OK when i first looked into kelly vs FLAT STAKING in horse racing i was against kelly for the reasons stated in the other threads and not knowing how kelly actually worked, but thanks to Wamy Einehouse, AaronBrown, heehaww explaining it in detail, i realized mathematically using the Kelly Criterion is the optimal way to maximize the (betting bank).

This is a bit of a long post but trust me if you read it properly you might actually agree with me. Why i used the word properly is that i probably came across as clueless in the other threads not knowing much about kelly which i agree, so why would anyone bother reading more from someone that's clueless on kelly, but when it comes to pricing horses, well this is my field hence why i have some questions regarding kelly.

So since i have gone through some previous records of horse bets where i had a run of 9 horses losing in a row which is not often but standard also in horse racing, in which 8 of those started favorite and one second favorite, and all very heavily backed to win the race at jumping as the clear popular picks.

Now in Australia the bookmakers offer early fixed odds 2 to 3 days before the race, and in this excel example below you will see how wrong the bookmakers had it when first opening their early fixed odds to the public to bet on which i backed each of these runners

Here is a excel screen shot showing the 9 bets

but as i mentioned the 9 bets were without a collect

but to prove my point i also added.....had the 9 horse bets all won..... what would the kelly bank looked like along the way after 3 winners 4 winners etc when compared to a flat staking bank.

The starting bank for this example just to keep it simple is $1000

If you look under each staking method column you will see what each bank finished up after 9 run of outs HIGHLIGHTED IN THE RED COLOR at the bottom of each staking column.

Kelly Full went from 1000 bank to 177 = minus 83% of bank
Kelly 1/2 went from 1000 bank to 530 = minus 47% of bank
Kelly 1/4 went from 1000 bank to 700 = minus 30% of bank

And using the 2% Flat staking with no increase in bets, the flat stake bank went from 1000 to 820 = minus 18% of bank

REMEMBER the red is what the bank actually finished up for each staking method after 9 losing bets, but just for this example i entered the amounts had they 9 bets won instead




So the columns in order just in-case you don't understand them are...

Race number
Horse name
MyRatedPrice (price i assessed the horse according to my analysis)
Win % (probability of each horse winning according to my analysis)
Odds Backed (odds i backed the horse)
Finale odds (the finale odds that the horse started when jumping)
Kelly 1
Kelly 1/2
Kelly 1/4
2% Flat no increase in bets (betting 2% of 1000 starting bank and not increasing it over a few day period, instead just increasing the bets to bank ratio weekly basis)



Now i debated the point in the previous threads that horses unlike sports betting is a totally different ball game due to sports being a 1 on 1 >> team vs team bet, while horse racing there are 10 15 and 20 runners in a single race.

My point is Team vs Team means when giving each team a probability of winning, you only have to get 2 teams right compared to horses where you have to get a full field of 20 horses correct when assessing and assigning each of them their probability to win the race -- which means a lot more margin of error in setting a line for horse racing compared to sports.


So i was told to use fraction kelly instead in the previous threads




So for this example lets use kelly 1/4 only to keep it simple

Now Kelly 1/4 vs Flat staking shows that after a run of 9 outs the bank decreased by 30% while the flat staking bank by 18%

So again to keep it simple lets say Kelly staking lost double vs flat staking which would be standard given its the quickest way to build a bank so it will have bigger swings.

Now this is over 9 bets sample only so we could say over 1000s of bets...that if one was to use Kelly 1/4 they should use 2 x the bank vs flat staking given its more swingy.

So now we come to my point

So lets say had those 9 horses won instead

Using The kelly 1/4 bank, it would have went from 1000 to 2557

While the flat 2% staking bank would have went from 1000 to 1546 had they all won in a row

now kelly didn't double the profit of the flat staking

But even if we keep it real, even though 9 winners in a row is capable, but lets only use 5 winners in a row and you will see that kelly never is double ahead of flat staking throughout the 9 winning bets






So my point is and i will get to it, is that if your going to use kelly 1/4 compared to flat staking 2% you really need to use a smaller bankroll due to the higher variance with kelly ON HORSE RACING 2x or even 3x smaller bankrolls.

So if you do - than if you use a $1000 kelly bank you should be able to use double of $2000 bank for flat staking .....because of the lower variance that comes with it vs kelly 1/4 .....meaning kelly when compared to flat staking really should not be compared on equal bank dollar amounts like kelly $1000 bank vs flat staking $1000 given kelly is much more swingy with variance in horse racing.

sry for long post and bad English but would really be interested to see if what i am saying is correct or not?

Everyone will say that kelly is the quickest way to build a bank i know this, but it also comes with a higher variance.

which when compare to poker would be like playing .50/$1 where you could use 40 to 60 buy ins to play full time... but you would need 150 to 200 buy ins to play high stakes and likely more.

So the same applies with Kelly 1/4 vs flat staking. although kelly makes money quicker vs flat staking, you could flat stake double the amount of dollars and still have a lower variance while showing a greater profit.

You keep saying flat stake 2% but it's only 2% on the first bet. As you win, it approaches 0% unless you periodically increase the wager. Or if you were talking about a constant 2% then that's not flat-staking, that's a fractional wager (like kelly, but a different fraction, presumably much smaller than Kelly in most instances). I'm not sure which you mean.

As time goes on, the kelly bank will approach infinity times the flat-stake bank. Kelly grows exponentially whereas flat-staking grows linearly. If you plot an exponential function divided by a linear one, the graph will tend to infinity. (Or if you were talking about fractional 2%, the same will be true for that. One exponential function divided by a slower one will tend to infinity.)

But it can still have a low risk of ruin, and you can tailor it to the risk of ruin you're comfortable with.

I suggested something a little different: underestimate your chance of winning. The end result might be about the same though. For the kind of betting you're doing, I haven't thought about whether 1/4 kelly is likely a safe fraction.

I'm betting 2% of the bank so if the bank is $1000 the bet is $20

But I'm not increasing the bets on a daily basis, but instead weekly

So say the bank gets to 1200 after a days bets i still bet the original 2% of $1000 which is $20, than after a weeks betting i adjust the bets to whatever the bank is.

I understand my OP was a Tl;dr type of post but I'm not sure heehaww if you just sped read it as my main point was that kelly vs level stakes when taking into account variance kelly 1/4 would not likely show that much greater profit because you could bet twice as much if not three times with level stakes due to the lesser variance vs kelly 1/4.

Ok I will try to explain this in simpler terms

You're a full time horse player with a $100k bankroll

Given Kelly full is not used by any horse players given its too hard to set realistic true probabilities for 20 horse fields for every horse...so most use a fraction kelly instead like 1/4.

Now with a 100k bankroll we are unlikely to use the whole 100k using kelly 1/4 because even kelly 1/4 is very swingy variance wise, so we likely use 50k or 25k instead

But using level stakes 2% bets to bank we can use the whole 100k because we aren't betting more than 2% stakes while kelly at times we are placing 10% of our bank which means kelly is risking 5x more vs level stakes 2%

So with level stakes we can use the whole 100k bank to bet with, but given kelly 1/4 is at times betting 5 times more of the bank total vs level stakes, i would assume we should use 5 times less a of bank....so instead of using the whole 100k we should use 20k

so in a typical bet like this $3 price 40% probability 20k bank

Kelly 1/4




But with level stakes the bet would be

100k bank
2% = $2000 placed on horse
Wins profit $4000 so 4 times greater return


But even if we used 50k of our 100k for kelly 1/4

its still short of the $4000 collect vs level stakes \




I know using kelly it will never likely go broke but at the same time no ones going to be betting and sticking to $10 or $2 bets after having a 100k bankroll

so lets say the 100k bankroll is none replaceable

That's the faulty assumption in your argument. I'm using my whole 100k, assuming none of that 100k is needed for non-gambling/investing things. If I calculated that my RoR with 1/4 kelly is 1% and I'm fine with a 1% RoR, then I'll have no regrets if I lose my 100k. 99% of the time it'll turn into millions.

I also won't panic when I have a 40% drawdown (if I'm confident that I'm not delusional about my edge).

What you're describing is more like fractional betting than flat betting. You start with 2% bets, then as the week progresses it will usually dip below 2% (sometimes higher ie when you're losing and you don't decrease your bet), then you restart at 2%. Overall it's similar to just always betting 1.9% or whatever your average percent-wager would be.

By betting 2%, you're still fraction-kelly betting but choosing 2/Kelly instead of Kelly/4.
Whichever fraction is smaller has a lower risk of ruin and a slower growth rate.

If my bank is $1000 i bet 2% which is $20 After a week of betting if my bank is $1200 my new bets will be $24 again 2%






This is where i think its very difficult for someone that doesn't play horses to understand how kelly used in horse betting is NOTHING like when used for all other codes of betting sports etc

That screen shot example i posted showed 9 losing bets in a row, which is really nothing in horse racing. Some of the best horse players have mentioned having 30 to 40 bet losing streaks, which is very standard in horse racing especially when you are betting in 20 horse races compared to a 2 team event.

This is why i really think its gong to be difficult to get a answer regarding kelly and horse betting, because 99.9 of the answers are coming from posters that don't bet 1 pick in a 20 horse field, but instead pick 1 pick in a 2 team field, and for this reason don't understand the variance associated with horse racing..........and that there is no such thing as setting a true handicappers line in HORSE RACING.

Just to give you a example when you get 3 of the leading handicappers in the country post their betting line...a sort of one off for the biggest race in the country once a year and the

1st handicapper rates the favorite a $4 chance to win
2nd handicapper rates it $15 while the
3rd has it $20

but the horse starts officially $8 with the public finale odds, into a 10 million betting pool...which is a lot of money for a public tote pool....This does not not include what the bookmakers have held on the race....and they the bookmakers simply copy the public tote odds, or close enough.

Now this margin of difference would never happen in sports betting -- where sports handicappers when different setting their lines....are only different by the smallest margin...nothing like the $4 $15 $20 example above...if anything they would be something like $5.20 .5.40 for a $5 chance or under slightly.



Any horse player that tells you they can set true or close enough to true lines is talking gelati.

And ofc you don't need to set true odds all the time i know this, as long as you set them better than what the bookmakers offer. But this still does not change the variance that comes with betting on a 20 horse fields. Especially when you mark a horse $2 thinking anything over $2 is a great value but the horse opens $2.50 and drifts out to $6.50

Yes EVEN money out to 6.50 it was like they were jumping out of trees to Lay the horse....and the horse who leads in its races every single time...now today in a field of scrubbers the jockey decides to NOT LEAD and sit behind and never ever get out to only go to the line pocketed .....when it should have lead easily on its ear from barrier 1 and instead been backed from 2.50 into $2 but instead went from 2.50 out to 6.50 for a very good reason, (obviously the jockey had a fill up)

In this example having the horse $2 thinking $2.20 would be great overs and you get offered $6.50

with a bank of 100k full Kelly you would have had 41k on he horse and using quarter Kelly $10,230 and horse was hooked and never allowed to win.

In horse racing having 41% or even 10% of your bank using kelly when you can have 20 to 30+ run of outs is just hmm

This doesn't refute what I was saying, it just means 1/4 kelly might be too high in horse betting. If your risk of ruin calculation turned out to be too low, that's not because math failed, it's because in each wager you were over-calculating your edge and what you called "kelly" was actually more than kelly. But I imagine one's edge estimate in horse-racing has an unavoidably wide margin of error.

Choosing 2% is arbitrary and for all you know, that's also too high. (From the wildness you're describing, maybe 2% is the full kelly for a lot of horse bets.) At least by consciously betting a fraction of kelly or underestimating your edge by a certain amount, you're being as objective and calculated as possible in your decision. My point is that it's always possible to estimate (and engineer) your RoR, even if you know that estimate can be off by 15%. Just because you're betting a chaotic sport doesn't mean all math goes out the window or that the only safe thing is to wager an arbitrary and tiny amount.

Were those guys betting underdogs / low-percentage combinations of bets? If so, maybe Kelly was telling them to bet tiny anyway and that 40-loss streak might not have even busted them.

Edit: if there existed a +EV lottery, with normal loss streaks being in the thousands, the Kelly bet would be well under 1%. So kelly already takes the swinginess of the game into account. I calculated that even if the Powerball lottery were +EV, it still wouldn't be worth it to buy a ticket unless you were already a billionaire (iirc).

Really ^^ good post ty

sry for my English but bit confused...I don't understand what you mean by this?

I'm betting a flat stake of 2% not 2% of kelly so if bet is $20 its $20 be the horse be 4-1 or 20-1 just adjusting for to bank on a weekly basis.



No.

I know one of them personally who had a streak of 28 losing bets and bet shorter priced horses....using kelly 1/4 this would have sent his bankroll into near busto. basically he would have had to get a job using kelly.

Now obviously we can say his selections might be questionable...but he has been a winning player for 25 years so unlikely but possible obv, but either way he is still backing them at overs, and usually requires 20% overs to place the bet himself, so even if he was a bit out when setting his lines, he still had a margin of error of 20% to make up for the amount he was out.

Yeah I knew what you meant by 2%. You arrived at that 2% arbitrarily (though it was an educated guess based on experience). But I was saying that based on how wild horse-betting is, 2% might be what Kelly says to bet anyway! (Of course, when I made that remark, I forgot that you had already calculated the kelly bet and saw that it was higher than 2%.)

The way you're using the phrase "flat stake", Kelly is also a flat stake, at least when the betting conditions are the same. The difference is your flat 2% doesn't change as the conditions change.

If you were gonna pick an arbitrary % like 2%, you should at least decrease it for lower probability wagers and smaller edges. And maybe increase it when betting higher probabilities for the same edge.

Why do you have your win probability set at 40%? Or am I misunderstanding how this calculator works?

Its a weird thing because many pro horse players will tell you that their best collects seem to come in races where no one is confident in playing where the favorite starts a longer price like 5-1 6-1 7-1 10-1 etc compared to 2.50 $2 favorites.

I find this to be true also, I don't understand why but when someone says to me why not have less on the longer priced ones like proportional staking where they back a horse to win say 10k

so if its 10-1 they have 1k on it and if 5-1 they have 2k on it

my reply is, your been told how much to bet by the bookmakers

So if i get 10-1 i bet less compared to 5-1 where i bet more

why would i bet less if i think the bookies got the odds wrong in such a swingy game, like i explained its not like sports betting.

you would want to make the most of their mistake and bet more, if you think your a better price assessor than who ever is doing their betting lines.


I know this seems weird when compared to other betting codes but in horse racing you will go to the track with 4-5 standout bets thinking they really should win and come home without a winner but on other days, think the racecard looks average but go home backing winner after winner and filling up.

the win probability is what i think the horse chances of winning are

Using kelly 1/4 in this example

bank 100k
probability 20%
odds offered $6
Stake $1000






compared to level staking let call it which would be $2000 on same circumstance

given 30 runs of outs as a likely number for RoR even if we use 40 or more with the above example we are betting 1% of our bankroll ONLY using kelly 1/4 which seems way to little and not making the most of it at times while other times over betting, it just seems this way in horse racing anyway.

I gtg soon so I quickly skimmed. But what I mean is, when YOU assess a small probability (and are doing it for the high payout), then you should bet smaller.

Generally speaking, the bookies won't be so far off that a 20:1 longshot is really 30% to win (correct me if I'm wrong? If so, I need to start betting horses pronto lol). So your bets will tend to be smaller on underdogs.

They're not "telling you what to bet". They're trying to set accurate lines and make themselves unexploitable. Or I don't know how influenced they are by public opinion / dumb money.

One thing that has me thinking, maybe kelly might not the be best staking method for horse racing is that no professional horse bettors use full kelly, or even half kelly, but for all the other codes they do use full and half, maybe this itself says something from experienced winning players, that have been in the game for a long time, that kelly might be flawed when it comes to horse racing, and that there are better staking option?

I'm not sure like i said hence why i asked.

No, obviously not but they do make a lot of mistakes




In Australian they have the main bookie which you call the TAB, they employ people to set lines, while the other 20 plus online bookmakers all basically follow the TAB as none will go up with prices until they see what the TAB have posted....and than basically copy to nearly the exact same price. The 20 online corporate bookies like William Hill etc and so who have bought most of the Austrian bookies out in Aus just follow as i said the TAB or the public money / dumb money as you said.

Its nothing for the TAB to post 10-1 about a horse and see it backed to firm into 5-1 as soon as they open up with their prices. And they do this usually with 1 to 3 runners per race, they put up the wrong prices very often.

The guys doing their betting lines, would be working for themselves and not the TAB if they were that good at setting lines, instead they work for the TAB and the smarties who work for themselves pick their mistakes.

What those guys know from experience is what day traders know about their craft -- that their edge estimates have a wide margin of error, which is why they leave room for such error by betting smaller than kelly. They'd much rather bet <kelly than >kelly. Betting >kelly (by accident) leads to a higher RoR (possibly 100% depending on how much higher) and a slower growth rate than 1x kelly. More risk for less reward.

Using a different staking strategy than Kelly won't get rid of the underlying issue of high margin of error in your probability estimates. Like I said before, if there were 0 margin of error (e.g. if it were as simple as card probabilities), you'd bet full kelly no questions asked.

[ ] Tastes the Pierian spring

Nothing will "maximize the betting bank" unless you're betting nothing but sure things. If you're betting with an edge you can maximize the expected value of the betting bank by betting it all each time - and most likely go broke. With Kelly you maximize the expected value of the "Rate" of growth of the betting bank where that "Rate" is understood as a random variable subject to chance. You'll get a smaller expected value of the betting bank that way but a high likelihood of a betting bank that grows instead goes bust.

PairTheBoard

Show the math where any series of +EG wagers leads to "bust."

Show the math where 0 EG = +EG

And how about trolling a different forum, one where you won't look like as much of an idiot.

The probability of being reduced to X% of your bankroll when wagering c*f, where c is a constant and f is the kelly stake, is

X^{2/c - 1}

In real life there is a minimum wager. Let's say it's 0.2% of your current bankroll, so you're broke if your bankroll goes below that. Let's pick a smaller percentage, say 0.1%.

P(ever fall to 0.1% when betting 2x kelly) = .01^(2/2 - 1) = .01^0 = 1

Since .2% and .1% were arbitrary examples, we can say that no matter how large your bankroll and how big your edge, if there is a minimum wager then your chance of going broke when betting 2x kelly is 100%. Any small number raised to the 0 equals 1.

(But you don't need a formula to see why that's true.)

No expected growth leads to no expected growth, genius. Positive expected growth leads to positive expected growth, genius.