This question is in reference to the Texas Lottery Commissions' Cash 5
Game in which you chose 5 different numbers from 1 - 37 for each play.
"What is the 'probability' that I will win back my money if I spent
$1,000 at $1.00 for each play; assuming no two plays have the exact 5
numbers in use.  If possible can you list the 'probability' in a
percentage form.

---

Clarification of Question by syam67-ga on 07 Feb 2005 07:08 PST

This question is in reference to the Texas Lottery Commissions' Cash 5
Game in which you chose 5 different numbers from 1 - 37 for each play.
"What is the 'probability' that I will win back my money if I spent
$1,000 in one drawing at $1.00 for each play; assuming each and every
one of the 1000 plays are different; in other words no one play is
duplicated.  If possible can you list the 'probability' in a
percentage form.

---

Clarification of Question by syam67-ga on 24 Feb 2005 07:01 PST

Thank you for your comments - you have answered my question.

If you assume that the 1000 plays (of $1.00 each) are all made in the
same extraction, then the probability heavily depends on how the 1000
5-ples are chosen. The "no two plays have the exact 5 numbers in use"
datum does not sufficiently constrain them.

$.58 gets paid out for every $1 taken in for Texas Lottery as a whole.
http://www.txlottery.org/faq/moneygoes.cfm

This site says taht Cash 5 actually only gives 50% payout, and here is
how it works:
http://www.lottoreport.com/c5money.htm
"Players receive 50% of sales - Let's pretend sales were $550,000 
which means there's $275,000 in the "prize pool." Since there is 
a new $2 "guaranteed" prize - the TLC opted to take those prizes 
right off the top of the players prize pool - the 50%. (They should 
do this for Lotto Texas & Texas 2 Step but they don't) 

So, let's say there were 64,924 people who won $2 each. 
The total for them is $129,848. 

Now you deduct $129,848 from the players prize pool ($275,000) 
which leaves $145,152 in the "residual prize pool." (They now 
have 2 prize pools)

The 5 of 5 winners share from the "residual prize pool" is 40.15% 
which means the 5 of 5 winner(s) will receive or divide $58,278.

The 4 of 5 winners share is 18.08% of the "residual prize pool." Let's 
say there are 278 winners so they will divide $26,243 by 278 
meaning each will receive $94.

The 3 of 5 winners share is 41.77% of the "residual prize pool." 
Let's say there are 6488 winners so they will divide $60,629 by 
6488 meaning each will receive $9."

So the prizes are so skrewy that it's quite difficult to determine
your odds of winning back your money since the payouts vary every
drawing depending on how many winners their are in each category.

But do keep in mind that for every $1,000 that they take in, only $500
comes out.  Put your money in an IRA and you're guaranteed a 25%
return this year (depending on your tax bracket... could be more or
less) and on top of that, you keep your entire $1,000 and interest.

Getting all 5 numbers right: 1 in 436  (.23%) (about $30,000)
Getting 4 numbers right    : 1 in 3    (33%)  (about $300)
Getting 3 numbers right    : 11 times         (about $10)
Getting 2 numbers right    : 110 times        ($2)

Let's assume you get 3 number right 11 times exactly and 2 numbers
right 110 times exactly.  That gives you $220 + $220 = $440.  As you
can see, it will be very unlikely for you to reach that $1000 you put
in by just getting 2 or 3 numbers right alot of times.

So in order to get your $1000, you'll most likely need to get 4
numbers right 2ce or all 5 numbers right once.

The odds of 4 numbers right 2ce is 33% * 33% = 11%
The odds of getting all 5 number is .23%

We'll add a little to that in the rare case that you'll actually get
alot more 2 and 3 numbers right (although I'm not sure how to do the
math for that)...

I'd say 15% chance that you'll get your money back. (notice that .23%
of the time you'll get significantly more than your money back)

Again, I'll highly recomend investing your money.  Feel free to ask
for investing advice if you're not too sure where your money should
be. http://flagship4.vanguard.com/VGApp/hnw/content/AccountServ/ATSOverviewContent.jsp?gh_sec=y