Re: When the winning probability grows proportionally with the number of lines
- From: gamble4pro <gamble4pro@xxxxxxxxx>
- Date: Fri, 27 Mar 2009 23:56:36 -0700 (PDT)
On 27 Mar, 19:51, duncan smith <buzz...@xxxxxxxxxxxxxxxxxxxxx> wrote:
gamble4pro wrote:
For a certain winning category, does the probability of winning with
one simple line grow proportionally as we raise the number of simple
lines in the played system? I have been asking myself this question
for some time and have argued with several "experienced" people. The
complete answer can be found in the book "The Mathematics of Lottery:
Odds, Combinations, Systems," which I bought recently. In brief, the
answer is that generally, it does not grow proportionally and depends
on the structure of the lines comprising the played system. The author
also gives some conditions: for example, in the 6/49 lottery, in the
third winning category (4 numbers), the condition is that any two
lines of the system must not contain more than 1 common number. A
general formula is also provided. By and large, for the same number of
lines, the winning probability of the system shrinks as we have more
common numbers in the lines. Does anyone know software programs that
generate lottery systems with filters based on conditions set for the
common numbers in the lines?
Has anyone studied that book?
The expected number of wins is proportional to the number of tickets
bought. By buying certain combinations of tickets you can increase you
chances of some sort of win, whilst lowering the chances of multiple
wins (but the expected number stays the same). If you can negate the
possibility of multiple wins then you've maximised the chance of some
sort of win. In the 4 number example you chose the chances are
maximised because it's impossible to get multiple wins if no more than
one number is shared amongst more than one ticket. i.e. If one ticket
wins, then the maximum number of matches on any other ticket is 3 (a
common number plus the two balls that didn't match the winning ticket).
Obviously, as you buy more tickets you reach a point where you can't
meet the "no more than one common number" criterion, at which point the
increase in the probability of some win isn't proportional, but you have
chances of multiple wins to compensate. How important it is to you to
even out the wins / losses, and how much you'd be willing to pay for
that I don't know. Others can advise on software (I don't use lottery
software, or play the lottery for that matter).
Duncan- Ascunde citatul -
- Afişare text în citat -
Thanks. It looks vey logical. So you are suggesting that, from two
systems with the same number of lines, so the same cost - one under
that condition that ensures the liniarity of the probability of
winning and the other with more common numbers within the lines - we
should play the latter, just because it offers multiple wins, while
the former offer only one win? The former has the maximal probability
at the same number of lines and those multiple wins of the latter are
only possible, not sure. So I think we must also know the
probabilities for those multiple wins to come into effect.
.
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