LuckyInLove's Calcs

[LuckyInLove]

Forgive my indulgence with this but I think it might well be as useful to some as it has been to me. I have been going on a bit of a journey tackling the maths behind matched betting and it has finally broke my dependence on the spreadsheets. It is something that has been on my list of 'good' things to do for a year now and picking up on Andy's preference to do it by hand (or old Nokia was it??) I thought it about time I worked it out. Lucky I did because the spreadsheet I was using for some reason was wrong, I played around with different ones in the beginning and pulled in the bits I wanted and used it for the past year. It was me that probably broke it - not enough to notice, it was only the bet commission calc that was off but that was proof to me how naive I have been doing this.

If it is useful I will continue adding bits to it as I work on more complex stuff - hopefully it will allow you too to see how this all works.

I started with the idea that I will use a variable convention throughout, so that when I see a calc I will immediately know what each bit is and as I get used to it myself it really does work well. So I made the following rules for the variables:

• Use the same one for the same meaning throughout any calcs I do
• Any currency ones use capitals
• The type of variable e.g. back or lay I gave an appropriate subscript
• Used a ' to denote any back commission ones

Well here is the variable list:

<table valign="top" style="border: 1pt solid rgb(163, 163, 163); direction: ltr; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody><tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Name
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> Back
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> Lay
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Stake
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> S_b
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> Sl
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Odds
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> Ob
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> Ol
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Commission
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> cb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> cl
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Profit
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> Pb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> Pl
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Winnings
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> Wb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> Wl
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Losses
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> Lb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> Ll (liability)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3548in;"> Return
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.2402in;"> Rb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.0291in;"> Rl
</td> </tr> </tbody></table>


Here is the list of calculations:


<table valign="top" style="border: 1pt solid rgb(163, 163, 163); direction: ltr; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"><tbody><tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Back Return
(no commission)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> Rb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> SbOb

If offsetting return by Fb then use
Rb+Fb
Fb is negative if you wish to lose at bet
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Back Profit
(no commission)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> Pb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> Sb(Ob-1)

SbOb-Sb

Rb-Sb
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Back Return
(with commission)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> R'b
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> Sb[(Ob-1)(1-cb)+1]

Sb(Ob-1)(1-cb)+Sb

If offsetting return by Fb then use
R'b+Fb
Fb is negative if you wish to lose at bet</td></tr></tbody></table>
tbc...

[LuckyInLove]

<table valign="top" style="border: 1pt solid rgb(163, 163, 163); direction: ltr; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody><tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Back Profit
(with commission)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> P'b
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> Sb(Ob-1)(1-cb)

(SbOb-Sb)(1-cb)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Back Loss
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> Lb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> Sb
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Lay Risk Liability

(Bet Wins = Lay Loses)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> Ll
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> Sl(Ol-1)

SlOl-Sl
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Lay Return / Lay Profit

(Return on Lay Winning - including commission)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> R'l
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> Sl(1-cl)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Matching Lay Stake

(Back Bet has commission)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> Sl
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> Sb[(Ob-1)(1-cb)+1] / (Ol-cl)

R'b / (Ol-cl)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.4937in;"> Matching Lay Stake

(No commission on Back Bet)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;"> Sl
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9319in;"> SbOb / (Ol-cl)

Rb / (Ol-cl)
</td> </tr> </tbody></table>

[LuckyInLove]

<table valign="top" style="border: 1pt solid rgb(163, 163, 163); direction: ltr; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody><tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Overall Profit / Loss - for full matched bet/lay

(No commission on Back Bet)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> Pb-Ll

Rb-Ll-Sb
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Matching Lay Stake
With amount of underlay to win/lose extra Fb on the bet if it wins
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> [SbOb+Fb] / (Ol-1)

(Rb+Fb) / (Ol-1)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Matching Lay Stake
With amount of underlay to win/lose extra Fb on the bet if it wins
(Back Bet has commission)
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> [Sb[(Ob-1)(1-cb)+1]+Fb] / (Ol-1)

(R'b+Fb) / (Ol-1)

</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Overall Risk
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> Sb+Ll
Sb+Sl(Ol-1)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Bet Zero Profit Lay Stake
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> (R'b-Fb -Sb)/(Ol-1)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Lay Zero Profit Lay Stake
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> Sb/(1-cl)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Arb Profit (based on back stake)- with no bet commission
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> 100[ Ob(1-cl)/(Ol-cl) -1 ]
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.5131in;"> Arb Profit (based on back stake)- including bet commission
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 0.7368in;">
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.9125in;"> 100[ [(Ob-1)(cb-1)(cl-1) - (Ol-1)]/(Ol-cl) ]
</td> </tr> </tbody></table>

[LuckyInLove]

This I found useful when figuring out how to do the calculations:

<table valign="top" style="border: 1pt solid rgb(163, 163, 163); direction: ltr; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody><tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3756in;"> Bet Event Table
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.6326in;"> Book / Exchange - where bet is made
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.1437in;"> Exchange - where bet is layed
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3756in;"> Bet Wins
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.6326in;"> Pb

Sb(Ob-1)

If Commission on bet then use

P'b

Sb(Ob-1)(1-cb)

Add / Subtract Fb for stake forfeit
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.1437in;"> -Ll

Sl(Ol-1)
</td> </tr> <tr> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 1.3756in;"> Bet Loses
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.6326in;"> -Sb
</td> <td style="border: 1pt solid rgb(163, 163, 163); padding: 4pt; vertical-align: top; width: 2.1437in;"> R'l

Sl(1-cl)
</td> </tr> </tbody></table>

[LuckyInLove]

Here's yet another post - (some people will do anything to achieve their RAF status won't they )

To show how using the Bet Event table and using the existing calculations to figure out the classic bet/lay formula. This was a complete mystery to me until I finally worked it out myself - now it all becomes simple.

So here's my working out - Create a calculation to make equal profit on both bet win and lose on a bet and lay



Overall Bet Profit on Win = Overall Bet Profit on Lose
So from the Bet Event Table put in the profits and make them equal

Pb+(-Ll) = (-Sb)+R'l


So

Sb(Ob-1) - Sl(Ol-1) = Sl(1-cl) - Sb
Sb(Ob-1) + Sb = Sl(1-cl) + Sl(Ol-1)
SbOb-Sb + Sb = Sl(1-cl + Ol-1)
SbOb = Sl(Ol-cl)
Sl = SbOb / (Ol-cl)


So the stake needed to lay - to create equal profit on back and lay is

Sl = Rb / (Ol-cl)



Above calculation but include commission on bet
Sl = R'b / (Ol-cl)
Sl= Sb[(Ob-1)(1-cb)+1] / (Ol-cl)

[LuckyInLove]

For those of you who have not done any equations for a while I assure you the calculations break down into quite simple entries on a calculator. Many of the things do not change much - like commission etc.

I hope to find some time to go through how you can do these calcs quickly and simply - even using an old Nokia .

Come one - put away those spreadsheet crutches

I admit I do still use mine, but I have now added lots of useful stuff now I understand to take care of underlaying to get the preferred results etc.

I am currently working through many of the 'if bets' and how they can be tackled on the run i.e. no spreadsheet

For now any feedback is welcome...
(I'll refrain temporarily from indiscriminately upping my post count to gain my RAF medal)

[Andy]

Those calculations are all probably correct, to be honest I didnt look that hard but I am sure they are. You have definitely taken a mole hill and made a mountain of it though, all you are really doing is placing two bets. You will Win £A and lose £B. It is KeyStage3 maths really and there is no need to take it to degree level.

If you cant do the maths of the bet, ie why you are placing it, in your head then im not sure its a great idea to place it. If you get it "wrong" you wont know that, or why, and you wont be able to get yourself out of it either if you dont fully grasp how/why you got into it. Im generalising there, but really if you dont 100% know why you placed a bet for £X, whats going to happen if A B or C occours, and why you layed for £Y, then dont place the bet. Using a Spreadsheet YOU MADE is fine I have ranted before that they are bad and have a lot to answer for, but I didnt mean the spreadsheets themselves, I mean if YOU made it then its just doing what you would do anyway but working it out quicker, its just a usefull tool. Thats fine. But using a Spreadsheet someone else made and basing your bets, stakes, etc on that without you knowing why, well that is just crazy.

But well done for making your own formulas and what have you, and its probably why other people make more £s than me that I dont go to any great depths of why I put £X stakes in, half the time i use round numbers with a dose of what I want to happen anyway, there is no point going into detail for me. Plough through as many as possible quickly and easily is the way I tend to do it.

I like your Signature by the way, it made me smile.

[LuckyInLove]

Ouch! - I should have thought twice about posting this... I do hope the effort is useful to someone out there.

This molehill has certainly been a mountain for me to understand, something I put off for a while but glad I finally got round to doing it. The main reason for me doing this is to understand how to get my head round 'grumblebuses', 'if bets' and properly handling large WR later on the US Books and to be more flexible with future bets.

When I started I began with an MSE FAQ and just followed it, crazy but true, trying different things out on the way, sometimes disasterously, mostly profitable - (so I am probably slated with a newbie brush by the die-hard gamblers here ).

If it is of no use to anyone then by all means ignore it - it was just so useful to me I really wanted to help others in the same boat.

The signature came about when you accidently deleted/moved my lengthy post a while ago - and it sort of stuck with me ever since.

[etherz]

No this is definately a great idea. Along with the people at uni here I know that do matched betting, we often work through equations and proofs of WHY each equation works. It helps me understand what is going on, and why I am doing it. It also means I can approximate the calculations on the fly ie: doing it in your head like andy does...

For example last night we discussed the goldbet offer for over an hour, and then settled on our first solution, treat it as a SNR (will make a more in depth post in that thread later, as I dont think anyone explains the best strategy to profit from the offer).

[munk]

I'm sorry I didn't post already, had meant to but was busy yesterday. Yes very good thread indeed I think and gives people who did want to 'work it out' for themselves formally (whether just for the sake of it or whether for applications programming) somewhere to look to double check what they're doing. I believe the user hazard was asking for something like this before, hopefully he will find this thread.