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From: wdr@security.UUCP (William D Ricker)
Newsgroups: net.math
Subject: re: lotto odds
Message-ID: <331@security.UUCP>
Date: Fri, 17-Jun-83 17:34:52 EDT
Article-I.D.: security.331
Posted: Fri Jun 17 17:34:52 1983
Date-Received: Fri, 17-Jun-83 22:07:23 EDT
References: <106@beesvax.UUCP>
Organization: MITRE Corp., Bedford MA
Lines: 63

We have a very similar game in Massacusetts called MegaBucks.  The
state picks 6 numbers from 36 without replacement.  Having picked all 6
on your betting slip, you win the Jackpot, minimum $400,000, paid over
20 years (present value =~ 1/2).  Additional prizes are given for 5
numbers and 4 numbers, with a free bet given for 3 numbers.  These
prizes are small potatoes, but add tremendously to the 'expected
value'.  Bet is $1.  Unclaimed jackpot money rolls over to next
jackpot.  Player pool expectation is 50%.

The state commission has also recently distributed coupons worth
a free bet and 25 cents off a bet.  I'm saving my free bet untill
the jackpot gets good and full.

The expected value calclution which I made when they changed the game
to $400k+, 6/36; from $200k+, 6/30; resulted in even odds when the
jackpot was $1.9m.  For the $200k+, 6/30 game it was $.9m.  Both of
these calculations assumed "If the bettor wins the Jackpot, s/he will
be SOLE winner", as the jackpot is split by multiple winners.

The massachussestts commission by law pockets 50% of the gross, less
any deficit in a minimum jackpot ($400k) game.  All gross over the
state cut and the mandated prizes (I think $400 and $40, they used to
be $200 and $20, for 5/6 and 3/6) is placed in the jackpot.  Unwon
jackpot funds rolls over to next week.

------------ ANALYSIS

The analyses on the net, taken as a whole are accurate.  The state will
not lose money to syndicate play because:

	(1)  Multiple winners of the Jackpot split the prize;

	(2)  The jackpot is payed over 20 years.  They could offer a
	jackpot equal to the entire take payable over 20 years and
	still pocket half the gross (after office costs) if they didn't
	have other prizes.  My estimate of the states cost for 19 year
	annuities specs very close to that.

	(3) In the Massachusetts game at least, the jackpot is limited
	to 1/2 the take less other prizes (?less 1/2 expenses?).  only
	if revenue (gross, or 'action') falls below $.8m, does the
	state loose money.  The state may actually loose money if on
	the first week of a new jackpot there is insufficient 'action'
	and someone wins.  Of course, if there is less than $.8m of
	action and they have to pay the $.4m prize (cost=$.2m), they
	are still have upto $.2m to payoff incidental prize winners
	before touching the profit, er, revenue.  On a light betting
	week it is not likely that there will be a BANKRUPTING run of
	small bets to pay.  They probably have occaisional weeks where
	the net take is less than 50%.  I don't know if they absorb
	that loss or take it back from the next rolled over jackpot.
	On weeks with a BIG jackpot, there is PLENTY of action, but
	most of the prize money is SURPLUS prize money from previous
	weeks.  The state alread got its 50% off the top of the rolled
	over jackpot.

             Bill Ricker 
		(617) 271-3725
             wdr@security.UUCP                                      (Internet)
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