Kelly betting live test - is it a madman's goal as some quants around here suggest?

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Duritz

Duritz

Scourge of Bookmakers
Veteran 30k Posts 10k Posts BeanCoiNFT Investor Bay 13: Vintage Bay
Oct 15, 2007
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Let's see.

If the mods will allow two threads by me on the bet tracker board, I want to live test Kelly betting. I have my Orb out and it's been rubbed and it's spitting out probabilities, and I am Kelly betting them. Some quants on this board have concluded - through losing large chunks of their bank - that Kelly betting is no good, even though at one point those same quants suggested it was the "only way to maximise bankroll" etc, etc...

However, IF you have accurate probabilities, Kelly betting IS the right way... the point is of course that "no-one" has accurate probabilities.

Well, I'd like to learn the hard way. It's the best way to learn, so let's go ahead and do it. Kelly betting, over various bet types on AFL, here we go.

All these bets are based on my probability estimates for these various bet types.

Bets this weekend -

wcst h2h 45 at 5.88 pinnacle
wcst line 32.5 310 at 1.971 pinnacle
hawks 1-39 285 at 2.30 sportsbet

syd line -37.5 890 at 1.952 pinnacle
syd h2h 260 at 1.12 pinnacle
syd over 39.5 890 at 1.99 sportsbet
syd over 15.5 490 at 1.31 sportsbet

stk u39.5 440 at 2.55 sportsbet
melb line 39.5 550 at 1.971 pinnacle

rich 40+ 295 at 2.10 sportingbet
rich line -34.5 360 at 1.926 pinnacle
rich h2h 145 at 1.154 pinnacle
rich over 15.5 245 at 1.34 sportsbet

north line 23.5 160 at 1.92 sportsbet
freo under 39.5 140 at 2.05 sportsbet

geel line -32.5 580 at 1.952 pinnacle
geel h2h 170 at 1.143 pinnacle
geel 40+ 495 at 2.15 sportsbet
geel over 15.5 pts 390 at 1.39 sportsbet

Total out: $7140
 
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I was in a rush last night so forgot to outline a few things -

1. This is using a $10,000 starting bank. It'll be adjusted weekly rather than game by game because of time constraints.
2. When there's more than one bet in a game, because they overlap the outlay is shared. So if there's 4 bets then I have 1/4 on each of what I should under full Kelly.
3. Bets being considered are h2h, line, margins (39.5) and tri bet.
 
Duritz said:
Let's see.

geel line -32.5 580 at 1.952 pinnacle
geel h2h 170 at 1.143 pinnacle
geel 40+ 495 at 2.15 sportsbet
geel over 15.5 pts 390 at 1.39 sportsbet
Click to expand...


You're betting sizes are massively out of wack, and you're taking correlated bets (I'm not talking about simultaneous games, which is fair enough, but different bet types within the same game). I cannot fathom how you came up with these bet sizes using Kelly. Only taking one of those bet types listed above maximizes expected bankroll growth, so I'm not sure how you get the mix you did.
 

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Duritz said:
Let's see.

Total out: $7140
Click to expand...



If you have bet all these plays simultaneously, you have over bet by around 100% if $7140 is 71.4% of your BR. Kelly is a dynamic formula that has a ceiling of around 35% of BR regardless of how many simultaneous events you link up.

If you are using some type of Kelly calculator created for single, sequential events, this is not adequate for what you are attempting to do.
 
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brett128 said:
If you have bet all these plays simultaneously, you have over bet by around 100% if $7140 is 71.4% of your BR. Kelly is a dynamic formula that has a ceiling of around 35% of BR regardless of how many simultaneous events you link up.

If you are using some type of Kelly calculator created for single, sequential events, this is not adequate for what you are attempting to do.
Click to expand...

All bets within the same game are correlated, so like I said above I share the outlay. If there's four bets, I divide the outlay by 4.

Re simultaneous games, not too fussed, adjusting weekly.
 
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brett128 said:
If you have bet all these plays simultaneously, you have over bet by around 100% if $7140 is 71.4% of your BR. Kelly is a dynamic formula that has a ceiling of around 35% of BR regardless of how many simultaneous events you link up.

If you are using some type of Kelly calculator created for single, sequential events, this is not adequate for what you are attempting to do.
Click to expand...

Further to my prior post, it's kind of a bastardised Kelly, because I am betting simultaneously. Sure I've outlayed 71% of my BR in one hit, but I figure none of them have lost yet (when placing the bets) so I don't want to restrict the outlay. Some of them will get up (in all likelihood) so just let it fly.

The constantly changing nature of Kelly betting is a pain, because when a bad period ends, your outlay is smallest, and when a good period ends, your outlay is biggest.

Personally, I think the Kelly formula needs to be applied to a stable BR, not a fluctuating one, and multiplied by a factor, to best take advantage of it's qualities.

With that in mind, I'll probably bet the Kelly method to a BR of 10k, whether it's winning or losing, until either the season ends, or the 10k is lost.
 
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I have just realised I input my Kelly formula slightly wrongly. I intended to use the Kelly formula as outlined in Wikipedia, which is this -

"
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:
9563314847f2d9ccaf6e4dff6cf6672a.png

where:
  • f* is the fraction of the current bankroll to wager;
  • b is the net odds received on the wager ("b to 1"); that is, you could win $b (plus the $1 wagered) for a $1 bet
  • p is the probability of winning;
  • q is the probability of losing, which is 1 − p."
But instead of dividing by b, which is the odds received (say, 0.97 if you're getting $1.97) I was dividing by the $1.97... in most cases this means I was only betting about half of what I should.

brett128 - you're the Kelly expert, can you confirm that what I am now doing, is the right way?

Example:

I had the WCST line +31.5 as a $1.67 chance. Odds received were $1.971. The Kelly formula should be, with a 10k BR -

(0.6 * (0.97 + 1) -1 ) / 0.97

= 0.1876 bet, or $1876

Is that about right?
 
Duritz said:
All bets within the same game are correlated, so like I said above I share the outlay. If there's four bets, I divide the outlay by 4.

Re simultaneous games, not too fussed, adjusting weekly.
Click to expand...




Dude just use this:

http://www.sbrforum.com/betting-tools/kelly-calculator/


Cut away your correlated bets on the one game. Pick the one that maximizes you expected BR growth. You're not using Kelly right at all at the moment.
 
Duritz said:
I have just realised I input my Kelly formula slightly wrongly. I intended to use the Kelly formula as outlined in Wikipedia, which is this -


I had the WCST line +31.5 as a $1.67 chance. Odds received were $1.971. The Kelly formula should be, with a 10k BR -

(0.6 * (0.97 + 1) -1 ) / 0.97

= 0.1876 bet, or $1876

Is that about right?
Click to expand...



Yeah that's right. Cap your plays at about 62%, I don't think much beyond 62% ATS can exist for an individual bet.
 

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brett128 said:
Cut away your correlated bets on the one game. Pick the one that maximizes you expected BR growth. You're not using Kelly right at all at the moment.
Click to expand...


Considered that, but had an issue with it...

Say you have two possible bets in the same match, Essendon vs GWS:

GWS the line +60.5, a strong overlay, the Kelly bet on a BR of 10k ends up 2k.
GWS H2H, a strong overlay also (but obviously a much smaller chance) and a slightly bigger overlay (therefore greater maximisation of BR growth), and a bet of $200

Figures only examples, but in this case, you'd say don't take the line bet, just back GWS H2H, because the model considers it's a bigger overlay?

If yes, my issue is of course that you're missing solid line bets here, for the hail mary H2H bet.
 
Duritz said:
Considered that, but had an issue with it...

Say you have two possible bets in the same match, Essendon vs GWS:

GWS the line +60.5, a strong overlay, the Kelly bet on a BR of 10k ends up 2k.
GWS H2H, a strong overlay also (but obviously a much smaller chance) and a slightly bigger overlay (therefore greater maximisation of BR growth), and a bet of $200

Figures only examples, but in this case, you'd say don't take the line bet, just back GWS H2H, because the model considers it's a bigger overlay?

If yes, my issue is of course that you're missing solid line bets here, for the hail mary H2H bet.
Click to expand...



That's the complete opposite of what i'd do. The line bet is what maximizes expected BR growth. You need to understand the difference between expected value and expected growth:

http://forum.sbrforum.com/handicapp...s-expected-growth-kelly-criterion-part-i.html

http://forum.sbrforum.com/handicapp...-expected-growth-kelly-criterion-part-ii.html

Even the SBR Kelly calculator will help you understand this concept. Input the two bet types with the same edge, and look at the difference in expected growth.
 
brett128 said:
That's the complete opposite of what i'd do. The line bet is what maximizes expected BR growth. You need to understand the difference between expected value and expected growth:

http://forum.sbrforum.com/handicapp...s-expected-growth-kelly-criterion-part-i.html

http://forum.sbrforum.com/handicapp...-expected-growth-kelly-criterion-part-ii.html

Even the SBR Kelly calculator will help you understand this concept. Input the two bet types with the same edge, and look at the difference in expected growth.
Click to expand...

Ah ha... Ok, so I'll concentrate on backing those with the best expected growth, from here on.

I'll program those formulas into a spreadsheet, have it automatically work out the EG for me.
 
brett128 one more question for you, if you have a moment... if you're pricing up all margin possibilities, how far out do you price? Say you predict Hawthorn will beat GWS by 85 points, then 85 is your most likely margin, and each point either side is the next likely, and so on... where do you draw the line? 90 points either side of your predicted margin? 120 points? 180??
 
Duritz said:
brett128 one more question for you, if you have a moment... if you're pricing up all margin possibilities, how far out do you price? Say you predict Hawthorn will beat GWS by 85 points, then 85 is your most likely margin, and each point either side is the next likely, and so on... where do you draw the line? 90 points either side of your predicted margin? 120 points? 180??
Click to expand...

I'd be questioning that your "ranking of most likely to least likely" expected result, based on your description above, forms a perfect bell.

In your example, Haw by 85 is most likely, Hawthorn by 84 or 86 is next most likely, Hawthorn by 83 or 87 next etc.

I'd be guessing Hawthorn 35-45 would be far more likely than Hawthorn 125-135? Are you comfortable with your expected margin/result being the midpoint, then all other probabilities falling away at an equal rate both sides of your most likely margin?
 
Jan Juc said:
I'd be questioning that your "ranking of most likely to least likely" expected result, based on your description above, forms a perfect bell.

In your example, Haw by 85 is most likely, Hawthorn by 84 or 86 is next most likely, Hawthorn by 83 or 87 next etc.

I'd be guessing Hawthorn 35-45 would be far more likely than Hawthorn 125-135? Are you comfortable with your expected margin/result being the midpoint, then all other probabilities falling away at an equal rate both sides of your most likely margin?
Click to expand...

In the absence of evidence as to why it shouldn't, yeah I am. I figure your predicted margin has to be your midpoint, and if 35-45 is more likely than 125-135, then it's not a true midpoint to start with.

I want to have a perfect bell curve branching down from the predicted margin - the midpoint - but that's where the question comes in: where to cut it off?

Obviously, 1000 points is too much, 10 points is too few... what's reasonable?
 
Duritz said:
So, perhaps the question should be, in a 50-50 game, how far out to each side of 0 should I price? 60 points each side? 90?
Click to expand...
Similar to this, have you (or anyone else) done any modelling on the value of a "middled" point around the line? What I mean is, if you can middle say -27.5 somewhere and +28.5 somewhere else, what do the effective odds have to be before it's value, generally?

I reckon on my limited research it's around 100-1 where it becomes "value" (i.e. if you can find -28.5 somewhere at $1.94, +31.5 somewhere at $1.95 then they are effective odds of ~$34 which multiplied by the three points you get ~$102 and thus it's value), but I'd be interested to see if any modelling had been done on it.

Obviously this doesn't mean that every single possible winning margin is value at 110-1, but I'd reckon those around what the line is probably are value. The other concern though is whether it's "false" value at times you can actually pull it off, given generally when these opportunities come up one half is a steam play based on changed information that a bookie hasn't updated as yet?
 
Lenny29 said:
Similar to this, have you (or anyone else) done any modelling on the value of a "middled" point around the line? What I mean is, if you can middle say -27.5 somewhere and +28.5 somewhere else, what do the effective odds have to be before it's value, generally?

I reckon on my limited research it's around 100-1 where it becomes "value" (i.e. if you can find -28.5 somewhere at $1.94, +31.5 somewhere at $1.95 then they are effective odds of ~$34 which multiplied by the three points you get ~$102 and thus it's value), but I'd be interested to see if any modelling had been done on it.

Obviously this doesn't mean that every single possible winning margin is value at 110-1, but I'd reckon those around what the line is probably are value. The other concern though is whether it's "false" value at times you can actually pull it off, given generally when these opportunities come up one half is a steam play based on changed information that a bookie hasn't updated as yet?
Click to expand...

Good question... my short answer is "no".

However, the method I use to price them up at the moment, the probability I assign to my predicted margin happening is $63, or 1.5% roughly. This might be a touch aggressive, but I have mucked around with it a little bit. I have been more aggressive, at $55, and less aggressive, at $72, but have found this in between is OK... for now.

I have been planning on doing more research on that, but if it's about right then obviously anything above $63 is value based on the true line, and if you find say $80+ then it's worth a look for sure, I would have thought.
 
Continuing the Kelly betting, though with a couple of straighten ups and adjustments from brett128 who has pointed out some things I was stuffing up. I have read and absorbed the EG stuff, and programmed it into my spreadsheet, and will be backing the best EG bet in each match, at HALF Kelly, to a $10,000 BR.

I am doing half Kelly because of a few things... one that there will be simultaneous events, but also because full Kelly is pretty bloody severe!

I am doing it to a non adjusting $10,000 BR, because even though Kelly is supposed to be bet for a fluctuating bank, the ups and downs that always happen in punt hinder Kelly greatly in this respect. IE, you always have your smallest amounts on the winning bets at the end of a bad cycle, and always have your biggest amounts on losing bets at the end of a winning cycle.

So, this will go on until one of two things happens:

1: $10,000 becomes $0.
2: The season ends.

I'm hoping it's #2. :D

Tonight's game - very similar to the market in this first game tonight. However, there are a couple of small overlays, and the one which has the best EG is -

Essington, H2H, $1.794 with Pinnacle, $260. I make this a $1.72 chance, or 58% chance. Not a big overlay, but then on a BR of 10k it's not a big bet, either.

Will post more bets later, if I do them tonight. If not, I'm drinking beer and watching the footy. Might be doing all three anyway.*






*will be
 
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