Don't approach playing the lottery like this. "Gee my odds are 9 billion to 1".
You can improve your chances by playing the odds.
That's just wrong. Sure, winning the lottery will always be a
matter of luck but with some thought, you can IMPROVE your odds
somewhat.
Check out Ars Conjectandi, "The Law Of Large Numbers", by
Jacob Bernoulli (sound familiar?) published eight years after
his death in 1713.
Just looking at the primary part of the game.. the 5 numbers
between 1..50. What are you chances of drawing an even number
or an odd number as the first draw? Well, there are 25 evens and
25 odds. So it's 50% that you will draw an odd or even number.
What are the chances you will draw ALL even or ALL odd? Very
unlikely. You'll find that if you look at the history of that
lottery game, that 2odd/3even is the most prevalent pattern.
What if you break it down more? What if you took the 50 numbers
and broke them down into three groups.. group A (17 balls 1..17), group B (17 balls 18..34),
and group C (16 balls 35..50). Initially, the odds favor drawing a
ball from group A or B, simply because there is one extra ball in each of
those groups. Going against the odds, say a ball is drawn from
group C. Now what are the odds of drawing a ball from group A or group B?
Better, eh?
By calculating how many number combinations are possible for each
group, you can calculate the odds for each type being drawn on a
given night. There are 21 different ways 5 numbers can be drawn
from 3 different number groups.
Moreover, you can time your bets. Going back to the odd/even theory,
if you know that an all odd or all even drawing takes place on average
about once every 1000 draws and that hasn't happened, the chance that
this happens increases (even though it still remains small).
The balls in the lottery drawings are physical things. When
there are more odd, for example, these odd numbers bounce around
and get in the way of the even numbers.
Don't take my word for it. Examine as many previous drawings
as possible and see how many all odd/even, 4 odd/1 even, 3 odd/2 even
drawings there are. See how many times all five numbers appeared in the
group A numbers and how many times it was distributed across the
three groups.
You may improve your odds by doing so.
| [reply] |
Sorry about the formatting.
To illustrate, I slapped some extra code into that powerball
program I found here.
#!/usr/bin/perl -w
use strict;
use LWP::Simple;
my (@numbers, %normals, %powers, %chiral );
my $content;
unless (defined ($content = get('http://www.powerball.com/results/pbhist.txt'))) {
die "Cannot get PB history.\n";
}
@numbers = split /\n/, $content;
my @data;
foreach my $line (@numbers) {
next if ($line =~ /^!/);
@data = split(/\s/, $line);
shift @data; # throw away the date
$powers{pop @data}++;
my $drawing_odd = 1;
my $drawing_even = 0;
my $group_a = 0;
my $group_b = 0;
my $group_c = 0;
$chiral{total}++;
$chiral{totalnums} += 5;
foreach (@data) {
if ($_ % 2 == 0) {
$chiral{even}++;
$drawing_even++;
} else {
$chiral{odd}++;
$drawing_odd++;
}
if ($_ < 17) {
$chiral{group_a}++;
$group_a++;
} elsif ($_ < 33) {
$chiral{group_b}++;
$group_b++;
} else {
$chiral{group_c}++;
$group_c++;
}
}
$chiral{"${drawing_even}_even"}++;
$chiral{"$group_a-$group_b-$group_c"}++;
foreach (@data) {
# print "Normal: $_\n";
$normals{$_}++;
}
}
print "Normal Pick Rate:\n\n";
my @norm_sort = sort { $normals{$a} <=> $normals{$b} } keys %normals;
foreach (@norm_sort) {
print "$_ :\t($normals{$_})\t", "*" x $normals{$_}, "\n";
}
print "\nPower Pick Rate:\n\n";
my @power_sort = sort { $powers{$a} <=> $powers{$b} } keys %powers;
foreach (@power_sort) {
print "$_ :\t($powers{$_})\t", "*" x $powers{$_}, "\n";
}
print "\nNormal Picks:\t";
print join(" ", sort (@norm_sort0 .. 11)), "\n";
print "\nPower Picks:\t";
print join(" ", sort (@power_sort0 .. 3)), "\n";
print "\nOdd/Even:\n";
printf "\t ODD: %d (%0.1f%%)\n", $chiral{odd}, ($chiral{odd}/$chiral{totalnums})*100;
printf "\tEVEN: %d (%0.1f%%)\n", $chiral{even}, ($chiral{even}/$chiral{totalnums})*100;
printf "\n0 Even/5 Odd: %d (%0.1f%%)\n",
$chiral{"0_even"},
($chiral{"0_even"}/$chiral{total})*100;
printf "1 Even/4 Odd: %d (%0.1f%%)\n",
$chiral{"1_even"},
($chiral{"1_even"}/$chiral{total})*100;
printf "2 Even/3 Odd: %d (%0.1f%%)\n",
$chiral{"2_even"},
($chiral{"2_even"}/$chiral{total})*100;
printf "3 Even/2 Odd: %d (%0.1f%%)\n",
$chiral{"3_even"},
($chiral{"3_even"}/$chiral{total})*100;
printf "4 Even/1 Odd: %d (%0.1f%%)\n",
$chiral{"4_even"},
($chiral{"4_even"}/$chiral{total})*100;
printf "5 Even/0 Odd: %d (%0.1f%%)\n",
$chiral{"5_even"},
($chiral{"5_even"}/$chiral{total})*100;
printf "\n\nGroup A: %d (%0.1f%%)\n",
$chiral{"group_a"},
($chiral{"group_a"}/$chiral{totalnums})*100;
printf "\n\nGroup B: %d (%0.1f%%)\n",
$chiral{"group_b"},
($chiral{"group_b"}/$chiral{totalnums})*100;
printf "\n\nGroup C: %d (%0.1f%%)\n",
$chiral{"group_c"},
($chiral{"group_c"}/$chiral{totalnums})*100;
foreach my $k (sort {$chiral{$a} <=> $chiral{$b}} keys %chiral) {
my $v = $chiral{$k};
if ($k =~ /^\d\-/) {
printf "\n\n%s: %d (%0.1f%%)\n",
$k, $v, ($v/$chiral{total})*100;
}
}
print "\nDisclaimer:\n\tThis is not statistically accurate, except in that the drawings are guaranteed.\nThi
s is just a quick frequency analysis making no pretenses as to predictive accuracy.\n"
Ok, it's not beautiful code but it works and illustrates my
point. Let's examine the output:
Odd/Even:
ODD: 677 (50.5%)
EVEN: 663 (49.5%)
0 Even/5 Odd: 7 (2.6%)
1 Even/4 Odd: 38 (14.2%)
2 Even/3 Odd: 96 (35.8%)
3 Even/2 Odd: 81 (30.2%)
4 Even/1 Odd: 40 (14.9%)
5 Even/0 Odd: 6 (2.2%)
Group A: 464 (34.6%)
Group B: 417 (31.1%)
Group C: 459 (34.3%)
0-5-0: 1 (0.4%)
0-4-1: 3 (1.1%)
1-4-0: 3 (1.1%)
0-1-4: 3 (1.1%)
4-1-0: 4 (1.5%)
4-0-1: 7 (2.6%)
0-2-3: 8 (3.0%)
3-2-0: 9 (3.4%)
1-0-4: 9 (3.4%)
0-3-2: 9 (3.4%)
2-0-3: 11 (4.1%)
2-3-0: 14 (5.2%)
3-0-2: 16 (6.0%)
3-1-1: 20 (7.5%)
1-3-1: 20 (7.5%)
1-1-3: 26 (9.7%)
1-2-2: 33 (12.3%)
2-2-1: 34 (12.7%)
2-1-2: 38 (14.2%)
As you can see, you increase your odds by playing 2 odd/3 even
and playing 1-2-2, 2-2-1, or 2-1-2 (e.g. 1-2-2 means 1 ball from
first group, 2 balls from second group, 2 balls from third group).
What do you think of this? :) | [reply] |
