UNCLE AL PLAYS THE LOTTO
(C)1998 Alan M. Schwartz
No, not with his own money, silly! State lotteries are voluntary
taxation upon the stupid. The unreservedly worst Las Vegas slot
machines (airports) average $0.95 payback for every dollar
invested. Casino slots run 98-99% payback. The 1-2% skim, the
vigorish, supports multi-$billion Vegas. State lotteries take
50% off the top for expenses and, in California, "investment in
education." I know a college professor whose classroom's share
of the roughly $20 million/week California State vigorish over a
seven year span was one battery-run wall clock.
The game in California is 6/51. For a one dollar fee a rube
submits a set of six different numbers each between 01 and 51
inclusive. Payoff comes for matching three or more of six
numbers in a twice-weekly random drawing. The odds are easily
run. The first number has 51 possibilities with six chances of
guessing it. The second number has 50 possibilities with five
chances of guessing it. The third number has 49 possibilities
with four chances of guessing it. The odds for guessing all six
numbers are (6)(5)(4)(3)(2)(1)/(51)(50)(49)(48)(47)(46) =
1/18,009,460. When the prize is $18 million you might invest
$1.00 (probability times payoff versus investment), if you can be
sure there will be only one winner.
Canada also runs a Lotto, Pick 6/49. The Great Dank North is
renowned for being kinder and gentler, and a little bit slow on
the uptake. We thus eschew sophisticated California for better
operational odds ((6)(5)(4)(3)(2)(1)/(49)(48)(47)(46)(45)(44) =
1/13,983,816) from a collection of 30 million folk whose idea of
a good time is tossing octopi onto hockey rinks.
From where will we obtain unbiased number sets? Decimal digits
of pi pass every test for randomness (save one - all together
they are pi), equal representation 0-9, and smooth distribution
over the first six billion digits (as of March 1996).
Digit occurrence for pi minus 3 to six billion decimal places:
"0": 599,963,005 "5": 600,017,176
"1": 600,033,260 "6": 600,016,588
"2": 599,999,169 "7": 600,009,044
"3": 600,000,243 "8": 599,987,038
"4": 599,957,439 "9": 600,017,038
Daisuke Takahashi, Kanada Lab, HITAC S-3800/480, Computer Centre,
University of Tokyo, Bunkyo-ku Yayoi 2-11-16, Tokyo 113 Japan
There is a little epiphenomenon of randomly tossing a toothpick
on a slat floor to generate pi. That sounds like a Lotto, eh?
1) Download Internet file of pi to 5 million decimal places.
2) Starting near the 2 million mark, grab 7500 consecutive
digits. Starting near the 4 million mark, grab 19,200 more.
3) Consecutively group into 6 pairs each - 2225 sets of six
two digit numbers 00-99.
4) Toss any set with 00 or 50 in it.
5) Leave 01-49 alone.
6) For 51-99 subtract 50 to reduce to 01-49.
7) Toss any set with duplicate numbers.
8) That leaves 1440 unique sets of 6 random numbers 01-49
inclusive.
Visit the Internet again, find a Canadian Lotto page, download 67
winning number sets (twice weekly). A 3/6 hit is worth $10. A
4/6 hit runs $60-80 depending on the weekly take. A 5/6 hit runs
about $2300 depending on the weekly take. Write a DOS batch file
to FIND all the three-, four-, five-, and sixfold matches input
winners vs. number set collection, collect and display the
results. Results:
67 runs, each into 1440 number sets
440 three number hits @ $10 ea = $4400
27 four number hits @ $70 ea = $1890
1 five number hit @ $2300 ea = $2300
$96,480 into State coffers
$8,590 back into gamer pockets
91.11% of capital lost.
The worst Las Vegas slot machine runs at a 5% investor loss. The
Lotto runs at 50% loss off the top, and 91% average loss fighting
over the remainder. Running a couple of dozen California winning
numbers gave a 95+% loss. Statistical analysis of both lotteries
shows them to be overall honest compared to incidence and
distribution of numbers arising.
California has higher payoffs! Plug in the statistics and allow
for multiple winners. A world awash in loudly self-proclaimed
psychics is oddly bereft of those selfsame adepts claiming the
big prize. Do they prefer answering psychic hotline phones in
boiler room operations? All you can do is have faith in luck.
(Faith is rotted optimism.) There are not infrequent drawings
wherein nobody among ten million participants grabs the one-in-
18,009,460 chance brass ring, psychics or otherwise.
State lotteries are voluntary taxation upon the stupid. Are you
stupid?