Subject: Re: Dutch
On Thu, 14 Mar 1996, Melvyn Watson wrote:
> Some friends of mine have mention a method of betting called "Dutch Book" > I think this means betting on say 3 or more horses to win and no matter > which one comes in the bet returns a given amount. > (That's of course IF one wins) Have I got it right ? > If so does anyone know the maths. >
The method is pretty simple. Use the following formula to determine bet size.
Bet Size = 100 / (win odds + 1) So for the following 3 selections your position is
A 3/1 100/(3+1) = 100/4 = $25
B 4/1 100/(4+1) = 100/5 = $20
C 9/1 100/(9+1) = 100/10= $10
Total Outlay $55
A couple of points to note:
1. Some people prefer to set their own markets and only take those horses where the available odds are better than your market. When setting your own market the percentages should add up to be less than 100 to ensure you are giving yourself profitable prices.
2. Dont adjust (reduce) your stakes simply because a horse is available at better odds. Thus if you price a horse at 4/1 ($20) and you get 6/1, then the $20 returns $140. This $40 extra represents your overlay and can be a huge boost to your bank occassionally when the odds are far over your wanted price. Andrew A
Date14/03/96
From: Niels Anker Hansen
Re: Dutch
Hi Melvyn.
It isn't that difficult. Let's assume we've got a race with 4 horses at
the odds
A: 2-3 (0.667-1)
B: 3-1
C: 4-1
D: 7-1
You need to convert every odds to the payback for 1 unit invested.
Then you calculate the reciproc of the odds + 1 (let's call it z)
A: 2-3 1 / (1+0.667) = 0.6
B: 3-1 1 / (1+3) = 0.25
C: 4-1 1 / (1+4) = 0.2
D: 7-1 1 / (1+7) = 0.125
Now we want to make a bet on A, B and C. The fraction of the total bet
put on each horse is the z-value of each horse divided by the sum of
z-values from all horses in the dutch-bet. For A, B and C this gives
A: 0.6 / (0.6+0.25+0.2) = 0.57
B: 0.25 / (0.6+0.25+0.2) = 0.24
C: 0.2 / (0.6+0.25+0.2) = 0.19
meaning 57 cent per $ on A etc. However the return for this bet if A wins
is only the investment 0.57 + (2/3)*0.57 = 0.95238, meaning a loosing bet
anyway.
If instead the bet was put on B, C and D the fractions are
B: 0.25 / (0.25+0.2+0.125) = 0.43
C: 0.2 / (0.25+0.2+0.125) = 0.35
D: 0.125 / (0.25+0.2+0.125) = 0.22
The return if B wins is 0.43 + 0.43*3 = 1.74 (and of course the same if C or
D wins, that's the whole idea).
1.74 means that you get 3-4 for the entire bet no matter which one of B, C
or D is coming first.
Hope this explains..
Niels