On Jan 3, 2009, at 5:37 AM, Taylor J. Smith wrote:
Quoting Pascal, "Lotteries are a tax on fools."
Pascal is certainly right about that, especially when they are used
to directly offset taxes, which is why not only the fools like
lotteries, but also those who see them as means to avoid taxes, and
those who profit directly from running them. As insidious as monthly
lotteries in lieu of taxes might be, they are benign in comparison to
various forms of casino gambling. In some communities, gambling
produces more costs for the communities than revenue, due to the
small community take and the demand on public services, insurance
companies, public safety, and the legal/penal system.
It might be asked why a monthly lottery with a 50 percent take and
less than a chance in a million of winning could be considered far
less harmful and addictive than, say, betting red or black in
roulette, which has an about 5.263 percent house take and nearly even
chances of winning each bet. The answer is that the roulette player
typically places much more than a single bet. According to Ian B
William's Slot Machines: Fun Machines or Tax Machines, $51 billion a
year is spent in the US on casino gambling, and about 70 percent of
that on slot machines. If the typical gambler bet only a few times,
then each slot machine and table would have lines of people going out
the door and down the street. This is not what you see at casinos.
People bet repeatedly for long periods. Repeated betting increases
the expected house win amount drastically.
To see which is better, a monthly lottery or roulette, take a look at
the expected purse amounts for the two alternatives over the one
month period of the lottery. If a gambler has $100 to bet for that
time he will likely gamble it all away. His expected purse value
after the 100 hours or so of roulette gambling time possible during
the month will be a tiny fraction of a cent. If a roulette wheel has
38 slots then 2 will be without color (or green, house take) and 18
will be black and 18 red. The house take will be about 5.26 cents per
dollar bet. Due to a typical house $5 minimum the gambler's $100
will likely only be a 20 bet purse. If allowed to make $1 bets the
gambler will have a 100 bet purse and can expect to be broke in less
than 1900 bets, or less than about 19 hours of betting. He will
probably try to obtain even more money with which to vindicate
himself. The following table shows in 100 bet intervals the
probability of being broke and the expected value of the purse for
roulette color bettors that start with a 20 bet purse.
Number of bets in better's starting purse 20
House percentage = 5.263 percent
Bet Prob. Alive Expected Value
---- -------------- ---------------
100 0.881083267382 14.891433066690
200 0.619848498510 10.952448130541
300 0.435274926086 8.199805170679
400 0.313261560357 6.245178037378
500 0.230621461565 4.823106110599
1000 0.062016797315 1.514700202615
2000 0.007334798455 0.206508730270
3000 0.001127300806 0.034033899035
4000 0.000195968405 0.006173086380
5000 0.000036627971 0.001187554885
6000 0.000007182650 0.000237810615
6900 0.000001707388 0.000057358537
The roulette gambler at a 5.263 percent house take and a $100 to bet
at $5 a bet can expect to be broke in less than 3 hours. In fact,
from the table, you can see that at bet 300, about 3 hours, he has a
43.5274926086 percent chance of being alive. He has about 1.7
chances in a million of lasting 6900 bets, or about 69 hours of
betting during the month, and only a small fraction of a cent
expected purse value by that time.
At $5 a bet and 100 bets an hour he can be expected to lose 0.05263 *
$5/bet * 100 bets/hour = $26.32 per hour. If he has 100 hours to
gamble in the month, and does so, he can be expected to lose about
$2,632 per month. The estimated 100 bets per hour may be high, and a
lower bet rate will reduce the expected loss per hour.
The lottery ticket buyer probably will not even spend the full $100
on tickets, unless there are lots of quick turnaround small pots,
which will in fact act just like casino gambling. A single large pot
can be expected to attract out of state money - especially when no
winner shows up and the expected win becomes positive on a subsequent
"let it ride" round. But let us assume the lottery player does spend
the full $100 on the lottery in order to compare apples to apples.
Lotteries typically take about half the proceeds. The $100 provides
about a $50 expected purse at the end, as opposed to the small
expected fraction of a cent purse for the roulette gambler that bets
more than 70 hours.
Typically both betters end up broke. However, the lottery ticket
buyer is more likely to stay on budget, more likely to win, and will
definitely be provided the truth about his approximate odds. If the
lottery goes into a "let it ride" round, a late ticket buyer may even
end up with more than fair odds. Lastly, the lottery ticket buyer
really only needs to buy one ticket a month to keep his dream alive.
The machine gambler has to find a way to keep feeding the beast to
keep his dream alive.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
