A1 = total number of balls in the lottery, eg 49
A2 = number of balls drawn in the game, eg 6
A3 = number of balls matched by player, eg 6
A4 = odds of this occurrence to one, eg 13,983,816

Where you have 49 numbers, the chance of drawing the first number are 1 in
49. To draw the second number, because only 48 balls remain, it's 1 in 48,
etc. So in a draw 6 game with 49 balls, the odds of drawing out 6 in any
order are (49*48*47*46*45*44)/(6*5*4*3*2*1) or 49!/(6!*(49-6)!) which is
10,068,347,520/720 and gives 13,983,816.

I would like a formula to calculate odds for variations in value of A1, A2
and A3.

=HYPGEOMDIST function would seem to do what I'm looking for, but in the help
function they have population size, which would be A1, Sample size is A2,
Sucesses in sample is A3, but not successes in population. Any ideas?

Jake formulated on Friday :
A1 = total number of balls in the lottery, eg 49
A2 = number of balls drawn in the game, eg 6
A3 = number of balls matched by player, eg 6
A4 = odds of this occurrence to one, eg 13,983,816

Where you have 49 numbers, the chance of drawing the first number are 1 in
49. To draw the second number, because only 48 balls remain, it's 1 in 48,
etc. So in a draw 6 game with 49 balls, the odds of drawing out 6 in any
order are (49*48*47*46*45*44)/(6*5*4*3*2*1) or 49!/(6!*(49-6)!) which is
10,068,347,520/720 and gives 13,983,816.

I would like a formula to calculate odds for variations in value of A1, A2
and A3.

=HYPGEOMDIST function would seem to do what I'm looking for, but in the help
function they have population size, which would be A1, Sample size is A2,
Sucesses in sample is A3, but not successes in population. Any ideas?

Actually, the odds of drawing 6 in any order is 6/6. What you probably
mean is the odds to draw a 6 number combo that matches a game draw of 6
winning numbers.

Example: 6/49 game +bonus#
6/6: 1:13,983,816
5/6+Bonus: 1:2,330,636
5/6: 1:55,492
4/6: 1:1,033
3/6: 1:56.7
2/6+Bonus 1:81.2
2/6: 1:32.3

...assuming your combos contain matches. This is also the case for
'wheeling' algorithms that promise minimum odds for a given set of
numbers; -YOU HAVE TO HAVE THE WINNING NUMBERS SOMEWHERE IN YOUR SET!

Otherwise, it's random hit & miss at best...

--
Garry

Free usenet access at http://www.eternal-september.org
ClassicVB Users Regroup! comp.lang.basic.visual.misc

You can let Excel pick your lottery numbers...
http://www.mediafire.com/PrimitiveSoftware
Numbers for 14 state/national (USA) lotteries - in the free folder.
'---
Jim Cone
Portland, Oregon USA




"GS"
wrote in message
...

-snip-

Otherwise, it's random hit & miss at best...
--
Garry

Jim Cone explained :
You can let Excel pick your lottery numbers...
http://www.mediafire.com/PrimitiveSoftware
Numbers for 14 state/national (USA) lotteries - in the free folder.
'--- Jim Cone
Portland, Oregon USA




"GS"
wrote in message
...

-snip-

Otherwise, it's random hit & miss at best...
-- Garry

Yeah, I knew about your free utility from another post on this topic. I
believe I looked at it back then. I use my own wheeling utility since
here (Canada) there's not that many lotteries worth their salt. I don't
even use my utility to play; -I just track the winning numbers and
check wheeling algorithms against them. My utility also generates
'quick picks' which, IMO, have as much chance of winning as any. It's
quite interesting, I find, to see all the scams going out there for
'secrets' to winning.<g It's fun to play quick picks every once in
awhile, but I absolutely have no aspirations about winning much, if
any.

--
Garry

Free usenet access at http://www.eternal-september.org
ClassicVB Users Regroup! comp.lang.basic.visual.misc

"Jake" wrote:
A1 = total number of balls in the lottery, eg 49
A2 = number of balls drawn in the game, eg 6
A3 = number of balls matched by player, eg 6
[....]
I would like a formula to calculate odds for variations
in value of A1, A2 and A3.

Instead of using A3, I find it useful to generate all possible number of
matches, A2 to zero. It serves as a check on the methodology: the sum
should equal the total possible. Then we can exclude any matches that the
lottery does not pay for, typically 0, 1 and 2. (You will see why below.)

If the presentation below is unclear due to formatting, see preview image or
download the Excel file "lottery odds.xls" at
http://www.box.com/s/uv8tggcbe1kvypqiynju.

The total possible combinations is =COMBIN(A1,A2). Set up the following
table.

#Balls #Possible
Row Match Matches Probability Odds[*]
6: 5 1 0.000026% 1:3,819,816
7: 4 255 0.006676% 1:14,980
8: 3 12750 0.333786% 1:300
9: 2 208250 5.451833% 1:18
10: 1 1249500 32.711000% 1:3
11: 0 2349060 61.496679% 1:2
12: 3819816
[*] I am using the term "odds" the same way that Mega Lottery and other
lotteries I am familiar with. But that is one too high according to the way
that "odds" is usually defined. See http://en.wikipedia.org/wiki/Odds. (I
do not agree with everything in that wiki page.)

Enter the following formulas:

A6: =A2
A7: =A2-1
B6: =COMBIN($A$2,A6)*COMBIN($A$1-$A$2,$A$2-A6)
C6: =B6/$B$12
D6: ="1:"&TEXT($B$12/B6,"#,##0")
B12: =SUM(B6:B11)
Copy A7 down until zero.
Copy B6:D6 down for the same number of rows.
After the last row, enter a formula similar to B12 in this example.

Explanation of B6....

COMBIN(A2,A6) is the number of ways A6 numbers match A2 balls drawn.

COMBIN(A1-A2,A2-A6) is the number of ways the remaining A2-A6 numbers do not
match any of the A2 balls drawn; that is, the number of ways the remaining
A2-A6 numbers can drawn from the remaining A1-A2 balls.

The second term ensures that we count exactly A6 matches. Otherwise, for
example, if one of the remaining A2-A6 numbers matches a drawn ball, we are
really talking about A6+1 matches, not A6. (This might be better understood
by considering A7 and fewer matches.)

PS: As you can see, the probability of matching 0, 1 and 2 balls is
relatively high. Presumably for that reason, the lotteries I am familiar
with do not pay for those matches.

-----

The lotteries I am familiar with also have a "bonus" ball (aka "mega" ball).
That greatly increases the total possible combinations, which reduces the
chances of matching.

Suppose A3 contains the number of "mega" balls (e.g. 46). The total
possible combinations is A3*COMIN(A1,A2). Set up the following table.

#Balls #Possible
Row Match Matches Probability Odds[*]
15: 5+M 1 0.00000057% 1:175,711,536
16: 5 45 0.00002561% 1:3,904,701
17: 4+M 255 0.00014512% 1:689,065
18: 4 11,475 0.00653059% 1:15,313
19: 3+M 12,750 0.00725621% 1:13,781
20: 3 573,750 0.32652950% 1:306
21: 2+M 208,250 0.11851811% 1:844
22: 2 9,371,250 5.33331517% 1:19
23: 1+M 1,249,500 0.71110869% 1:141
24: 1 56,227,500 31.99989100% 1:3
25: 0+M 2,349,060 1.33688434% 1:75
26: 0 105,707,700 60.15979509% 1:2
27: 175,711,536

Enter the following formulas:

A15: =A16&"+M"
A16: =A2&""
A17: =A18&"+M"
A18: =A16-1&""
B15: =COMBIN($A$2,LEFT(A15,1))*COMBIN($A$1-$A$2,$A$2-LEFT(A15,1))
*IF(OR($A$3=0,RIGHT(A15,1)="m"),1,$A$3-1)
C15: =B15/$B$27
D15: ="1:"&TEXT($B$27/B15,"#,##0")
Copy A17:A18 down until zero.
Copy B15:C15 down for the same number of rows.
After the last row, enter a formula similar to B27 in this example.

The explanation of B15 is essentially the same as for B6 above. But when
column A does not contain an "M", we multiply by the number of ways of not
matching the drawn "mega" ball; that is, the remaining numbers that do not
match the drawn "mega" ball, namely A3-1.

"GS" wrote in message ...
Jim Cone explained :
You can let Excel pick your lottery numbers...
http://www.mediafire.com/PrimitiveSoftware
Numbers for 14 state/national (USA) lotteries - in the free folder.
'--- Jim Cone
Portland, Oregon USA




"GS"
wrote in message
...

-snip-

Otherwise, it's random hit & miss at best...
-- Garry

Yeah, I knew about your free utility from another post on this topic. I
believe I looked at it back then. I use my own wheeling utility since here
(Canada) there's not that many lotteries worth their salt. I don't even
use my utility to play; -I just track the winning numbers and check
wheeling algorithms against them. My utility also generates 'quick picks'
which, IMO, have as much chance of winning as any. It's quite interesting,
I find, to see all the scams going out there for 'secrets' to winning.<g
It's fun to play quick picks every once in awhile, but I absolutely have
no aspirations about winning much, if any.

Should always play quick picks at random. If you have a set of numbers you
always play, then you're going to have to play them for the rest of your
life, lest you miss one week, when they come up and make you feel rotten for
the rest of your life.

PS....

I wrote:
Set up the following table.
#Balls #Possible
Row Match Matches Probability Odds[*]
6: 5 1 0.000026% 1:3,819,816

I forgot to mention that this table is for the (US) Mega Millions lottery.
The number of balls (A1) is 56, and the number of balls drawn (A2) is 5.

I should have used Jake's example of 49 and 6. Sorry if it causes any
confusion.

I wrote:
Suppose A3 contains the number of "mega" balls (e.g. 46). The total
possible combinations is A3*COMIN(A1,A2).

This assumes that the bonus ball is drawn from a separate pool of balls, and
that only one bonus ball is drawn. This is similar to the (US) Powerball
and Mega Millions lotteries.

Apparently, some lotteries draw multiple bonus balls (Euromillions). And
some lotteries draw a bonus ball from the same pool as the other balls
(Canadian and UK national lotteries). See
http://en.wikipedia.org/wiki/Lottery_mathematics.

I wrote:
Set up the following table.
#Balls #Possible
Row Match Matches Probability Odds[*]
15: 5+M 1 0.00000057% 1:175,711,536
16: 5 45 0.00002561% 1:3,904,701

Again, this table is for the (US) Mega Millions lottery. The bonus ball (M)
is drawn from a separate pool of 46 (A3). The number of regular balls (A1)
is 56, and the number of balls drawn (A2) is 5.

Errata.... I wrote:
The lotteries I am familiar with also have a "bonus" ball
(aka "mega" ball). That greatly increases the total possible
combinations, which reduces the chances of matching.

While it does increase the total possible combinations, and it does reduce
the chance of matching the winning the __main__ prize ("winning the
lottery"), it does __not__ reduce the chances of matching in general.

In fact, the chance of matching k of n regardless of the bonus ball is
unchanged.

But more to the point, the chance of matching __some__ paid combination
increases.

For example, in a game that draws 5 balls from 56 and no bonus ball, the
lottery is likely to pay only for matching 5, 4 or 3. That's a total of
13,006 combinations out of 3,819,816. So the probability of matching any of
the paid combinations is 13006/3819816, or about 0.34%. The odds are about
1:294.

But in a game that draws 5 balls from 56 plus a bonus ball from 49 (US
Megamillions), the lottery pays for matching 2+M, 1+M and 0+M as well
matching 5,4 and 3 with and without matching the bonus ball. That's a total
of 4,405,086 combinations out of 175,711,536. So the probability of
matching any of the paid combinations is 4405086/175711536, or about 2.507%.
The odds are about 1:40.