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Algebra / Probability Genius Required

  
 
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HiLo
Old 01-19-2008, 07:53 PM     Post subject: Algebra / Probability Genius Required #1 (permalink)  
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Can one of you maths geniuses help me solve this problem:

I am being offered decimal odds on 4 possible outcomes of a race @
1.79, 5.48, 9.35 & 6.35

I can work out the implied probabilities from these odds as follows:
runner A: 1.79 = 55.86%
runner B: 5.48 = 18.25%
runner C: 9.35 = 10.69%
runner D: 6.35 = 15.75%

The total implied probability comes to 100.55% showing a slight advantage to the bookmaker and thus preventing me from using a dutching system to make this +EV.

However, I earlier placed a $2 bet on runner A at odds of 2.6 (showing a $3.20 profit if this runner wins). This means I can now use a dutching system to make this +EV in all 4 outcomes. (I threw some bets into the spreadsheet until I came up with A=18, B=7, C=4 & D=6 which appears to work.)

What formula should I use to work out the best bet sizes to extract most profit from this situation???

(I am guessing it is something to do with dividing the $3.20 by the .55 overround but am getting lost somewhere....)
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spoonitnow
Old 01-19-2008, 08:07 PM #2 (permalink)  
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 What the fuck is dutching? This is interesting to me.
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HiLo
Old 01-19-2008, 08:25 PM #3 (permalink)  
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dutching is where you place a bet on every runner with the stakes adjusted so that all outcomes show a profit. (Named after Al Capone's accountant reputedly)

In order to successfully apply a dutching system the total implied probability must be <100
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spoonitnow
Old 01-19-2008, 08:59 PM #4 (permalink)  
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Quote:
Originally Posted by HiLo
dutching is where you place a bet on every runner with the stakes adjusted so that all outcomes show a profit. (Named after Al Capone's accountant reputedly)

In order to successfully apply a dutching system the total implied probability must be <100
Gotcha.
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Originally Posted by Ripptyde
I only have 2 simple rules when I am coaching a new student.

Rule # 1: don't ask questions

Rule # 2: don't ask questions

I have no interest in discussing strategy with a protege'. Your job is to remain quiet and listen. I have a very systematic approach that I will share with the right candidate and I promise that I will turn you into a force of nature and show you elements of the game of poker that you never knew existed.
 
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Galapogos
Old 01-19-2008, 09:27 PM #5 (permalink)  
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 Dutching sounds dirty.


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mrickett
Old 01-22-2008, 10:50 AM #6 (permalink)  
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wow I just finished my probability and statistics course 3 months ago and already this makes no sense. The second I left that class room for the last time I left my knowledge there!
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biondino
Old 01-22-2008, 04:29 PM #7 (permalink)  
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Is the technical term "arbitrage"?
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Numbr2intheWorld
Old 01-22-2008, 06:27 PM #8 (permalink)  
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 sorry i don't know.
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euphoricism
Old 01-22-2008, 06:46 PM #9 (permalink)  
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Quote:
Originally Posted by biondino
Is the technical term "arbitrage"?
Basically the same thing, I think. Betting both sides with a gaurenteed +EV result as in sportsbetting.
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HiLo
Old 01-22-2008, 08:00 PM #10 (permalink)  
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Thanks to those who showed an interest:
I have since confirmed that you can't increase the equity by backing runner A at the new odds.

If I wish to guarantee a win by dutching the other 3 selections that is fine, but the return will always be limited by the earlier bet.
i.e. bet sizes should be:
B = (5.2 / 5.48) = 0.95
C = (5.2 / 9.35) = 0.96
D = (5.2/6.35) = 0.82
producing a guaranteed return of $0.88 on any outcome.

If i add to runner A at the new odds then dutch it across the other 3 I will return less than $0.88.

Wish I could express this in terms of algebra though...
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swiggidy
Old 01-22-2008, 08:52 PM #11 (permalink)  
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 I never tried to do the math because I haven't been that bored.

Intuition tells me that if the sum of the odds is > 100% it doesn't really matter how you spread the money profit wise. You could minimize variance, but eV is typically eV in a non-decision based environment.
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