Kelly Re-Visited

[tsty]

lol am i getting math lessons from kvb? this thread keeps on delivering

the reason i called your post dribble is because it has nothing to do with anything

just read what you wrote a few times and it will come to you hopefully why you are wrong

[tsty]

also lol at losing 5 5% bets in a row leading to 750...

most of your worries are solved by betting more...you guys are looking at the worst possible outcome caused by short term variance...

it has already been posted in this thread what happens after 10k bets but hey lets worry about losing 5 bets in a row

[u21c3f6]

BSims, I'll take one step back + give my two cents. Compound interest is a monster. People don't quite grasp the power of compound-interest.
Kelly Criterion betting is really an application of Compound-interest. If one can harness the power of compound-interest, they will see their $$ grow at a very fast rate.
It is not easy to quantify the true probability of your NEXT bet. If you can, you're on your way. I view Kelly as a guide to making proper bet-size. Half-Kelly should be viewed as a way to not over-bet your edge. The REAL problem w/ all of this is that it's REALLY HARD to build a portfolio that's filled with a series of +EV bets.

This is actually one of the best posts in this thread. The only exception I have is that I do not look at it from the perspective of my NEXT bet. My focus is on a group or series of wagers. Such as ATS wagers with reduced juice (average -105) and a win % greater than breakeven. By estimating the win %, I can calculate my Kelly wager amount. As long as my selections win at the estimated (or close to) rate, I will be compounding my bankroll and it does not matter the order of the wins and losses. Try it, you will see.

Bsims, as far as your table above, if your wagers are +ev, I don't know how the average Kelly wager is less than the flat wager. I am either missing something or it is very arbitrary to me. To me, this is the same error made by the article that was linked.

Joe.

[tsty]

https://i2.wp.com/www.aussportsbetting.com/images/kelly_3d_01.gif?zoom=4&w=676

[turbobets]

What are you talking about?

You have the kelly bet averaged at 5% where it seems to be around $60 but the flat bettor is betting 100?

Do you even understand what you're doing?

lets not even get into the other horseshit in that sim

If they do what I suggested the average wager size for flat and kelly will be the same, 1% of bank. Then you can do an honest comparison. Obviously kelly comes out ahead if bets that are predicted to have a larger edge actually do.

[tsty]

If they do what I suggested the average wager size for flat and kelly will be the same, 1% of bank. Then you can do an honest comparison. Obviously kelly comes out ahead if bets that are predicted to have a larger edge actually do.

Then what's the difference if you make both bet sizes 1% of the roll? THERE IS NO DIFFERENCE THEN IS THERE

they both become flat bets...

Why are there so many stupid people on this forum?

[tsty]

Bsims, as far as your table above, if your wagers are +ev, I don't know how the average Kelly wager is less than the flat wager. I am either missing something or it is very arbitrary to me. To me, this is the same error made by the article that was linked.

notice how someone with a brain notices that instantly?

funny aint it

[turbobets]

Then what's the difference if you make both bet sizes 1% of the roll? THERE IS NO DIFFERENCE THEN IS THERE

they both become flat bets...

Why are there so many stupid people on this forum?

Not even close smart ass. Keywords: "average wager size".

[tsty]

Not even close smart ass. Keywords: "average wager size".

you have no idea what you are talking about

[tsty]

itt : people who hate money

You guys should just put your money in an index fund

[ChuckyTheGoat]

Bill, I'll throw out an idea for u. On stuff like this, it's pretty ez to talk theory. True litmus test comes when we try to put it into practice.

Idea I have in mind is to run a 100-play prospective sample. We could run two bet-sizes, one at Full Kelly and one at Half-Kelly. As I mentioned above, the real crux is that means we would have to put a prospective win% on each play and then calculate the appropriate bet size.

This is NOT easily done (imho). Worth a shot, tho. If you want to put our minds together on this, let me know.

[tsty]

Bill, I'll throw out an idea for u. On stuff like this, it's pretty ez to talk theory. True litmus test comes when we try to put it into practice.

Does math change in the real world? Where do you think this theory comes from?

All jokes aside I'm honestly shocked that so many people with 10k+ posts on a sportsbetting forum are just downright stupid

Have any of you even made 100k lifetime?

[HeeeHAWWWW]

Idea I have in mind is to run a 100-play prospective sample. We could run two bet-sizes, one at Full Kelly and one at Half-Kelly. As I mentioned above, the real crux is that means we would have to put a prospective win% on each play and then calculate the appropriate bet size.

It really needs to be 1000, or better 2000. Kelly works best for high-volume, the compounding effect as someone else mentioned.



For what it's worth, syndicates I've heard of using 1/3, 2/5 and 1/2 Kelly. Personally I'm on half-Kelly, which suits my volume/yield and finances - used to be 1/3, and it's gradually increased over the years. That's a lot riskier than most i

ndividual pro gamblers go for though - which makes sense, looking at the drawdown probabilities, and given you have to pay yourself a wage. It works for me but won't for most.

The optimal very much depends on the individual though - could you cope with a 75% drawdown? It's pretty likely to happen at some stage with full-Kelly. At 0.67Kelly it's 4x less likely, at 0.5 16x less likely, at 0.4 64x, at 0.333 256x.

The EG tradeoff against this volatility then depends on volume - what's your "longterm"? Personally, I looked at two years, worked out what 1%ile outcome was manageable for my finances, and set my Kelly multiplier as appropriate.

[ChuckyTheGoat]

Good post, Heehaw. I like it.

[Bsims]

I’ve run across something a bit perplexing. I decided to modify the simulator and replace the random edge selection with a rotating one. This removes one random variable in each season’s wager simulations and only leaves one, the random decision on whether the wager won or lost (with a 55% chance of winning). I’ve uploaded the Excel log of the 1,000 seasons in a shareable file. You can access it at bit.ly/2twM3zp.

The log is sorted by the number of games won in a season. Notice in particular cases 276 and 682. In these season simulations, 61 wagers were won. That should make for a good season. In season 276, Kelly made a profit of $2,513.38 (Ret/$ of $1.201). But in season 682, Kelly only made $2.09 (Ret/$ of $1.000). So, what is the difference? It almost has to be in the sequence of the wins and losses. I’m going to look at the individual wagers in detail to see if I can learn anything. Hopefully, I’ll have an answer by tomorrow morning. Meanwhile, does anyone have an explanation?

My guess in the previous post was wrong. From my past experiences with using Kelly I suspected that it was caused by how the season started. When you win early the bet size increases and presumably so do your profits (kind of like the mutual funds example mentioned). Conversely, when you lose early, your bet size decreases along with your net results. Even though both cases ended with 61 wins, I assumed case 276 got off to a significantly better start than case 682. But looking at the details of the simulated wagers, it wasn’t until the 50^th game that the good season got ahead of the bad season in wins. So much for that theory.

OK, if it wasn’t the season start, then it must have been winning streaks. I had counted these and found that the good season’s longest winning streak was 7 games and the longest losing streak was 4 games. For the bad season the streaks were 9 and 6 respectively. Not a big difference here.

Next, I looked at the number of winning bets by the edge and generated the following table.

Edge	Won 276	Lost 276	Won 682	Lost 682
3	11	9	14	6
4	9	11	15	5
5	13	7	15	5
6	12	8	9	11
7	16	4	8	12
All	61	39	61	39

Bingo, the winning season had a better won-lost record in the games with the highest edge. Meanwhile, the bad season’s best win-lost record occurred in the games with the lowest edge. The higher the edge, the higher the Kelly bet. Therefore, the difference between the good season and the bad season was that the good season won more of the largest bets than the bad season. That explains the overall better net.

Unfortunately, that is bad news for Kelly as it introduces a 3^rd element of variability. The first variable is the accuracy of your estimated edge. Then there is the outcome of the game variability. And with Kelly we now have the variable of how these two matchup.

[tsty]

for the nits https://www.degruyter.com/view/j/jqa...-2017-0122.xml

[ChuckyTheGoat]

BSims, read Heehaw's post above. I really like his points. Consider the concept of "Probability of Ruin."

Heehaw uses the term "dropdown." Dropdown may be a more appropriate term. 75% drop-down puts a huge dent in one's bankroll. That would mean that you have to quadruple-up just to return to your starting point.

Keep chopping away, BSims. Talk to u later.

[Bsims]

I’m afraid I haven’t done a good enough job with explaining the role of the “Ret/$” metric that is the primary way of comparing results. There seems to be some concern about the bet size I’ve chosen for the flat bets, $100. That choice is irrelevant if you use “Ret/$” as your ultimate measure.

Ret/$ = (Bet + Net) / Bet

So, if you bet $100 and win $5 then your Ret/$=$1.05. The guy who only bet $50 and won $2.50 has exactly the same Ret/$ of $1.05. The original anti-Kelly link I posted was rightly criticized for making his flat bet size equal to the average Kelly bet size after the fact. He should have used “Ret/$” for comparison and avoided this.

I am taking a look at using partial Kelly before drawing my conclusions. I will be posting this analysis on the blog and summarizing the results here.

[u21c3f6]

I’m afraid I haven’t done a good enough job with explaining the role of the “Ret/$” metric that is the primary way of comparing results. There seems to be some concern about the bet size I’ve chosen for the flat bets, $100. That choice is irrelevant if you use “Ret/$” as your ultimate measure.

Bsims, the problem is that your metric has nothing to do with Kelly. Kelly is about maximizing bankroll growth, not maximizing Ret/$.

Joe.

[tsty]

Unfortunately, that is bad news for Kelly as it introduces a 3^rd element of variability. The first variable is the accuracy of your estimated edge. Then there is the outcome of the game variability. And with Kelly we now have the variable of how these two matchup.

just fking lol

You just described sportsbetting

well done
Modelling an outcome and hoping pinny has it wrong...
Also the only way to beat variance is by betting more
If you can't even understand the basics then why bother with this?

[turbobets]

tsty I am on your side, kelly wins. I was trying to point out that if they want to compare kelly to flat then the average bet size over a large number wagers needs to be the same. Not that each individual kelly wager is 1% of bank but they average 1% of bank as would the flat wagers. Done with thread have fun boys.

[tsty]

tsty I am on your side, kelly wins. I was trying to point out that if they want to compare kelly to flat then the average bet size over a large number wagers needs to be the same. Not that each individual kelly wager is 1% of bank but they average 1% of bank as would the flat wagers. Done with thread have fun boys.

no they don't

Why would you think that?

[Bsims]

Following is the chart that compares full Kelly versus half Kelly (with just wagering 10% of your bankroll thrown in just for the heck of it). Besides each column I've included flat bets equivalent to the average bet size.

Simulations of 1,000 Seasons	Kelly	Flat vs Kelly		50% Kelly	Flat vs 50% Kelly		10% Always	Flat vs 10% Always
Average Kelly Pct	5.50%	n/a		2.75%	n/a		10.00%	n/a
Average Bet Size	$65.69	$65.69		$30.06	$30.06		$128.06	$128.06
Average Net Per Bet	$4.27	$3.31		$1.98	$1.52		$5.95	$6.46
Average Final Net	$427.41	$331.31		$197.56	$151.71		$595.05	$645.90
Maximum Season Gain	$5,610.41	$1,968.00		$1,680.21	$896.52		$11,746.27	$3,836.68
Maximum Season Loss	-$827.79	-$1,434.00		-$564.75	-$653.01		-$929.28	-$2,795.63
Average Ret/$ Per Season	$1.065	$1.050		$1.066	$1.050		$1.046	$1.050
Best Using Ret/$	40.0%	60.0%		50.7%	49.3%		3.5%	96.5%

Please use confirmation bias to draw your own conclusions. (Also, my apologies for generating so much anger with this thread.)

[tsty]

its like talking to a brick wall lol

quit while youre ahead

this isnt for u

[Bsims]

its like talking to a brick wall lol

quit while youre ahead

this isnt for u

Give it a rest tsty. I'm headed down a road trying to demonstrate what you believe about Kelly is true. Give me a break.

[ChuckyTheGoat]

Bsims, I think u made it. You have a stalker.

There's some good info in this thread. I really like the implications of how much your variance swings when moving from Half-Kelly to Full-Kelly.

[Larkman]

tsty I am on your side, kelly wins. I was trying to point out that if they want to compare kelly to flat then the average bet size over a large number wagers needs to be the same. Not that each individual kelly wager is 1% of bank but they average 1% of bank as would the flat wagers. Done with thread have fun boys.

The problem is that the only way to possibly know the neccessary average bet size is to calculate kelly first for all bets of the simulation, and then divide the total % by number of bets. Which is impossible in real life without a time machine, making testing it moot.

Furthermore, we are testing (or at least we should be) for bankroll growth, its perfectly possible for a strategy which has a lower total % staked to outperform one with a higher total %, and vice versa, so there's no reason to insist on symmetry of this property.

[Larkman]

Bsims, the problem is that your metric has nothing to do with Kelly. Kelly is about maximizing bankroll growth, not maximizing Ret/$.

Joe.

Even if Kelly wasn't the thing under scrutiny, yield would be a bad measurement for any simulation utilising a growing bankroll because of the bias towards the larger bets at the end of the simulation compared to the smaller bets at the begining.

[tsty]

Even if Kelly wasn't the thing under scrutiny, yield would be a bad measurement for any simulation utilising a growing bankroll because of the bias towards the larger bets at the end of the simulation compared to the smaller bets at the begining.

another genius appears

[tsty]

Give it a rest tsty. I'm headed down a road trying to demonstrate what you believe about Kelly is true. Give me a break.

Why do you need to demonstrate something that has already been proven?

Kelly is backed by mathematical evidence that it gives you the most money in the long run. There is no argument against this. Heck nobody in this thread has even brought forth an argument against it.

What's funny to me is that sportsbettors make bets everyday which they deem to be +EV and know that they might not win those bets because of variance. They are OK with this because they know in the long run it will lead to a positive return. However for some reason they can't do it with bet sizing. They can make plays which they deem to be optimal but can't make a bet size which is optimal? The math is right in front of their face but they can't do it. Why?

Does that mean kelly is the problem or is it something else?

There are two excuses in this thread. One is that edge can't be calculated and the other one is that they can't handle losing large amounts of money. These two excuses have nothing to do with kelly. Get better at modelling and improve your mental game. It ain't hard.

[Larkman]

another genius appears

Whats inaccurate about I posted?

[HeeeHAWWWW]

Found this I did a while back, hopefully someone finds useful. It's a Kelly bankroll simulated 100k times, with estimate errors, over 100/200/400/800/1600/3200 bets, with figures for 1%/10%/25%/50%/75%ile outcomes

Unfortunately seem to have chopped off the 75%ile graph, but it's basically the same as the 50%ile, just better growth.

https://cdn.pbrd.co/images/Hs8jAyX.png

Few comments:

1) The 1%ile graph illustrates the volatility of full-Kelly. If you're at that unlucky 1% marker, your bankroll could be down -93% after 3200 bets. Recovering from that will not be quick. Half-Kelly is still brutal, but it's only -49%, having bottomed out earlier.

2) Half-Kelly is superior at 3200 bets to the other three options at both the 10%ile and 25%ile. Below about 10% the more conservative options do better, and above about 30% a higher multiplier does better.

3) As expected, full-Kelly blazes away ahead of the rest at the 50%ile, and even more so above that. The practical problem there: if you're hitting massive growth numbers with that sort of volume, with 1% to 7% edge, you're going to hit market stake limits fairly soon.

4) These figures vary quite a bit if you bet far from evens.

[Bsims]

Found this I did a while back, hopefully someone finds useful.

Interesting HeeeHAWWWW. Just finished a similar simulation with the following results. I did go more than full Kelly.

Kelly Multiplier	Ave Kelly Pct	Ave Kelly Bet	Ave Kelly Net	Ave Final Net	Max Last Balance	Min Last Balance	Positive Seasons	Ave Wins	Ret/$
0.1	0.56%	$5.61	$0.38	$37.98	$237.26	-$154.09	73.1%	55.1	1.068
0.2	1.10%	$11.45	$0.77	$77.29	$525.66	-$287.08	72.0%	55.1	1.068
0.3	1.66%	$17.52	$1.18	$117.95	$875.00	-$401.38	71.6%	55.1	1.067
0.4	2.20%	$23.84	$1.60	$159.96	$1,296.68	-$499.24	70.5%	55.1	1.067
0.5	2.74%	$30.42	$2.03	$203.34	$1,803.90	-$582.67	69.4%	55.1	1.067
0.6	3.30%	$37.26	$2.48	$248.09	$2,411.88	-$653.53	68.3%	55.1	1.067
0.7	3.86%	$44.38	$2.94	$294.21	$3,138.12	-$713.45	66.8%	55.1	1.066
0.8	4.40%	$51.78	$3.42	$341.71	$4,002.61	-$763.93	66.2%	55.1	1.066
0.9	4.96%	$59.47	$3.91	$390.59	$5,028.12	-$806.27	65.6%	55.1	1.066
1.0	5.50%	$67.47	$4.41	$440.84	$6,240.41	-$841.65	64.5%	55.1	1.065
1.1	6.06%	$75.79	$4.92	$492.46	$7,668.55	-$871.08	62.7%	55.1	1.065
1.2	6.60%	$84.43	$5.45	$545.44	$9,345.14	-$895.46	61.6%	55.1	1.065
1.3	7.16%	$93.42	$6.00	$599.78	$11,306.56	-$915.57	60.1%	55.1	1.064
1.4	7.70%	$102.75	$6.55	$655.46	$13,593.26	-$932.09	57.9%	55.1	1.064
1.5	8.24%	$112.44	$7.12	$712.47	$16,249.87	-$945.61	57.0%	55.1	1.063
1.6	8.80%	$122.50	$7.71	$770.80	$19,325.46	-$956.62	56.3%	55.1	1.063
1.7	9.36%	$132.94	$8.30	$830.42	$22,873.61	-$965.55	55.4%	55.1	1.062
1.8	9.90%	$143.77	$8.91	$891.31	$26,952.55	-$972.76	54.1%	55.1	1.062
1.9	10.46%	$155.01	$9.53	$953.44	$31,625.06	-$978.55	52.9%	55.1	1.062
2.0	11.00%	$166.67	$10.17	$1,016.80	$36,958.46	-$983.18	51.0%	55.1	1.061

Really haven't thought about the implications. But right off the top, why not go with more than full Kelly? Pretty high upside, but limited downside.

[HeeeHAWWWW]

But right off the top, why not go with more than full Kelly? Pretty high upside, but limited downside.

If you go beyond a 1.0 Kelly multi then EG drops - this is the mathematical origin of Kelly, that it's the point where EG is maximised.

The formula for EG is (2/K -1)/(K^-2), so say 1/2 Kelly=0.75, full Kelly=1.00, 1.5 Kelly=0.75 again. At 2*Kelly your EG is zero!

[Bsims]

If you go beyond a 1.0 Kelly multi then EG drops - this is the mathematical origin of Kelly, that it's the point where EG is maximised.

The formula for EG is (2/K -1)/(K^-2), so say 1/2 Kelly=0.75, full Kelly=1.00, 1.5 Kelly=0.75 again. At 2*Kelly your EG is zero!

I'm not familiar with this formula. Can you provide a link to a paper describing it?