Sun Wakong , no smokie  unlees  your  talking  real  smokie ..

Compound  so Rain Lover  won  .. zip here  how much did you have on   are you still spending to winnings ?

Compound Magic,
appreciate your help, but it seems we are having a http://www.youtube.com/watch?v=n5PvAi8PTsI&feature=related
What I wanted to write was that average odds of horses that won the race and I lost the bet (because I was laying) were 7 in decimal odds. Your second part of post confirmed what I was thinking. The numbers are made up, just wanted to make sure I got it right.

How do you calculate the stake using calculator on the link I posted before? Seems to me that it does not differentiate between backing and laying.

Yes, that's true, because of commission.
I remember a similar thread where you mentioned a staking plan in relation to odds:

Betfair price 6.5 lay chance = 1-(1/6.5) = .854 * (100*10%) = 85.40 (liability) Not stake

When I apply it, it produces the best results, so I was wondering where did you find it and where could I read more about it?

Snapper and Trevh, what you're missing is that his edge is not 1/6. If you're calculating the edge (value) of back bets you can do so by dividing the achieved odds by the true odds but it's not quite so simple for lay bets - if you want to use the method of dividing one set of odds by the other then first you have to work out the equivalent back odds.

The equivalent back odds of a lay at 3 are 1.5, the equivalent back odds of a lay at 2.5 are 1.66 (recurring), divide 1.66 by 1.5 and you get the correct figure of 1.11 - +11% value.

A quicker way is to look at the relationship between the book percentages - 2.5 is 40% of the book, which leaves 60% 3 is 33% of the book, which leaves 66.66% - 66.66(recurring)/40 = 1.11 (recurring), so that's an edge/value of 11%.

I also posted a worked through example above that shows the same edge by working through an example of 100 bets matched. Any of these methods is fine and all will get you to the same answer.


As regards the Kelly calculation, I haven't done it and it's not my thing, but I would point out that in theory 20%ish is not an unreasonable figure for a bet with such a big edge, after all- the stake is a percentage of the bank so you can never go bust even if you hit really bad variance. In practice of course %of bank is usually meaningless because you are limited by the market's capacity to take your bets rather than the size of your bank.

It seems to me that there are problems calculating the stake for laying so I did a little googling.

http://www.punterslounge.com/forum/f23/kelly-criterion-laying-68644/

This page was very helpful, there is no need to reverse the odds using the calculator Compound Magic posted (and I thing that is not correct, if you reverse the odds you should then reverse the probability as well). Just put the numbers in for backing and the negative result means a liability to risk.

Trevh, in your example the punter is betting (backing) the selection, so in your second example the result 16,6 is correct for backing (backing odds 3 for a 2,5 shot that is). When laying the percentage should adjust like aye robot posted - backing odds*(backing odds-1) or reversing the percentages.

Trevh, I understand why you ask, the answer is that there's a difference between the backer's edge (which in this case is negative) and layer's edge - which in this case is positive. It's not simply a matter of reversing the backer's negative edge to get the layer's edge. Really it's a matter of how we understand percentages, which is something that catches a lot of people out.

I'll come to roulette in a minute but first let's work through FAFH's example to show that the layer's edge is not just the opposite of the backer's edge. In this example FAFH and his counter-party strike 90 bets at 2.5 with true odds of 3:

First we look from the backer's perspective -
The backer strikes 90 bets at odds of 2.5 and in line with our expectancy he wins 30 of them, which return 45 stakes, and loses 60, so he makes a total loss of 15 stakes.

Since he put 90 stakes at risk to lose 15 he lost 16.66% of his total exposure, therefore his edge is -16.66%
As you know, this can more simply be worked out as (3-2.5)/3 or 1/6.


However this does not mean that FAFH's edge is also 16.66%, look at the same example from his perspective:

FAFH wins 60 of the events returning 1 stake each, and loses 30 events and therefore 45 stakes - that leaves a profit of 15 stakes, exactly what his counter-party lost. However, to win those 15 stakes FAFH had to put a lot more money at risk, to cover 90 events laying at 2.5 he had to put 135 stakes at risk, his return as a percentage of this is only 11.11% - and that's his edge. You can get to this figure in a number of ways which I've shown above.

We can apply the same logic to Roulette. When you do 1/37 to get the roulette edge you are calculating the backer's negative expectancy - which is 2.7% of whatever he risks. For most people this is the relevant figure because it tells them how much and how fast they will lose. However, if a casino were to calculate how much of their bank they could risk laying a roulette bet they would not be able to use 2.7% as their edge because from their perspective the edge is much smaller than that.

Say the wheel is spun 37 times, if it falls in line with expectancy the backer will win once at odds of 36(a profit of 35 stakes) and lose 36 times, showing a total loss of 1 stake out of 37 put at risk - that's where 1/37 comes from.
When you think about it from the house' perspective though, they had to put 35 stakes at risk 37 times to get their profit of 1 stake, that's a total exposure of 1295 stakes. If the house wanted to use kelly to calculate their optimal liability the figure they used for edge would be just 1/1295, or 0.0007%.

You can get to "layer's edge" figures in a number of ways, but the quickest would be -backer's edge / (lay odds -1).

So in the FAFH example that would be  (1/6)/(2.5-1)
Which is better expressed as 1/(6*1.5) = 0.111

For Roulette it would be 1/(37*35)




You probably understand the concept of "back equivalence" already, but since I know many don't I may as well explain that too whilst I'm here.
Basically, you can see laying at 5 as being the same as backing at 1.25, in both cases you expect to win 4/5 of the events you bet in, and if you lose then you lose four times what you would have won.
You work out the equivalent by taking the reciprocal of the remainder of the proportion of the book- so for example:
5 is a book proportion of 0.2 (1/5), which leaves a remainder of 0.8 (4/5) the reciprocal is just 1/this figure, in this case that's 1/0.8, which is better expressed as 5/4 or 1.25. 
If you rationalise this you see that the shortcut is to just do (lay odds)/(lay odds-1).

So another quick way to calculate layer's edge is simply to take back equivalents of the odds and divide one by the other.
For The FAFH example this comes out as (2.5/1.5)/(3/2)
Which simplifies to (10/9) or 1.1111

It's the same Sandown.... you just didn't spend ages explaining it!

Sure they were.... I was going to let that one go. A rare moment of compassion.

Deliberate mistake mate - a la Sandown.... keepin you on your toes.

Edge is the same thing as value, when we use the term "value" for shorthand we mean "positive expected value" or "positive edge".
ROI is an ill-deined term that different people use in different ways, I avoid it all-together because I think it's ambiguous at best and in many ways misleading. However you could make a good case for saying your edge was your "expected return on investment."

I'm not into Kelly because it's not relevant to me, but if you want to use a Kelly formula made for calculating back stakes in order to calculate lay stakes then all you have to do is work out back odd equivalents and then use the result of the formula as your liability. Presumably it would be pretty easy to re-jig the formula to do all that for you.

Although I'm not really into Kelly I did read about it once and I remember working through it and finding (no surprise) that it really did optimise returns against risk. I find it a bit weird that people argue about it because ultimately it's a matter of mathematical proof - so really there's no discussion. It's like arguing about whether pythagorus' theorem is right, once it's shown to be right that's it, no argument. I don't know whether you've worked it out correctly or not, but assuming that you have then that is the optimal stake. Whether it "feels right" or not is neither here nor there, we know that humans have an extremely bad intuitive sense of anything to do with risk or probability. We see this a million times a day - so forget your feeling and trust the numbers.

When it comes to applying Kelly to the real world there are areas for discussion. As I've said many times I don't think percentage of bank is really applicable to sports betting (unless your bank is very small) but that aside the other area of interest is how you make allowances for your uncertainty about your edge. In sports betting your edge is never known as you can never know the true probability of the outcome you're betting on. Since your edge is always an estimate you should also make an allowance for your uncertainty about that estimate.
We ought to be able to do that pretty well here, since ultimately we're experts in uncertainty. That's what probability is - the art of calculating uncertainty.

So your M.O. would be this: Calculate/estimate your edge, then quantify your uncertainty about your edge with a value between 0 an 1. 0 meaning "it's a totally made up guess" and 1 meaning "Since I'm betting on something totally known (like roulette) I'm absolutely certain of my edge. Then multiply that figure by your calculated edge -which will give you an adjusted edge ideal to use for Kelly calculations. The problem is finding a good way of calculating how confident you can be about your edge.....

I guess I would go about that by building myself a track record. In other words I would keep a record of estimated edges and how those edges panned out over a series of results. So if I consistently mis-estimated my edges by 20% (0.2) then I'd allow myself a "confidence" factor of 0.8. It looks like this would give a correct result because it would award a guesser who's previous calculation of his edges was completely wrong a confidence factor of 0, which would mean "don't bet."

Heres the short cut to all that kelly  nonsence if you backed one  and it won  you got the value if you back one and it lost  there was no value .
my nap today see div 2  2.30  The Happy  Hammer  won in a three way  Photo  but it WON  zip was  on  4.5 on here   S/P  3/1  so i got the value  only cause it won  5 yards from the line  you could have had  25/1   bet none of you value men were on   at 25/1   value my backside

Kelly or any other staking plan doesn't pick horses (value or no value), it only tries to maximise your profit using your selecions. How you pick them doesn't matter, but if you achieve consistent profit, you do use value betting, only name it skill. Or the majority is right and not me.

Robot
Just be thankful that most people either can't or are too lazy to do value calculations, or else there would be no " suckers" for you to fleece consistently ?
Btw many tks for spending such a lot of time and effort in your very comprehensive posts on here.

aye robot, estimating yr uncertainty about yr edge that way wd see someone end up arbing, cultivating contacts and having small fun bets (which of course is what a lot of people do...)

Even looking at past results it is difficult to arrive at a single number for how good one in estimating one's degree of certainty about one's edge. In my experience, it is usually much easier to get a consistent fig. for some yards than others, based first on knowledge of trainer habits and second on odds movement before races. This is itself is the basis of a winning method, tho' trading and making books will return steadier profits than outright bets.

The general prob. w/ Kelly (and one that has seen me blow off chunks of my bank too often) is that the bigger edge you think you have, the more likely you are to have missed something fundamental about a market. Moderating yr Kelly stake by a measure of confidence won't always help you here.

To be honest Askari that "confidence" stuff is just a bit of fluff - it's not really practicable for all sorts of reasons. I like to try to think through these things though... you never know what might come out of it.

5.10  Kempton  zip picks Steel City Boy  about 4/1  now if it win  i got the value ,  if it gets stuffed  there was no value   this Kelly  nonsence  as nowt to do with it . the only value is the winner  any walk of life

Btw Robot, whilst I follow and understand the points you make regarding calculating the edge from a backer or layer point of view, in that essentially it's a question of your different outlay or (liability) in each case, I am struggling a bit with your extension of that into the roulette example.
In what is a zero sum situation, the backer's disadvantage surely has to be exactly the converse as the casino's advantage ?

Steel City Boy  zip had  the  value , ran ok but got beat  you cannot eat value or pay off the  Mortgage  ,Kelly  my  backside .