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May 30th, 2007, 08:55 PM   #1
Joined: May 2007

Posts: 1
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math formula for trading

Hi Guys,

It's my first post, so apologies if this isn't in the right section

Ok where do I start.

I recently came across a small software program on the net called "Arbcruncher" which effectively allows the user to "dutch" a horse race.

For those of you who are unfamilar with the term, to "dutch" a horse race is to bet on multiple selections, betting varying amounts on each selection, based upon the odds available, so that no matter which of your selctions wins, you earn the same amount of profit.

A very simple example would be to have two horses, with the following odds:

1. Red Rum - 2.0
2. Kauto Star - 4.0

Now if I bet £20 on Red Rum, and £10 on Kauto Star, I will get a return of £40, no matter which horse wins....and my initial layout was a total of £30 on the two horses, so my net profit would be £10

With me so far? this Arb cruncher software does this with ease, but I thought that rather than purchase the software, i'd figure out how it works (by working out the calculations) and create my own version in an excel spreadheet

I managed to do quite well, in that I realised the calculations were as follows:


To acheive £X net profit on the race with four horses:

horse 1 odds=a
horse 2 odds=b
horse 3 odds=c
horse 4 odds=d

Amount to bet on horse 1

Amount to bet on horse 2

Amount to bet on horse 3

Amount to bet on horse 4


So for example, lets say I wanted to make £75

horse 1 odds=4
horse 2 odds=6
horse 3 odds=8
horse 4 odds=10

Amount to bet on horse 1
=75/100-((100/4)+(100/6)+(100/8 )+(100/10))/100)/4

Amount to bet on horse 2
=75/100-((100/4)+(100/6)+(100/8 )+(100/10))/100)/6

Amount to bet on horse 3
=75/100-((100/4)+(100/6)+(100/8 )+(100/10))/100)/8

Amount to bet on horse 4
=75/100-((100/4)+(100/6)+(100/8 )+(100/10))/100)/10


Bet £52.33 on horse1
Bet £34.88 on horse2
Bet £26.16 on horse3
Bet £20.93 on horse4

Total layout = £134.30

Return if any horse wins = £209.30

Net profit = £75

Ok so hopefully you understand what I mean......At this stage I wanted to try out my new spreadsheet, and I chose to test this on Betfair, an online exchange.

But...... unfortunately, Betfair charge a 5% commission on all winning bets, so this makes my calculations incorrect.

Take the above example.....if horse 1 had won the race, I would have lost 5% of the winning bet (i.e. 5% of £209.30 = 198.84) which means my net profit would now be 198.84-134.30 = £64.54

What I need to do is work out the calculations to take into account the 5% commisison on the winning bet.

I've tried dividing everything by 95, then multiplying by 100, but this doesn't work.

The calculations need to be able to be applied to be able to dutch anywhere between 2 and 6 horses per race (the example above is on four horses), and needs to take into account the 5% commission so that the net profit always equals X

If anyone could help me with this i'd be forever grateful....i've spent hours trying to figure it out but can't!

Thanks in advance
jpowell79 is offline  
May 31st, 2007, 12:34 AM   #2
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Joined: Dec 2006

Posts: 20,373
Thanks: 2010

You just need the effective odds, which include any return of stake and allow for any commission due. Choose an amount Y, then divide it by these odds to get your stake amounts. Calculate your profit (or loss). Now repeat the calculations with a new Y chosen so that your profit/loss is as desired.

Suppose, for example, the effective odds are as below.

horse 1 odds=3
horse 2 odds=5
horse 3 odds=7
horse 4 odds=10
horse 5 odds=105

You choose Y = 210, giving stakes as below.

horse 1 stake=70
horse 2 stake=42
horse 3 stake=30
horse 4 stake=21
horse 5 stake=2

The total staked is 165, so your profit is 45.

If your tarket profit is 75, you need to scale up by 75/45 = 5/3. You recalculate using Y = 210 × 5/3 = 350.

horse 1 stake=116.67
horse 2 stake=70
horse 3 stake=50
horse 4 stake=35
horse 5 stake=3.33
Total: 275

Apart from the tiny error (if horse 1 or 5 wins) caused by the fact that two of the original stakes were not exactly divisible by 3, you then achieve your objective. Note that you will normally find that the odds are less favourable, so that you make a loss rather than a profit.
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