Betting well

I love games.  Games of all sorts.

Gambling, to me, is just another sort of game but with a more accurate form of scorekeeping (money).  I love finding strategies to win games.  Sarah shares some of this as well, which is how we
once found ourselves at the National zoo with $20 with which to buy raffle tickets at the sea
lion habitat.  It was a fundraiser for the sea lions, and first prize was the chance to feed them.

A good friend of ours, Ted, was a volunteer for the zoo and was coming
in later that day to volunteer at the habitat and, little did we know,
man the raffle table.

We took our $20 of raffle tickets, and like all good gamblers, gave
ourselves an edge by folding them into an accordian shape.  This way
they would take up more space inside the drawing bowl.  Since we
weren’t going to be around, we drew a blank on who to write as the
benficiary for the drawing, so we put in Ted’s name.

I’m sure you see this coming.  Our technique worked and our entries
actually won, and the announcer, with hundreds of small children
waiting to see if they won, reads out Ted’s name.  Ted.  The guy
manning the raffle table.  The hipster in his late 20’s who clearly now
was suspected of cheating at a kids raffle at the zoo.  I’m sure they
all looked at him and thought, "Jerk."  I was told that pretty much
ended his volunteering gig at the zoo.

Recently I had another gambling challenge that makes an excellent
exercise in probability.  Today I withdrew some money from an online
poker site (woo-hoo!  I’m a profitable poker player!!!!  BRINGIN’ HOME

Ok, I’m better now.   Anyways…

As I withdrew my money, I saw that my money transfer site has a contest
going.  For all your transactions they give you "points", which you can
use to buy entries into a drawing for cash.  For the $500 drawing, I
could afford to buy 32 entries, and there were 18,179 entries already
purchased.  For the $1,000 drawing, I could afford to buy 13 entries,
and there were 41,788 entries already purchased.  And for the $3,000
drawing, I could afford 6 entries, and there were 89,109 entries
already outstanding.

I thought, "There must be a mathematically optimal way to place this bet."  And indeed, there was.

The first, and easiest way to evaluate this is to compute the odds of
winning.  With the entries I could buy, I concluded that my odds would
be 568 to 1 to win $500, 3,214 to 1 to win $1,000, and 14,851 to 1 to
win $3,000.   After computing them, I looked at them and thought about
the problem.  It was then that I realized that the odds of winning did
not increase in correlation with the prizes!

In theory, if the $500 contest and the $1,000 contest are equal, you
should win twice as much money for eating twice as much probability.
While the prize is only twice as big, the $1,000 contest is over five
times worse odds than the $500 contest.  And the $3,000 contest is more
than the requisite three times worse than the $1,000 contest.

So while all the odds are longshots, the $500 contest are clearly the
best odds.  If you have Neteller points, you should play the $500
contest.  (Although, don’t do it this week, you’ll screw up my odds.)

And a bit more…
As a further exercise, I thought, "If you had to actually buy this raffle ticket, would it be worth it?"  This requires computing the value of an entry.  Long story short, for every $100 you flow through Neteller, they give you 1,000 points, or the equivalent of a single entry into the $500 contest.  But then what, might you ask, is the value of a $100 transfer?  Well at an ATM we know it’s $2 or even $2.50.  However in online banking terms, it’s practically nothing.  Since it’s all electronic, and doesn’t involve retail channels, I chose to use a number that’s lower, such as $1.  (It also makes the math easy.)

This means that for my $1 that I spent in moving my money, I got a 568 to 1 shot at a $500 prize.  This means that if you actually bought that ticket $1 over and over again, you’d win one in every 568 tries (assuming the same number of tickets were bought for every drawing) and lose the other 567.  You don’t have to be a math wiz to realize this has a negative Expected Value (-EV) and you will eventually go broke.

But for a (nearly) free ticket, it’s not bad.