denny@beesvax.UUCP (06/16/83)
The problem with buying all of the numbers for the lotto game is what happens if there are multiple winners. Since the payoff is probably split evenly among the winners the expected return on the 'investment' is less than you would think it is. If there was a way to find out the numbers that are not played by anyone and purchase these numbers when the jackpot is greater than $1.9 million, then the odds are in your favor. The only trick is to obtain this information. There was a mention to something similar to this in the math games section in Scientific American some time ago. The general idea was to buy 'unpopular' numbers in a parimutual type state lottery. The idea of this was that the payoff was greater than the odds. According to the article it is possible to determine certain numbers that are not played or seldom played.
leichter@yale-com.UUCP (06/17/83)
For some interesting information on these games, see "Lotto Baloney" by Curt Suplee in the July 1983 Harper's. Quote: "You're seven times more likely to be struck by lightning than to win the state lottery." -- Jerry
wdr@security.UUCP (William D Ricker) (06/18/83)
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)chris@grkermit.UUCP (Chris Hibbert) (06/20/83)
The following article appeared in the April '83 Issue of "Software Engineering Notes, an Informal Newsletter of the ACM SIG on Software Engineering". I couldn't find a copyright notice, but the usual notice in ACM SIG publications is something like: "Copyright 1983 by the Association for Computing Machinery, Inc. Copying without fee is permitted provided that the copies are not made or distributed for direct commercial advantage and credit to the source is given." Fronton-Center Tickets for the Pick-Six Papers In case you missed the brute-force example of almost-fail-safe betting in the papers on 10 March 1983, it bears mention here for its implications on fail-safe programming. In Palm Beach Pick-Six Jai-Alai, the jackpot payoff results from picking the winner of six games each of which has eight teams competing. Thus, there are 8**6 = 262,144 possible outcomes. (The outcome of each game is naively thought to be relatively random, although years ago I did a little calculation showing that there are surprisingly significant probabilistic biases due to order -- even given equally matched opponents.) If no one gets all six winners exactly right, 25% of the pool is split among the closest pickers, and the remaining 75% is added to the jackpot payoff-- which accumulates. On this occasion the jackpot had gone untouched for 146 consecutive events, and had built to $551,331. A well-organized group of people placed 262,144 different bets ($2) -- covering every possible outcome at a cost of $524,288. The resulting payoff was $988,326.20 (the night's pool [minus the fronton cut] plus all of the accumulated jackpot). Thus success depended critically upon no one else picking the winning combination. Even a two-way split resulting from a competing winning ticket would have resulted in a $30,000 loss. (An off-night had been chosen on which a small crowd would normally be expected to place only about 10,000 bets -- covering a somewhat lesser number of distinct combinations, with some replications.) Well, you may ask, what does all this have to do with software engineering? The moral of the story is that if superficial analysis shows you have covered all your bets, you may still lose your shirt. How do you ensure that you got a ticket for each combination? What if the ticket seller dropped one [out of 262,144<!>] on the floor? What if the equipment malfunctions in the midst of betting? What if you don't finish placing all the bets in time? (The process is still largely manual , but now deserves an indivisible transaction "BET * * * * * *".) And now that this exhaustive strategy has been used successfully, you also have to beware of someone else trying it on the same evening as you! Worse yet, if it were easy to make the power-set bet, then you could probably not detect that someone else was trying the same exhaustive strategy -- which tied up betting counters for about half an hour at Palm Beach. "Expect the unexpected" is an adage given to system designers and programmers, urging them to anticipate every possible unusual event. But, as we saw in the ARPANET collapse [Eric Rosen, SEN Vol. 6, #1, January 1981], for example, that means anticipating hardware problems as well as algorithmic problems. [I note in passing for those interested in proving fault-tolerance properties that the word "admonish" means "to reprove for a fault".]