only a indicaror to start the formula and is not actually a part of the kelly formula.

A good website to use to calculate kelly is http://www.albionresearch.com/kelly/default.php

Baker

Best link I could find (requires Adobe Acrobat reader):

http://www.sportsdiscover.com/3/MoneyManagement.pdf

Baker,

I realize that the optimal bets are not EXACTLY the same, but according to Thorpe's paper, section 6 (sports betting), talking about simultaneous bets and any reduction required:

"Since the m(i) are typically a few percent, the reduction factors are typically very close to 1"

http://www.bjmath.com/bjmath/thorp/ch6.pdf

Using Thorpe's formula, if the optimal bet size is 3 units and we assume a very juicy 3% edge, then for two simultaneous bets the optimal bet becomes 2.997 units each.

My apologies for not being mathematically 100% exact, but I think we are splitting hairs here.

As for parlays vs. straight wagers, I offer the following proposition which, for lack of seeing it in this exact form and lack of a better name I call Darryl's Theorem:

Given any set of at least 2 independent positive EV betting propositions (events) and any wagering strategy involving at least one parlay of 2 events or more, there exists a strategy involving straight wagers only which DOMINATES the parlay strategy, ie. it provides a higher expected return AND a lower standard deviation of return (ie. lower risk of ruin in repeated trials).

In light of that I have trouble seeing how any parlay strategy could "mimic" an optimal straight wager strategy, but I am open-minded and would be curious to see what Northern Star wrote about the subject.

Baker that calculator is outstanding, thank you very much for that, Ithink it will work great for bases dogs.

I'll be interested in what you do for multiple bets.

What do you think of just rounding down 10% of an individual bet if you have like 5 or more plays?

like if a bet calls to wager $166 round down to $150 if you have 5 games or so to play?

Darryl P. thanks a lot for your help too!

Patriot,

You're welcome, but I must caution you to be careful with that calculator (and with the Kelly Criterion in general)...

I'm sure it applies the formula correctly but just consider a wager on a dog in MLB priced at +120 (6 to 5), say...

The amount it tells you to bet is VERY sensitive to the probability you input which CANNOT be very accurate and is usually OVERESTIMATED by 98% of gamblers (otherwise they wouldn't gamble, right?)

If you have a B/R of $10,000 then the following probabilities give the following bets:

Prob. Suggested Bet

50% ......$833
49 ..........649
48 ..........466
47 ..........283
46 ..........99
45 ..........0

You just go by your gut and say it's about a 50-50 shot and because of the nifty calculator you confidently plop down 8.3% of bankroll -- a HUGE overbet which will cause you to go BUST because there is NO WAY you have an 8.3% edge at the time you place your bet unless you're BW and have some inside info or are hitting a bad line.

Your true probability is probably more like 46-47%, but can you REALLY tell the difference between 47% and 50% just by gut feel? I know I can't and I bet very few others can either.

Therefore, the best way to apply Kelly IMO is to just ACCEPT that most of your bets will have an advantage of 1-2%, and maybe your POW will be 3%, POM will be 4%, and POY be 5%, but here POY means just that -- ONE play in the entire YEAR.

After a couple of years of your own experience, you may realize that your actual advantage was more like 2.5% in which case you can assume 2-3% the following year, with 4%, 5%, and 6% for the special plays,

OR you may realize that it was more like 0.5% in which case you've been overbetting and are lucky to still be alive.

Most people come to the second realization, so even to assume 1-2% is a bit aggressive.

So to summarize: Kelly simply says to bet a percentage of your bankroll which is equal to your advantage, and since it is very difficult to estimate your advantage in sports betting (unlike blackjack, say), you should be VERY conservative and assume only 1-2%. Then there is no magic math involved...just bet 1-2% of your bankroll on 95% of your plays and you are following Kelly as closely as you can for practical purposes.

Darryl Parsons said:

If your bankroll is 100 units and Kelly calls for betting 1 unit because of an assumed 1% advantage, there is no problem whatsoever in putting your whole bankroll down on 100 independent simultaneous bets of 1 unit each.
.

Click to expand...

Clearly this can not be the case as this would attribute non-zero probability to a scenario where all the bettor's money is lost. Since Kelly strives to maxmize the expected log of future bankroll, any non-zero likelihood of the bankroll equalling zero (the log of which is -INFINITY) is unacceptable by the Kelly Critierion.

OK you're right, 2.88 x 10^-31 is not zero. There's a better chance that we'll both get a heart attack in the next hundredth of a second, but you're right, it's not zero....carry on...

http://www.professionalgambler.com/debunking.html

http://www.professionalgambler.com/binomial.html

Never too old to learn something new ganchrow, enjoy.

NOTE: According to expert researcher Dr. Nigel E. Turner, Ph.D., Scientist, Centre for Addiction and Mental Health ( ntsci@hotmail.com ), incremental betting is one of the telltale signs of someone with a gambling problem.

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Whats...is he fxckin nuts?

So does anyone know of a closed form solution to Kelly for n different simultaneous uncorrelated bets?

~Falco~ said:

http://www.professionalgambler.com/debunking.html

http://www.professionalgambler.com/binomial.html

Click to expand...

A well thought out succinct critique of the above is given at http://www.sharpsportsbetting.com/forums/free/general/index.cgi/read/5729.

When it is impossible to figure an edge before a game in 1% increments, I don't see how using a formula that most guys don't even understand that is based on the assumption you can determine that small an edge is going to work.


If a guy was good enough to say "I have a 3% edge here" or a "5% edge in this game" Then he would be GODD enough not to need some theory that requires an advanced math degree to understand.

My philosophy is that the more complex and difficult the theories, the more bullshit they are trying to shovel. Especially when it comes to something as rudimentary as money management.

The only real advantages available that are proofable (if that is a word) are when you have set of numbers for the same event/team/side and look at the dicsrepncies between them

But when you look a line that is -5 and think you can determine you edge on a stand alone, in a vaccum situation is foolhearty at best. Now if you see that -5 somehwere with a -200 ML attached to it, and you see a -5.5 somewhere else with a -210 ML and then a thrid place with a -5 with a -185 ML attached to it. THEN you CAN determine some sort of advantage.

You cannot determine an advantage based on opinion, I am sorry. As has been mentioned here, even the VERY BEST have maybe a 3-4% BETTER opinion than anyone else or even a coin flip for that matter. So trying to break that down into 1% increments in a precise pattern is not going to work.

If it did work, then people would be making millions upon millions of dollars gambling on sports, and every MIT geek with a pocket protector would have been betting sports not starting websites a few years ago. Marc Cuban would have been fading the Mavericks not BUYING the Mavericks.

Kelley is a nice thing for guys that have some brains that think they are smarter thaneveryone else to hang their hats on, nothing more, nothing less. It is the ego of the genius to think they can figure something out that the stereotypical crooked nosed guy in a fadorra smoking a cigar couldn't. Thus beating them at their own game.

I haven't seen many guys breaking casinos with the Kelley Criterion. A ferw computer uys did bet enough to manipulate lines in the old days thus getting buy back and middle opppurtunities on their own money. Basicallt generating line moves to take advanatge of. Ultimatley that is the advantgae a player has, and it isn't theoretical, it is easilly proven. If you have a team -130, and get the other side +140, you CANNOT lose. It desn't matter which side has the advantgae, you don't even need to know. Some guys might wieght both sides at equal value in that case. -130 has a 1% advantage, and the +140 has a 1% advatage. One team has to win right, so why are they both an advanatge stand alone? they aren't that is it. If a guy only has one book and is using Kelley he is losing money no matter how "correct" he is. Depending on what line he sees and has available to him he is going to bet a "wrong" side more than a few times. But if he has mulitple places to bet, and SEES the lines for himslef with no need for guessing he doesn't need to give an advantgae to one side over another. He simply bets both sides.

People like to make gambling into rocket science. It isn't anywhere near that difficult. If done correctly you dont even have to pick winners. Just recognize the edges that are avaialble at any given moment and take them.

But when you look a line that is -5 and think you can determine you edge on a stand alone, in a vaccum situation is foolhearty at best. Now if you see that -5 somehwere with a -200 ML attached to it, and you see a -5.5 somewhere else with a -210 ML and then a thrid place with a -5 with a -185 ML attached to it. THEN you CAN determine some sort of advantage.

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1. The Kelly Critieren does not apply for scapling. A scalp is a 100% advantage by definition.

2. The Kelly Critieren generally is applied against special situations, and not ALL situations. The situation quoted above lists descrpecies amoung bookmakers, something seen 100 times per day. Furthermore, one of those lines is probably right, and the other two are proablaby wrong. Kelly is only concerned when you think you are right more often than not. When comparing lines like this way, you're not thinking if you're right, you're thinking about if someone else is right. And Kelly is about how yourself thinks, and how yourself would bet.

3. The Kelly Critiean is applied all the time, with varying degrees of sucess. Look at Bucsfan and his best bet of the day in the baseball thread. Looks like a text book example of the Kelly Ceiritean. Bucsfan does not provide a theoretical argument the Kelly Critiean works, he provides a factual experience that it works, and that one's estimation of an assumed edge over the game would yeild a higher ROI if the appropriate sized wager is made.

Baker called me and asked me to reply to this thread. I wrote a paper about 15 years ago in reagards to the above subject. I gave Baker a copy of it. I haven't had time to read the thread because I just got back from vacation and I am swamped at work. I will try to dig it out and give you some idea on the Kelly Criterion and some equations and off shoots of the Kelly critierion you might want to consider for money management purposes.


As Always Good Luck

Northern Star

Northern Star said:

Baker called me and asked me to reply to this thread. I wrote a paper about 15 years ago in reagards to the above subject. I gave Baker a copy of it. I haven't had time to read the thread because I just got back from vacation and I am swamped at work. I will try to dig it out and give you some idea on the Kelly Criterion and some equations and off shoots of the Kelly critierion you might want to consider for money management purposes.

Click to expand...

Much appreciated, NStar. I very much look forward to seeing it