Here, in comparison with the usual flat, not the sum of the stake is fixed earlier, but the sum of the “pure” income from each stake. And the sum of the stake varies depending on the coefficient and determines with the formula:
The size of the wanted pure income / (the coefficient – 1 )
Let’s look at the situation when the coefficient is 2, then the sum of the stake will be equal to the size of the wanted pure income. And it’s not obligatory at all to set for yourself only one meaning of the pure income for all the stakes.
For example, you can divide your stakes in the categories of the levels of confidence in the credibility, and to every level of the confidence you give the meaning of the fixed income. It can increase with the increasing of the level of the confidence.
Both systems, the fixed sum of the stake and the fixed sum of the income can be used.
The preferences can be given to that system, which you like most and depending on coefficients. Let’s look at this from the mathematical point of view. We can equal the functions of the amount of the pure income for each of the strategies. We have
then:
Fixed sum of the stake (FSS): f1 (k) = S1*(K-1)*p (K) – S1*(1-p (K)) MF: f2 (k) = S2*p (K) – S2*(1-p (K))/ (K-1),
Where the S1 – it’s the fixed sum of the stake,
S2 – is the fixed size of the income,
K – it’s the coefficient,
p(K) – it’s the credibility of our guessing the stakes with the coefficient K.
let’s the p (K)=1/K+V(K),
where the V(K) – it’s the function, which is expressing our preference above the book-maker’s line, which obviously should depend on the K too.
We can also pretend the V(c)-C/K, where C – it’s the constant, showing the effectiveness of our guesses (for example, if for the K=2 our guesses have the preference 10% on the line, we can think that C=0.20).
So we have:
FSS: f1(k) = S1*(K-1)*(1/K+C/K) – S1*(1-1/K-C/K) = = S1*((K-1)*(1/K+C/K) – (1-1/K-C/K)) = = S1*(1+C-1/K-C/K-1+1/K+C/K) = = S1*C; MF: f2(k) = S2*p(K) – S2*(1-p(K))/(K-1) = = (S2/(K-1))*((K-1)*(1/K+C/K) – (1-1/K-C/K)) = = (S2/(K-1))*(1+C-1/K-C/K-1+1/K+C/K) = = S2*C/(K-1);
Both this functions have the kind of the S (K)*C,
where S (K) – it’s the function of depending the sum of the stake on the coefficient.
Besides for the fixed sum of the stake,
the function S (K) – isn’t even a function, but a constant (concerning with the terms) and that’s why the function of the average pure income for this strategy – is the constant too and it doesn’t depend on the coefficient.