Kelly betting and simultaneous events

**brettd** · 01-27-10, 08:02 PM

Can anyone answer this? I didn't think it was that hard of a Kelly question. Or am I mistaken?

**roasthawg** · 01-27-10, 08:06 PM

I have never understood this... I believe that it's trying to lower your risk of ruin but I'm not sure of the mathematics behind it. I personally don't lower my bet size for simulataneous events... during football season I'll have my whole roll bet out on Saturdays sometimes at full kelly.

**brettd** · 01-27-10, 11:05 PM

Yeah me too with Soccer. On busy Saturday's i'm turning over my bank roll around 1.5x times using Kelly unadjusted for simultaneous events, just because of the multitude of games on that day. I don't wanna be doing this though if it's not optimal to bet with Kelly unadjusted.

Can any math gurus shed some light on this? What happened to Ganchrow?

**Wrecktangle** · 01-27-10, 11:24 PM

I've had up to 40% of my bankroll out on simul events. And then went 0-10 one Sunday.

This will rapidly separate you from Kelly. I've had way too many 0-6, 7-0, 0-10, 9-1, etc events over just the last 6 months to be explained away as random independent events. After running all the events thru the binomial, I was finding that I had a 3 in 10000 chance, a 4 in 1000, a 1.5 in 10000, etc. i.e. these events are not results from a Gaussian Dist. as the tails were much too thick.

**brettd** · 01-28-10, 12:28 AM

So are you saying that there is a mathematical reason why Kelly adjusted for simulatenous events seemingly dictates that you should bet less per individual event within a simultaneous group?

**Pancho sanza** · 01-28-10, 12:43 AM

Way too complicated and tedious to implement, your better off just assuming the bets that haven't gone final will lose and reduce your bankroll accordingly, then bet size off that.

**brettd** · 01-28-10, 02:27 AM

Implementing this for me is not that difficult, I use a program in assisting me to generate correct betting amounts according to my inferred edge. I just want to know whether it is actually 'correct' to use Kelly adjusted for simultaneous events. Because right now, I do not factor in betting events that are scheduled at the same time.

**Wrecktangle** · 01-28-10, 08:48 AM

Originally posted by Pancho sanza

Way too complicated and tedious to implement, your better off just assuming the bets that haven't gone final will lose and reduce your bankroll accordingly, then bet size off that.

If you are full Kelly, even this will kill you. 1/2 - 1/4 Kelly at the most might work.

I'm starting to lose faith in anything close to full Kelly. In the past I've run a bankroll up 10x+ and 5x+ but as the number of simul bets increased the variance increased for me over the last 6 months. The distribution governing sports has much flatter kurtosis than a Gaussian dist. IMO.

**Justin7** · 01-28-10, 08:56 AM

There are some complex solutions. I have a simplified process that gets you close.

Assume you have 10 simultaneous bets, each that you think justifies a 5% risk alone.

If you bet these sequentially and lost them all, your remaining bankroll would be 0.95 ^ 10 = 59.9%. In essence, this collection of 10 sequential bets would risk up to 40.1% of your bankroll.

They are not sequential. I would risk 4.01% on each bet. This actually works out to be too conservative, but it is a decent "quick and dirty" approach.

**brettd** · 01-28-10, 09:31 AM

Cheers. Much appreciated, thanks Justin.

**Sinister Cat** · 01-28-10, 10:09 AM

Here is the thread which explains it:

SBR Forum - Sports Betting Talk - Sportsbook Review Forum

http://forum.sbrforum.com/handicapper-think-tank/24829-simultaneous-bet-kelly-staking-simplest-case.html

Sports betting and handicapping forum: discuss picks, odds, and predictions for upcoming games and results on latest bets.

**brettd** · 01-28-10, 07:16 PM

Justin. If you could, I also have another question.

How would one Kelly stake simultaneous sets of mutually exclusive outcomes? For example, in English soccer leagues on Saturday's I may have selections on correct scores for 10+ games starting at the same time. For each individual game, I may have a range of bets for a particular scoreline. I understand that the range of bets for any particular game are mutually exclusive. One cannot hit a 0-0 scoreline while also hitting 1-1 in the same game. But what are the kelly implications (if there are any) of stringing together a series of bets that start at the same time?

I.E 10 simultaneous games with correct scores selections * 3 selections per game = 30 selections

**roasthawg** · 01-28-10, 07:40 PM

Originally posted by Wrecktangle

I've had up to 40% of my bankroll out on simul events. And then went 0-10 one Sunday.

This will rapidly separate you from Kelly. I've had way too many 0-6, 7-0, 0-10, 9-1, etc events over just the last 6 months to be explained away as random independent events. After running all the events thru the binomial, I was finding that I had a 3 in 10000 chance, a 4 in 1000, a 1.5 in 10000, etc. i.e. these events are not results from a Gaussian Dist. as the tails were much too thick.

I agree that sports gambling is VERY streaky... an 0-10 would drop my roll by 25%, it would take a simultaneous 0-40 to wipe me out. Not gonna happen.

**brettd** · 01-28-10, 08:32 PM

oh yeah, and cheers for the link sinister cat. good article

**Justin7** · 01-28-10, 09:59 PM

brettd,

You need to estimate how correlated (or negatively correlated) they are. Once you do that, you can start adjusting (and considering risk).

**brettd** · 01-28-10, 11:41 PM

Hhmmm, I don't really know how correlated they are. In what ways can a game correlate with another? I thought I was dealing with 10 simultaneous (but independent) events, that each had a set of mutually exclusive outcomes for their correct score lines.

How do I begin to figure this out Justin?

**Pancho sanza** · 01-29-10, 02:28 AM

Originally posted by brettd

Hhmmm, I don't really know how correlated they are. In what ways can a game correlate with another? I thought I was dealing with 10 simultaneous (but independent) events, that each had a set of mutually exclusive outcomes for their correct score lines.

How do I begin to figure this out Justin?

Figure out all the possible outcomes of your bets that could give you unique bankroll sizes, for each possibility calculate p*log(bankroll) where p is the probability of each series of outcomes, sum these numbers, maximize this, solver will do it for you.

**brettd** · 01-29-10, 08:56 AM

Hey Pancho thanks for the answer. I don't completely understand the solution you provide, but I'll ask a mate more mathematically inclined than myself that can help interpret and work through this.

**saunkarter** · 01-29-10, 11:29 AM

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