__Round Robin
Calculator.__

Round Robin bet is a combination bet, which is
combined of several simple bets. Round Robin by M bets of N bets is set of all
possible parlays of M bets, which are selected from N bets full set. For
example Round Robin by 2 of 6 is a set of 21 parlays, each containing 2 bets.
They are selected in various combinations from all 6 bets. The number of
parlays is ,
which is a number combinations by 2 of 6. Each parlay is assigned by equal sum,
so that total sum is equal of total round robin bet sum. In our sample if round
robin bet sum is $21, then each parlay is $1 bet. After all games are over,
results of all parlay bet are totaled.

M and N parameter are selected in upper left part of
calculator window. In order to rebuild page you need click __Change Table__
button.

Lines (coefficients) for simple original bets
can be entered manually, each entered in corresponding text box under bet
number. But they can be entered all at once if they are entered in large text
area under calculator window. To get these lines you click __Read Coefficients__
button. Coefficients are to be entered in d.dd format, for example, 1.22, 4.53,
12.10 and so on. Thus you need to enter two digits after point delimiter. You
can get the odds from bookmaker page by copy-paste operation. All extra text
will be ignored. The coefficients will be placed in bet boxes in order which
they are located in the whole large text area. Extra coefficients will be ignored.

The bets won are marked by checkboxes under
corresponding coefficients. To get payout value you need to click __PayOut__
button. There is a possibility to calculate partial round robin, unchecking
checkboxes from unneeded parlays, in the left part of the table.

If you need not detailed information for each
parley then you could remove it by clicking button __Remove Details__.

You can get payout for various combinations of
won and lost bets by checking or unchecking checkboxes under games coefficients
and then clicking __PayOut__ button. Another way to get similar information
is to use Report button. When pressing __Repor__t button you get new window
where various combinations of won/lost bets are supplied with corresponding
payouts.

Another unique feature or the
calculator is __Optimal Round Robin Selection__ button. If you press the
button maximum and minimal winnings are calculated for a given bets set when
using various round robin cases and various numbers of lost bets. Then you can
select optimal, in some sense, round robin parameters depending on bets
coefficients. Various cases of round robin bet give us a set of facilities from
ordinary bets up to full parlay. The more length has parlay in round robin, the
more are you potential winning in favorite case, but the more you lose in total
if some bets are lost. For example, you can calculate round robin so, that
losing one bet does not lead to loosing round robin as a whole.

In this sample round robin we see that in case
you lose one bet round robin 6/2 and round robin 6/3 give approximately the
same winning. But if you lose two bets, then round robin 6/3 is a bit more
risky than round robin 6/2. From other point of view if all bets win, then
round robin 6/3 is much better than 6/2.

All data entered in the form, including round
robin parameters, coefficients, checkboxes for bets that win, can be saved in a
file. Later we can load this data set and continue round robin analysis.

__Consecutive Round Robin.__

It is a kind of my own ‘invention’. Everybody knows that parlay can be rolled
in time, that is can be ‘emulated’ by ordinary consecutive bets, each made one
after another. This kind of parlay can
be titled as ‘parlay in time’. It has several advantages upon traditional
(simultaneous) parlay and is used by some bettors as a kind of interesting
financial strategy. But there is another combination bet besides parlay – it is
round robin. Here we develop new version of round robin, called consecutive
round robin, which is related to traditional round robin the same way as consecutive
parlay (parlay in time) is related to ordinary parlay.

The same way as in parlay in time, bets in consecutive round robin are not
made in one moment, but one after another. All advantages of parlay in time are
enabled in consecutive round robin. Among the advantages – possibility to
select bets not restricted by bookmaker rules for round robins, possibility to
wait ‘good’ bet if you have not any at the moment.

To execute consecutive round robin we need to develop its plan. For parlay in time we have very simple plan,
it is even need not to be formulated. But in consecutive round robin we can not
work without plan, and the plan can be produced only using a program.

Let us suppose that we need to execute consecutive round robin by 3 of 5.
Below you see a picture, which represents calculations for ordinary round robin
and was produced using our Round Robin Calculator. In case or ordinary,
nonconsecutive round robin we know all lines (coefficients) in advance and the
picture gives us not only round robin plan, but also demonstrates financial
results.

Now let us suppose that we execute the round robin consecutively. Firstly
we have only one bet and we make it. What is to be its size, taking into
account that full round robin bet size is to be $100. Looking at the round
robin plan we see that first step consists of a start of 6 parlays each $10 in
size. So, when emulating the round robin we need to finance our first bet by
$60 = $10 * 6. This sum we can see at
the bottom row having title __Total Bet__, in the first column. This row is
specially added to the calculator for planning consecutive round robin.

Let us suppose that first bet won. For second bet we have three parlays
continuing and three parlays starting.
Because three parlay continue and the first bet has coefficient 1.2 and won,
then the sum of these three bets is $10*1.2 = $12 each, or $36 in total. Also
we start three new parlays each $10 in size. So, we have calculated for second
bet the value equal $36+$30=$66.

Let us suppose then that the second bet also won. For next, third bet we
have according to our plan:

We continue parlay N1 – its sum is now $10*1.2*1.3 = $15.6

We continue parlays N4 and N5 – they are equal (till the moment), each
having $10*1.2 = $12, $24 in total for
two parlays.

We continue parlays N7 and N7 – they are equal (till the moment), each
having $10*1.3 = $13, $26 in total for
two parlays.

We start parlay N10 – its initial sum is $10.

So, we have for the third bet $15.6+$24+$26+$10 = $75.6. This value we see
in 3^{rd} column of the last row in calculator table.

Further we could continue the same way and get bet sizes form all next
consecutive bets. You can see them in last calculator row: 4^{th} bet =
$89.6, 5^{th} bet = $105.2

__By defining bets sums according this scheme we will get exactly the same
financial result as if we have made ordinary round robin, which is made at one
moment. __

In case when all bets won. It is the idea for building the consecutive
round robin scheme.

We have considered in details the case when all bets won. But round robin
is usually used instead of parlay in order to insure bettor in case of one or
two bets possibly lose. In this case round robin does not lose the whole sum as
in parlay. But round robin has a lower total coefficient for case when all bets
won.

Let us describe the similar consecutive round robin scheme when one bet
loses, in the middle of the course.

As we see first three bets we make using the same scheme as in previous
example. But in this case third bet
loses. It means that we decrease of the following bets by the sum of parlays
that were stopped. After third bet was lost we have parlays N1, N4, N5, N7, N8,
N10 stopped. But parlay N1 is already over and does not influence next bets.

Thus consider how these parlays influence next bet sum. The only active
parlays, where bet N4 is contained in, are parlays N2,N6,N9. They have current
sizes:

Parlay N2: $10*1.2*1.3 = $15.6.

Parlay N6: $10*1.2 = $12.

Parlay N9: $10*1.3 = $13.

Thus we get $40.6 for 4^{th} bet when emulating consecutive round
robin. The value we can see in the 4^{th} column of the last row (do no
forget to mark 3^{rd} bet as lost in the calculator table). The
financial result of this round robin emulation is exactly the same if when we
make it in one moment.

When emulating round
robin we can run against the situation when bet loses. What to do then. We can
continue realizing the initial scheme in order to have minimal loss which is
defined by calculation of financial result when losing one bet. In our previous
example when we lose one bet and no more, we get 82.56% of initial bet sum
invested. Thus we lose only 17% of the bet sum.

The second way is to
increase sums for remaining parlays – that is, to use slight progression
strategy, hoping we will not lose no more (especially when coefficients are
low). For example, in order to try to return our money back we need to increase
each bet in scheme by 100/82.56 = 1.2 times. If we get first bet in our scheme
lost then to get money back we could try to increase each next bet by 100/92.68
= 1.07 times. If despite one bet loss we are aiming at getting the same profit
as before we need to increase all next 4 bets by 2.4 times. In this case total
round robin size will be increased to $60+$4*24= $156., a bit more than in 1.5 times.

The third way: stop round robin and start new one. In our example we go
out the round robin having sum equal $10*1.2*1.3+$10*1.2*1.3+1.2*$10+1.3*$10 = $31.2+$13+$12
= $56.2. Thus we leave our round robin when losing less than 50% of initial bet
size. If we lose at the first bet of round robin and go out it - we lose 60% of
initial bet size.

Mathematically neither parlay nor round robin has neither advantages,
nor drawbacks in comparison with single ordinary bets when our edge is equal to
zero. Thus I described the consecutive round robin only in order to fill the
gap in combination bets set.
Nevertheless there is a series of nonmathematical advantages that allow
including this consecutive round robin it bettor toolbox. Taking into account
that we have software that can build consecutive round robin plans.

In conclusion I will emphasize once more that no manipulation with bets sizes,
which can be seen in parlays or round robin, are they made consecutively or at
one moment, cannot increase bettor edge for a given bet(s). They only can make
some insurance when risking money, find compromise between bankroll growth and
risk of losing it. It is valid only when a bettor has an edge- that is has
capability to select sets at relatively (reality) high coefficients.