Greening Up Maths

[geoffw123]

Hi

I have been trying to figure out how to green up a market with more than 1 selection having been bet on. I have managed to totally confuse myself now Let me give a concrete simple example.

Starting point that we are trying to Green up

SelId	 Profit/Loss	Back Price   Lay Price
1               6.15	    4.90	4.90
2              -4.65	    4.70	4.70

For the purpose of this example I have made the back and lay prices the same.

If I work out how to make profit loss the same using a Back bet, I get
Back Bet on SelId = 2 Amount = £2.298

SelId	 Profit/Loss	Back Price   Lay Price
1               3.85	    4.90	4.90
2               3.85	    4.70	4.70

If however I green up using a Lay Bet I got this

Lay Bet on SelId = 1 Amount = £2.20

SelId	 Profit/Loss	Back Price   Lay Price
1              -2.45	    4.90	4.90
2              -2.45	    4.70	4.70

Greened up to identical values but hugely different from the £3.85 I got from using back bets.

OK, so have I made a stupid calculation error here as instinctively I was expecting Lay and back bets to converge to the same Profit Loss value ?

Can anyone offer any insight into this please ?

[Franklin1]

That's an interesting example, but think you are asking a trick question!

SelId Profit/Loss Back Price Lay Price
1 3.85 4.90 4.90
2 3.85 4.70 4.70
3! -2.298


SelId Profit/Loss Back Price Lay Price
1 -2.45 4.90 4.90
2 -2.45 4.70 4.70
3! +2.20

Basically I think your numbers are ok, but if you back something in a two runner market at a 41.6% overround you'll tend to make lots of money and if you lay things at 41.6% overround you'll lose money. If there are runners not mentioned in your example then they will have P&L's too

[geoffw123]

Hi Franklin

Thanks for the reply. Yes, I was trying to solve a more general and complex question, and was trying to simplify it with a fictional example here. My intuition was that if you have any 2 selections with the same back and lay prices, you ought to be able to green them up to the same figure if you use either a back or a lay. The numbers say that is blatantly wrong.

Anyway, the more general question I am still stuck on is :

If you have an arbitrary market of n selections where they may have been a number of back and lay bets on any selections, how do you green that up ?

More specifically, how do you calculate which selections do you place the greening bet(s) on and for each bet whether it is a back or a Lay bet in order to maximise the final greened up total P/L.

I am finding that a very tricky bit of maths at the moment.

Regards Geoff

That's an interesting example, but think you are asking a trick question!

SelId Profit/Loss Back Price Lay Price
1 3.85 4.90 4.90
2 3.85 4.70 4.70
3! -2.298


SelId Profit/Loss Back Price Lay Price
1 -2.45 4.90 4.90
2 -2.45 4.70 4.70
3! +2.20

Basically I think your numbers are ok, but if you back something in a two runner market at a 41.6% overround you'll tend to make lots of money and if you lay things at 41.6% overround you'll lose money. If there are runners not mentioned in your example then they will have P&L's too

[Franklin1]

My intuition was that if you have any 2 selections with the same back and lay prices, you ought to be able to green them up to the same figure if you use either a back or a lay. The numbers say that is blatantly wrong.

If there are more than 2 selections then your intuition is wrong. Laying will make profit on the other selections and backing will lose and IF your intuition was right the P&L on those other selections would be 'free'.

If you have an arbitrary market of n selections where they may have been a number of back and lay bets on any selections, how do you green that up ?

This can be done, but it's pretty involved and there are lots of solutions. Greening up is over-rated anyway.

[JayBee]

http://www.betfairprotrader.co.uk/20...fair-bots.html

One of many methods.

I'll write some code for the blog, eventually.

Hi

I have been trying to figure out how to green up a market with more than 1 selection having been bet on. I have managed to totally confuse myself now Let me give a concrete simple example.

Starting point that we are trying to Green up

SelId	 Profit/Loss	Back Price   Lay Price
1               6.15	    4.90	4.90
2              -4.65	    4.70	4.70

For the purpose of this example I have made the back and lay prices the same.

If I work out how to make profit loss the same using a Back bet, I get
Back Bet on SelId = 2 Amount = £2.298

SelId	 Profit/Loss	Back Price   Lay Price
1               3.85	    4.90	4.90
2               3.85	    4.70	4.70

If however I green up using a Lay Bet I got this

Lay Bet on SelId = 1 Amount = £2.20

SelId	 Profit/Loss	Back Price   Lay Price
1              -2.45	    4.90	4.90
2              -2.45	    4.70	4.70

Greened up to identical values but hugely different from the £3.85 I got from using back bets.

OK, so have I made a stupid calculation error here as instinctively I was expecting Lay and back bets to converge to the same Profit Loss value ?

Can anyone offer any insight into this please ?

[davecon]

http://www.betfairprotrader.co.uk/20...fair-bots.html

One of many methods.

I'll write some code for the blog, eventually.

Many Thanks for this JayBee even though I don't trade anymore
But nice to see when a member of our little clan here submits such very helpful and valuable input
Nice site stuff as well btw - Cool
Cheers
Dave