Lottery Odds

Power Ball, PB, 30 yr payment period, 5 out of 59 and 1 out of 32, 1:146 mil, min pot $20 mil, sliding gross payout:, 27% IRS withholding, plus State income tax - if any. Changes to the current game are to be in place 1-4-2009.

Big Game, BG, now Mega-Millions, MM, 26 yr payment period, 5 out of 56 and 1 out of 46, 1:176 mil, min pot $12 mil, gross payout: $38,461/mil prize per yr, 27% IRS withholding, plus State income tax - if any.

Washington State, WA, Lotto Plus, 25 yr payment period, 6 out of 49, 1:7 mil, min pot $1 mil, gross payout: $40,000/mil prize per yr, 27% IRS withholding. No state income tax here, 0% (see next section for other state's taxes). As of 2-14-05, drawings are held Mon, Wed, & Sat for Lotto. Quinto ends 3-17-07 and Hit 5 starts.

Odds of winning a prize, jackpot in:
PB              1 in 36    1 in 120 mil
MM            1 in 40    1 in 175 mil
WA Lotto   1 in 27    1 in 7 mil
WA Hit 5    1 in 9      1 in 0.576 mil

PB Arizona 5.4%, Colorado, Connecticut, Washington D.C., Delaware, Florida, Indiana (Hoosier), Idaho 25%+7.8%, Iowa, Kansas, Kentucky, Louisiana, Maine 25%Fed 5%St, Minnesota, Missouri, Montana, Nebraska, New Hampshire 0%, New Mexico, North Carolina, North Dakota, Oklahoma, Oregon 8%, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Vermont, Virgin Islands, West Virginia, and Wisconsin. - 32ea (x%: St tax)

MM Calif 0%, Georgia, Illinois, Maryland 25% + 7%, Mass 5%, Michigan, New Jersey, NY, Ohio, Texas, Virginia 4%+25%, WA 0% - 12ea

WA used to be: pick 6 from a pool of 40 then 44 then 49 numbers
then 5 from 43 numbers and one from 23, 5/43, 1/23
As of Oct 8, 2003 we returned to 6/49 numbers.
As of 2-14-05, drawings are held Mon, Wed, & Sat for Lotto & Hit 5.
odds against winning jackpot are 7 mil to one,
http://www.wa.gov/lot/prizes.htm
Overall chances of winning a prize are 1 in 27

Match 5 of 5 win Jackpot, 100K min
o Match 4 of 5, win $100
o Match 3 of 5, win $10
o Match 2 of 5, win $1

PowerBall, PB payout
5+1 Jackpot 1:1xx mil
5+0 $ 200,000
4+1 $ 10,000
4+0 $ 100
3+1 $ 100
3+0 $ 7
2+1 $ 7
1+1 $ 4
0+1 $ 3

For a 59/39 game
5/59, 1/39
p(6) = (59!/(5!54!))(39!/(1!38!)) see below for details
= 1/1xx mil

BG odds 176 mil to one http://www.megamillions.com/
Overall chances of winning a prize are 1 in 40.
Which makes this lottery by far the worst one since the 2005 PB changes

Typical pot increases for successive drawings

Pot
Incr

Big Game, MM Payout
1. Five balls and "Big Money Ball"       Jackpot    1:176 mil
2. Five balls                                              $250,000    3.905M
3. Four balls and "Big Money Ball"       $10,000    689K
4. Four balls                                                    $150    15.3K
5. Three balls and "Big Money Ball"          $150    13.8K
6. Two balls and "Big Money Ball"              $10    844
7. Three balls                                                      $7    306
8. One ball and "Big Money Ball"                   $3    141
9. "Big Money Ball                                            $2    75

New WA Lottery odds for 6/49, picking 6 out of one pool of 49 numbers is:
6/49, (49 choose 6)
p(6) = (49 choose 6) = (49!/1!(6!43!)) = (49 sub 6)/ 6!
= (49x48x47x46x45x44)/(6 x 120) = 14 mil
or, 7 million to one odds as we get 2 sets of numbers per $1

For 5/43, 1/23 - 5 from 43 numbers and one from 23 numbers:
p(6) = (43 choose 5) times (23 choose 1)

* this is written in math as two tall parens next to each other (mult) with the 43 above the 5 within one paren, and 23 above the 1 in the other paren

*(n choose k) is n!/((k!(n-k)!),
where n is 43 and k is 5 in the first part, and n is 23 and k is 1 in the 2nd.
and, where n factorial, n!, is n(n-1)(n-2)...1

since we get 2 sets of numbers for $1 divide by 2 for the 11 mil to one odds against getting all 6 numbers