Sometimes even best lines have values that do not constitute real
surebets, arbs.
But there is one interesting possibility even in that case. Suppose we have 3-Way line 1-X-2. Very often draw line (K_{X}) is less than
estimated by player (which is considered by him as ‘fair’) and, consequently, ‘fair’
probability of the draw is less than estimated by bookmaker. More over,
suppose remaining two outcomes (1-2) constitute a real ‘surebet’. If we neglect the probability of draw we could make
bets on outcomes ‘team 1 wins’, and ‘team 2 wins’ and get profit in any case
when some team wins. But when teams
draw, we loose the bet. It is so
called __incomplete surebet__.

As you see the incomplete does not guaranty profit in any case – there is
possibility of loosing the ‘incomplete surebet’.
But let us go further and see what can be done to overcome the drawback. Remember there is so called ‘value bet’. This is a bet with overestimated line
(coefficient) – that is, book set it to a value which is more than fair line. It is clear enough how to use that situation –
just make a bet on overestimated line and you will get a profit in a long run. The same way, a line (coefficient) can be
underestimated. That is – book set
it to a value that is less than fair line.
Can
we use the situation in some way? Sure
we can not make a bet using the line – it is nonsense.
If we have 2-way line we can have a situation when an opposite line is ‘value
bet’. But we can not guaranty that opposite bet is
‘value bet’ if principal one is underestimated bet.
This is because of book margin which could have rather big value making
opposite bet as having no value. So,
what can we do in order to make incomplete surebet to be a profitable one?

Suppose we have 3-way line: 1-X-2 and we know that line X is
underestimated – have less value than fair.
It means that we somehow can estimate probability of X as PF_{X} (Fair
P_{X}), which is less than P_{X}.

As it was stated before we could consider incomplete 3-Way surebet.

L = 1/K_{1} + 1/K_{2} < 1,

Let us denote P3_{ }as probability of the third outcome, which
was not taken into account. Then we
shall with a probability equal to (1-P_{3}) win V*(1/L-1) using the
incomplete surebet, and we shall loose bet sum V with probability equal to P_{3}. That is, in average we will have a profit equal to:

(1-P_{3})* V*(1/L-1)- P_{3}* V

For
this expression to be positive, we need to satisfy the following conditions:

(1-P_{3})*(1/L-1)- P_{3
}> 0

or

1/L-1-P_{3 }/L > 0

or

L+P_{3 }< 1

or

1/K_{1} + 1/K_{2} + 1/K_{3} < 1

Where
K_{3 }= 1/P_{3,.}

Thus
is order to insure profitability of the statistical surebet, we are to
calculate the minimal value of coefficient for the third outcome using
coefficients of the other two outcomes as

K_{3
}= 1/(1- 1/K_{1} - 1/K_{2}),

Then, calculate maximal acceptable probability of the third income as P_{3 }= 1/K_{3}
and ask ourselves: “Are we sure that fair probability of the third outcome is
not higher than P_{3}”. If
we answer YES, then we can use the incomplete surebet.
In this case we can consider incomplete surebet as full surebets, but
statistical one, which guaranties profit but only in a long run. But maybe you doubt after you calculated value of
P_{3 }for the bet? – it depends.

Now let us show that there always
exists an incomplete surebet 1-X-2, even using lines within the same bookmaker. Suppose there is no incomplete surebet available
for no pair of coefficients: 1-2, 1-X, 2-X.
That is:

1/K_{1} + 1/K_{2} >= 1

1/K_{1} + 1/K_{3} >= 1

1/K_{2} + 1/K_{3} >= 1

Summing
the three inequalities we get:

2*(1/K_{1} + 1/K_{2} + 1/K_{3})>= 3

or

1/K_{1} + 1/K_{2} + 1/K_{3 }>= 1.5

Thus we can see that if there are coefficients from the same bookmaker
then a margin of the bets is no less than 50% - practically impossible. So, it means that at least one pair if outcomes:
constitute __incomplete__ surebet, even using lines of the same bookmaker. But for practical use you need to seek incomplete
surebets with maximal profit combining lines from several bookmakers.