Help with basic (ahem) Maths question
OK I was just revising the basic Matching Mathematics (using the Matching Spreadsheet as reference), and one of the calculations has is confusing me a little, because I'm trying to understand why each calculation works.
Lets say you are backing £10 at odds of 3.0, and also laying at odds of 3.0.
Also assume that there is no betfair commission.
To find out how much you need to lay in order to ensure the same return whichever way the bet goes, you divide your potential return by the lay odds.
£30/3.0 = £10.
So far so good.
Of course we need to factor in Betfair commission.
Instead of Dividing your potential return by the lay odds, you subtract 0.05 from the lay odds and THEN divide the potential return.
£30/2.95 = £10.17.
Thus your lay stake would be £10.17, and the return either way would be an equeal amount - £9.66.
The thing is, I can't get my head round why you always subtract 0.05 from the lay odds,as this is not 5% of the odds.
However, I know this is correct (£10.17 lay stake) because I have checked it on umpteen matcher sheets.
Can anyone clarify this for me?
The equation in my matcher sheet reads like this.
Back Return / (Lay Odds - Commision/100)
So the 0.05 doesn't represent 5% of the odds but represents the 5% of the return on the lay, i.e. commision
Here is how I calculate the formulas for spreadsheets:
Lets look at your bet and assume there are only 2 outcomes.
S1 = stake at bookie
S2 = stake at betfair (the amount you will lay)
O1 = odds at bookie
O2 = lay odds at betfair
C = commision at betfair
So you have 2 equations that you want to be equal, these are the two results that can happen, 'win bookie' and 'win betfair'. You know all of the above variables but S2 (this is what you are trying to solve for), so set the 2 equations equal and solve for S2:
Win bookie = win betfair
S1*(O1-1) - S2*(O2-1) = -S1 + S2*(1-C)
Get the S2's on the right and the S1's on the left
S2*(O2-1)+S2*(1-C) = S1 + S1*(O1-1)
S2* [(O2-1) + (1-C)] = S1*[1 + (O1-1)]
S2 = S1*[1+(O1-1)]
That is the unsimplified equation for your betfair stake. I hope you can follow along with that and see where each part of the equation originally came from.
Now simplify the top of the righthand side and you get S1*O1 and simplify the bottom of the righthand side and you get .... (O2-C) ! This gives the expected:
S2 = (S1*O1)/(O2-C)
In other words, there is no reason like 'It's 5% of the odds" or anything like that, it's just that the equation simplifies to that.
That is what I think, anyway
Can you clarify the first equattion;
S1*(O1-1) - S2*(O2-1) = -S1 + S2*(1-C)
I get S1*(O1-1) - S2*(O2-1) = -£0.34
But S1 + S2*(1-C) = £19.16
Am I reading this wrong?
So the left side is what happens if you win at the bookie, we'll assume you've matched correctly at 3.0/3.0 so £10.17 lay stake:
Originally Posted by Landprofits
S1*(O1-) - S2*(O2-1) = £10*(3.0-1) - £10.17*(3.0-1) = £20 - £20.34 = -£0.34
The right side is what happens if you win at betfair:
-S1 + S2*(1-C) = -£10 + £10.17*(0.95) = -£10 + £9.66 = -£0.34
Oh, looking at your post again, it seems you missed the - (minus) sign in front of S1 maybe on the right side calculation?
Oh yeah, I missed the - (minus) sign.
And the hospital told me the other week I had 20/20 vision....
I understand that 0.05 represents 5% if the return on the lay (BF commission).
Originally Posted by SteveSharpe
What is confusing me is why, whatever the odds are you always subtract 0.05 from the odds. I didn't expect this to be a static figure.
(Still working through Slims formulas.......)
Slim, do you mind if I ask.. would you recommend any books that you have read for equations etc applicable to Gambling?
I haven't read any maths books that relate to gambling in specific, but I have done a maths degree.
So for me it's all about systems of equations and unknown variables.
For a 2 outcome event, like a back/lay you have 2 equations (win bookie and win betfair) and one unknown - the betfair lay stake.
For a 3 outcome event, like a 3-way dutch, you have 3 equations (Team A win, Draw win, Team B win) and 2 unknowns - the stakes on the draw and Team B (assuming you know what you want to bet on Team A).
These kind of systems of equations, where you have more equations than unknowns, will have unique answers that can be solved using basic algebra.