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Duiscussed at length on here before but it’s nice to revisit these from time to time.
Problem with Kelly, for me, is that it doesn’t solve the problem of dealing with calculated probabilities that are wrong. I accept that it is a secure method of staking when you have strong confidence in the differences between actual odds available and your own, calculated, probabilities.
However, betting on racing, that statistical confidence is unlikely to be strong enough to base a staking system on.
Thoughts from the Kelly practitioners?
- Total Posts 84
Cormack,
I agree. The Kelly formula is tautological, I think, rather than truly informative. I don’t know what the answer is, but I suspect it isn’t to be found in simple mathematics.
Brian
My own staking plan is this:
In my opinion something that has double the chance of something else should have double the stake. A 50% chance should have double stake of a 25% which should have double a 12.5% and so on.
Anything that is exceptional value, should have more staked on than marginal value.
So if I believe something has a 25% chance of winning, it gets 25 points staked. Plus the amount of value which I believe is in the bet.
ie. If I can get 4/1 (fair 20%), The difference between 25% and 20% is 5%. Therefore I add 5 points to the 25 making 30 points @ 4/1. If I could get 9/2 (18.2%) about my 25% shot, I’d stake 32 (25 + 7) points @ 9/2.
Although am thinking of adding 2 points per % difference (instead of 1) so to increase more on the exceptional value bets.
Value Is EverythingOne of the stories is that Kelly formulated his method for finding the optimum stake after realising the formula he developed for investigating transmission noise in telephone systems could be adapted to betting. That sounds a bit implausible to me and would think that came about because he worked for Bell telephones.
Another story is that he developed the formula after hearing about a scam being operated by some horse players in the US. Evidently in the 50’s the race results were transmitted by wire (slower than telephone), and these horse players discovered that they could phone the result from one side of the continent to an accomplice on the other side who would then place a bet on the winner before the result came through by wire.
This sounds more plausible but could still be untrue. If it is true then the Kelly only works if you cheat which over the years has been diluted into ‘having an edge’.
I don’t think anyone really knows if it works in reality because three things are needed –
1 The probability of the outcome
2 The size of the bank
3 The odds offered.2 and 3 are known but 1 is the problem. If the probability is known then the odds makers also know this and offer under the odds which prevents Kelly from generating a bet.
In horse racing where the probability is not known but is an educated guess, Kelly can get you into all sorts of trouble if your estimate is right out of whack. You also have to be arrogant enough to believe that your implied probability is right and the rest of the world and his dog are wrong. That is why half Kelly and quarter Kelly are used as a stake to tame the wrong guesses.
When I was experimenting with The MARS formula which as far as I can see is pretty much the same as Kelly, was to assume that my probability calculation was wrong and everyone else more likely right. If I estimate a 50% (2.0) probability and the general price available was 5.0 (20%), I would make allowances for that by adding 50% and 20% and dividing by 2 making my probability 35%(2.86). It still doesn’t make any of the probabilities right but does tame the equation.
In my opinion something that has double the chance of something else should have double the stake. A 50% chance should have double stake of a 25% which should have double a 12.5% and so on.
GT – at face value that seems to make sense, but why does it make sense, what’s the logic behind it? Why should something with double the chance have double the stake? Isn’t that just arbitrary?
Shouldn’t it be the case that the entire size of the stake should be based on the ‘value’ part – the bigger the ‘value’ (the % difference between your odds and the bookmakers) the bigger the bet? (I know you do build that in but only to a small extent – in your example only 16.6% of your stake is based on the ‘value’ element.)
That sounds plausible too but the trouble with that is then that the more wrong you are in your assessment (the more value you mistakenly think you have) then the more you lose. (And also, the more you stray in your value assessment from the rest of the world – the bigger edge you think you have – the more likely you are to be wrong about the size of the ‘gap’)
Dolus – great post – exactly my point – if your calculated probabilities are wrong then Kelly can lead you up the garden path (and empty your pockets while you’re on your way).
Thank you
Cormack
for your kind considerations.
GT
Could you not simplify your staking method by establishing a base stake and then dividing your percentage by the percentage of the odds on offer and multiply by the base stake.
Base stake £10
Your odds 1/1 50%
Available odds 4/1 20%
(50/20)x £10 = £25Cormack,
If A has double the chance of B then there is half the risk of losing with A than B. Therefore A in my opinion should get double the stake of B.
I do think you are right about the "value" part though. It should be a greater share of the overall stake.
Am ok with the fact the more I am wrong the more I lose, having belief in my ability to identify value and how much of it is there. Conversely, the more I am right the more money I win.
Dolus,
Thanks for the suggestion, but if I have it right:
The bigger the price, the bigger the stake. Which is the opposite of what I want to achieve. If we take three examples with roughly 5% difference in my price and price available:
My price 3/1 (25%) Price available 4/1 (20%) 5% difference
25/20 = 1.25 x 10 = 12.5 points staked @ 4/1To my current stakes it would be 30 points staked @ 4/1
My price 2/1 (33.3%) Available 5/2 (28.6) 4.7% difference
33.3/28.6 = 1.16 x 10 = 11.6Current stake 38 points staked @ 5/2.
My price 11/2 (15.4%) Available 8/1 (11.1%) 4.3% difference
15.4/11.1 = 1.39 x 10 = 13.9Current stake 19.7 (20) points staked @ 8/1
In these three examples:
5/2 my current stake 38 points
4/1 my current stake 30 points
8/1 my current stake 20 pointsUnder your stakes:
5/2 = 11.6 points
4/1 = 12.5 points
8/1 = 13.9 pointsObviously there’s a difference in the amount of points between staking plans but that’s no problem. It’s the fact:
With my stakes the better chance the more staked.
With yours Dolus, the less chance the more staked.Will try to find a better way of including value to stake.
Value Is EverythingThis gives My current stakes with 1 point added per % difference between my price and price available. 2 points per % difference… and 3 points per % difference…
My price 3/1 (25%) Price available 4/1 (20%) 5% difference
To my current stakes it would be 30 points staked @ 4/1 = 120 profit. 16.66% of stake being to do with how much value is in the bet.
With 2 points added per % difference it would be:
25 (for my price) + 10 (for 5% difference) = 35 points staked @ 4/1 = 140 profit. 28.6% of stake being to do with how much value I believe is available.3 points added per % difference it would be:
40 points @ 4/1 = 160 profit. 37.5% Amount value.My price 2/1 (33.3%) Available 5/2 (28.6) 4.7% difference
Current stake 38 points staked @ 5/2 = 95 profit. 12.4% of stake being amount of value.
With 2 points added:
33.3 + 9.4 = 42.7 rounded to 43 points staked @ 5/2 = 107 profit. 22.5% of stake being amount of value.3 points added:
47 points @ 5/2 = 117.5 profit. 30% of stake amount of value.My price 11/2 (15.4%) Available 8/1 (11.1%) 4.3% difference
Current stake 19.7 (20) points staked @ 8/1 = 160 profit. 23% being amount of value.
With 2 points added:
15.4 + 8.6 = 24 points @ 8/1 = 192 profit. 35.8% of stake being amount of value.3 points added:
28.3 (28) points @ 8/1 = 224 profit. 45% of stake amount of value.A bet with a more realistic difference at the higher price range might be:
My price 20/1 (4.8%) Available 33/1 (2.9%) 1.9% differenceCurrent stake 6.7 (7) points @ 33/1 = 231 proft. 31% being amount of value.
With 2 points added:
4.8 + 3.8 = 8.6 (9) points @ 33/1 = 297 profit. 44.66% of stake being amount of value.3 points added:
10.5 (11) points @ 33/1 = 363 profit. 56.4% of stake amount of value.With 2 points per % difference for how much value I believe is in the bet may be the way forward.
Or, should it be 3 points added per % difference?
Or, would it be a good idea to have two staking plans? One where I have the normal amount of confidence in the value. 2 points added per % difference.
And another if I am very confident (the race is easy to work out). 3 points added per % diference.
When I am not confident (the race is too difficult to work out) there is no bet anyway.Value Is EverythingOne of the stories is that Kelly formulated his method for finding the optimum stake after realising the formula he developed for investigating transmission noise in telephone systems could be adapted to betting. That sounds a bit implausible to me and would think that came about because he worked for Bell telephones.
Another story is that he developed the formula after hearing about a scam being operated by some horse players in the US. Evidently in the 50’s the race results were transmitted by wire (slower than telephone), and these horse players discovered that they could phone the result from one side of the continent to an accomplice on the other side who would then place a bet on the winner before the result came through by wire.
A great book on this subject, which people may or may not have read is "Fortune’s Formula" by William Poundstone. It can be heavy going in places, but the first few chapters give a wonderfully rich history of American gambling from 1900 to 1970 and backs up what you are saying above Dolus. For anyone who has not read it, I highly recommend it.
On another note, I came across this site the other day. I’m not overly sure what they are doing and they don’t give too much away.
http://www.makebetterbets.com
They seem to imply you use the site in conjunction with other systems to help "make better bets". Anyway, it looks like it could develop into something good so I think I’m going to follow it for a while to how it pans out.
DO NOT BOTHER READING THIS POST MOST OF IT IS WRONG
I wrote it so I should know
Hi GT
The bigger the price, the bigger the stake
It may look like that but in fact it is ‘
The bigger the edge the bigger the stake.’
I know there is no right or wrong answer to this but having read your next post I think you are over complicating this staking. I also think that you have taken a wrong turn at he beginning.
1) Regardless of what you make the chance of the horse, 60%, 50%, 40% , 30% if the odds on offer are 4/1 your stake is 20 points. This isn’t taking into account your odds, probability or perception of value.
2) From another angle. You think the horse has 50% of winning. If the odds are –
2/1 your stake is 33 points
3/1 ………………. 25 points
4/1 ………………. 20 pointsSo now as your edge increases your stake decreases, which is the opposite of what should happen.
At this point you do not even need to know or work out the correct price/probability of the horse.
You are basing the stake on what everyone else thinks the chance of the horse is, not what you think it is.
The next thing you do is add the difference between your percentage and the percentage of the odds on offer. This does nothing but just compensates for the mistake already made.
If you forget the first part and construct your stakes around the percentage difference this would be more correct and give you larger stakes the greater your edge.
But even that does not capitalise fully on the value aspect as while 20-25% and 25-30% are both 5% differences, the edge is greater on one than the other.
20-25 1/4 or 25% advantage
25-30 1/5 or 20% advantageThat’s why I suggested dividing your percentage by the odds on offer percentage and then multiplying by your base stake.
25/20 = 1.25 x base stake
30/25 = 1.20 x base stakefreddyflaps
‘Fortunes Formula’, Have seen that book often but never read it, must put it on my to do list.
http://www.makebetterbets.com Looks an interesting site though at the time of writing 9:00am they only have the last race from last night up.
Looking at that I have a feeling that the horses they give the best chance to will always be over bet compared to the prices they suggest, but at least it is something different and FREE at the moment.
Dolus,
Agreed, it is complicated.
You’ve got my staking wrong.If
I believe
a horse has a
20%
chance I stake
20
points on if I can get better than
4/1
, (well 9/2 really with a margin for error). The 20 points is
not
the figure
everyone else
thinks it is, it’s what
I believe
it’s chance is. Plus the "amount of value" addition.
That means with the "3 x amount of value" addition:
Something I believe is a 50% it’s not 33 points @ 2/1, 25 points @ 3/1, 20 points @ 4/1 or 17 points @ 5/1. It would be:
@ 2/1 50 points + (50 – 33.3 = 16.7 x 3 =) 50.1. So 100 points @ 2/1 = 200 points profit.
@ 3/1 50 points + (50 – 25 = 25 x 3 =) 75. So 125 points @ 3/1 = 375 points profit.
@ 4/1 50 points + (50 – 20 = 30 x 3 =) 90. So 140 points @ 4/1 = 560 points profit.
@ 5/1 50 points + (50 – 16.7 = 33.3 x 3 =) 100. So 150 points @ 5/1 = 750 points profit.
I wish I could get a 50% chance at 5/1. Biggest difference I’ve ever worked out is 12%. That is after going back to see if I’ve made a mistake.For any horse I believe has a
20%
chance of winning:
If I can get5/1
then it is 20 points (for 20% chance). Then the difference between 20% and 16.7% is 3.3. So 3.3 x 3 = 9.9. so 20 + 9.9 = 29.9 rounded up to
30 points @ 5/1 winning 150 points
.
If my 20% chance is best price
11/2
, the difference between the two (20 – 15.4) is 4.6. So 13.8 (4.6 x 3) is added to 20 = 33.8 rounded up to
34 points @ 11/2 winning 187 points
.
If my 20% chance is available at 6/1 it would be
37 points @ 6/1 winning 222 points
.
If 13/2 it would be40 points @ 13/2 winning 260 points
.
At 7/143 points @ 7/1 winning 301 points
. Winning over
double
the amount of a 20% chance @ 5/1 bet.
Value Is EverythingHi GT
The bigger the price, the bigger the stake
It may look like that but in fact it is ‘
The bigger the edge the bigger the stake.’
But even that does not capitalise fully on the value aspect as while 20-25% and 25-30% are both 5% differences, the edge is greater on one than the other.
20-25 1/4 or 25% advantage
25-30 1/5 or 20% advantageThat’s why I suggested dividing your percentage by the odds on offer percentage and then multiplying by your base stake.
25/20 = 1.25 x base stake
30/25 = 1.20 x base stakeI understand this point Dolus. Have considered it before.
The beauty (as I see it) of my staking plan, is it takes in to account probability of winning as well as value. Which means the less risk in the bet the bigger the stake. Yet strangely enough, the less money risked the more is won (in a way).
Something I believe has a 50% chance has 50 points staked. So if I can get 5/4 addding
5.6
difference x 3 = 16.8 points, it’s 67 points @ 5/4 wins
83.75
points.
Something I believe has a 25% chance (half of 50). At 4/1 with addition of 15 points (3 x
5
difference) the stake is 40 points @ 4/1 wins
160
. So for half the percentage (25% not 50%) and almost as much value (5% not 5.6%), I make a profit of almost double.
So in my opinion the price I take automatically takes in to account the bigger percentage of value in the bigger priced horse.
With 12.5% (half again) @ 14/1 (5.8% difference) would be 30 points @ 14/1 wins
420
points. Although it is far less likely the difference will be as much at bigger prices.
As has been said before. There is no right and wrong in this. It’s just what people prefer.
Value Is EverythingI don’t often feel moved to comment but on this occasion I thought I might give my opinion
It appears to me that you may be making the problem more complicated than it needs to be. If you are confident that the odds calculated for a selection represent value then stake at those odds to return say £100.
If you are correct and thew selections wins but at shorter odds then you should still get a reduced return, but if the odds lengthen it will be a skinner for you.Formath,
When I first started out betting it was all level stakes. Which was fine, although I found it did not matter much about the short priced horses. Everything depended on how many outsiders won. Obviously, you need ten Even money chances to win to make the same profit as one 10/1 shot or twenty Even money shots to one 20/1 winner.
So I changed to do as you say, bet to win the same amount. Yet found then it mattered more about the shorties than outsiders. Obviously to do as you say; With an even money shot you’d lose £100 if it lost. Where as on a 10/1 shot it would be just £10 or £5 for 20/1.
With "Ginger Staking", the shorter the horse the more money is staked. Which makes sense, because the shorter priced horses have less risk of losing. Where as with less money risked on the outsiders they also deserve to win more money.
It also takes account of how much value is (believed) in the bet.Do think Cormack had a good point, value did not have enough say in stake. Does now, although will only change for the Jumps, not back end of the flat.
Realise it’s a bit complicated but once you’re used to the calculation, it’s easy. Well, sort of.
Value Is EverythingHi GT
For some reason I thought you were basing your stake on the odds available.
The only thing I can add is that to capitalise on the value is to consider taking the difference between the percentages and multiply by your edge.
20 – 25% = 5%
25/20 = 1.25
1.25 x 5 = 6.25
6.25 x 3 = 18.75
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