Approach to bet
Betting can be approached in many ways, one of them completely wrong and others- less wrong
The center of gravity around which each approach revolves is-turnover
The biggest obstacle to achieving turnover is the lack of software that would have a strong enough predictive power and that would be widely available.
The only reasonable option is to approach betting as an investment process
On the home page of Bet Kathedra, some introductory but very important terms are given, such as Expected value, decimal odds, and similar
The concept of muffling(the probability of losing a bet!) is also touched on, albeit only lightly.
Muffling is entirely based on the concept of the geometric probability distribution of the so-called Bernoulli process
It sounds complex, but the idea behind it is very, very simple
As for profit, it is based on this inequality
It must be satisfied for any chosen investment method
-let Sbankroll(0) indicate the initial state of the punter’s bankroll
-after 1 period of time(hour, day, week,..), one cycle state of the same bankroll is Sbankroll(1):
Sbankroll(1)= Sbankroll(0) + φ * Sbankroll(0) ………………..Fortuna’s flux
with warm hope that φ > 0 because only then it is fulfilled:
Sbankroll(1)> Sbankroll(0)
or after n cycles,
Sbankroll(n)> Sbankroll(n-1) J
Above inequality is the ground for creating all kinds of plausible models based on high-frequency investments
Cycle approach-high frequency wagering
Each and every bet slip can be identified with this pair: (odds, stake) with absolute revenue value,ARV:
|(odds, stake) |=odds*stake*δ
For a successful bet δ=1 otherwise δ=0
Obviously because by definition, odds must be expressed in decimal odds!
Example: Bet slip,bs1 with Burnley home win and stake 10(eu, pounds, dollars…. it doesn’t matter)
b.s1=(2.15,10)
revenue value b.s1=2.15*10 *δ
b.s1=21.5 *δ
In the same manner, we can introduce sequential arrays of bet slips:
b.s1 , b.s2 , b.s3 , …, b.sn
and observe the final, cumulative revenue value within a larger or smaller betting cycle
We will call this by name- the Diachronic array, Dia
Dia(n)=odds1*s1* δ1 + odds2*s2* δ2 + odds3*s3* δ3 +……+ oddsn*sn* δn
Example:
Say someone put one bet per day throughout :
Monday odds=3 s1=4
Tuesday odds=5 s2=3
Wednesday odds=2 s3=5
Thursday odds=8 s4=2
Friday odds=15 s5=1
Saturday odds=3 s6=5
Sunday odds=7 s7=2
In a given week cycle, Dia has the following form
Dia(7)=3*4* δ1 + 5*3* δ2 +2*5* δ3 +8*2* δ4 +15*1* δ5 +3*5* δ6 + 7*2* δ7
Dia(7)=12* δ1 + 15* δ2 +10* δ3 +16* δ4 +15* δ5 +15* δ6 + 14* δ7
If the touch of fortune happened to him only on Wednesday then we have:
Dia(7)=12* 0+ 15* 0+10*1+16* 0+15*0+15*0+ 14*0
Dia(7) revenue =10
Dia(7) profit=10-5=5
Total stake throughout the week:4+3+5+2+1+5+2=22
If our bankroll at begging week before the first bet was Sbankroll(0) then after last Sunday’s bet:
Sbankroll (1)= Sbankroll(0) -22 + 5= Sbankroll(0)-17 which can hardly be considered as successful investment cycle!
From the above instructive example, the following form of Dia(7) can be observed as a canonical product:
Dia(7)=[odds1*s1, odds2*s2 , odds3*s3 odds4*s4 , odds5*s5, odds6*s6 , odds7*s7] x [δ1 , δ2 ,δ3 , δ4 , δ5 , δ6 . δ7]
From the previous discussion isn’t hard to introduce the next important entities with tide correlation with Dia:
Revenue vector, Vr : [odds1*s1, odds 2*s2 , odds 3*s3, odds4*s4 , odds5*s5, odds6*s6 , odds7*s7] and
Vector of success, Vos: [δ1 , δ2 ,δ3 , δ4 , δ5 , δ6 , δ7]
These 3 entities are interrelated with:
Dia(n)=Vr(n) x Vos(n)
Dia(n)==[odds1*s1, odds2*s2 , ……, oddsn-1*sn-1 , oddsn*sn ] x [δ1 , δ2 ,….., δn-1 , δn ] ………………….. JJ