Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site security.UUCP Path: utzoo!linus!security!wdr 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) {allegra,genrad,ihnp4,utzoo,philabs,uw-beaver}!linus!security!wdr (UUCP) wdr@mitre-bedford (ARPA)