
The math of gambling  - peter123
http://www.newscientist.com/article/mg20327202.600-whats-luck-got-to-do-with-it-the-maths-of-gambling.html?full=true
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jvdh
The way she describes winning at roulette is bogus.

First of all, if your money is doubled when you hit the right colour, you
don't make any profit in the long run. You will stay on the same amount.

Second of all, there is a 0, and often also a 00 on the roulette wheel, which
is neither red nor black. This means that the chance you're correct is less
than 50%, so you stand to make a loss in the long run.

There is no way to win at roulette, without using a computer to predict where
the ball is going to be, based on the movement and spinning of the wheel. And
I seriously doubt that even that is possible using just human observation and
a trigger in your foot.

[edit: the author is female, sorry about that]

~~~
splat
I think you're misinterpreting the author's point about roulette. She never
claimed that you could profit off of roulette in the long run. You can,
however, almost certainly profit off of it in the short run. The strategy she
describes has one double one's bet if one loses. If you bring enough money to
cover 7 losses (which means you would have to have roughly 100 times your
initial bet), then you have a >98% chance of coming out ahead. You won't be
ahead by much, and the strategy won't work in the long run (i.e. you can only
do it a couple of times--when you inevitably end up with 7 consecutive losses
it will more than wipe out any earnings you make), but it is nevertheless a
legitimate strategy to "beat" roulette in the short term.

~~~
jvdh
True, I did misinterpret that. And she does own up to it that after 7 streaks
you'd need 1280 pounds if you initially start with 10.

Still, the article states that there's a 50:50 chance of landing on black or
red, which is simply not true.

~~~
splat
Fair enough. The article also claims that the outcome of a coin flip is 50:50,
which is also not true.

~~~
req2
You're mixing theoretical odds and practical odds, which might be considered
sloppy.

Additionally, unfair coins can trivially be used as fair coins, but unbalanced
roulette wheels cannot easily be used as fair roulette wheels.

~~~
splat
A fair coin has a roughly 51% chance of landing with the same side up as it
started with. See the paper by Diaconis et al. "Dynamical Bias in the Coin
Toss."

~~~
req2
A fair coin is one on which p = 0.5. A coin that has a 51% chance is clearly
not a fair coin. This isn't even what I was talking about, but is still
equally easy to turn into a fair coin.

In this case, caller calls in the air after flipper hides the side that starts
up. 0.5 * 0.51 + 0.5 * 0.49 = 0.5

For any other case, flip a coin twice. Assign one person HT and the other
person TH, reflipping TT and HH. Since p * (1 - p) = (1 - p) * p, the dual
flip is a fair flip.

Please don't mention the possibility of sleight of hand next.

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pyre
One way that I would 'win' at roulette in Grand Theft Auto: San Andreas was to
always bet equal amounts on red/black and even/odd. My reasoning was that
there are 4 possible outcomes. I have a 50% chance of breaking even, a 25%
chance of winning, and a 25% change of losing.

You probably can't 'win big' with such a strategy, but you've at least
minimized the probability of a loss from 50% to 25%. You've also minimized the
probability of a win by as much too, though. I'm no stats guru so I don't know
how well this would work out on an actual roulette table...

{edit} I should mention that I worked at a casino for a while, and roulette is
the game with the highest probability in favor of the house. Blackjack is the
lowest. Casinos really only have Blackjack tables because patrons want them,
or else they would probably get rid of them pretty quickly. {/edit}

~~~
jvdh
_Casinos really only have Blackjack tables because patrons want them, or else
they would probably get rid of them pretty quickly._

True, even with a simple strategy you can cut your theoretical loss to about
1-2% (without counting cards). But casinos have blackjack because most players
don't know how to play. Most people don't follow that simple strategy (they
often have leaflets explaining it too!).

With counting cards you can make it profitable for you. But casinos will make
life very difficult for you if they find out you're counting cards. See also
the movie about the MIT Blackjack team:
<http://en.wikipedia.org/wiki/21_(2008_film)>

~~~
pyre
The casino I worked at used some formula to generate the number of 'points'
you would earn towards free stuff based partially on the risk of the game that
you were playing. They used the ~1-2% number for blackjack (or whatever the
low number of when you play what blackjack players call 'the perfect game')
rather than a larger number that might be closer to the 'average' skill of
players.

This signaled to me that the casinos -- or at least the one I worked at -- in
general treat the overall risk of blackjack as the low risk that skilled (non-
counting) players can achieve, regardless of the number of people that might
come in and ignore the simple, effective strategies to the game. Personally I
think that the casinos would rather reduce the risk to themselves from skilled
players as well as card counters and just remove all the blackjack tables,
sending all those inexperienced gamblers onto games like roulette where they
might lose a larger portion of the money they brought with them.

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mattheww
Incidentally, if I wanted to put my math skills to work in a casino, I would
play poker. This game is one where the odds have not been stacked against me
and a little math drastically alters my expected values.

------
TriinT
I never, ever learned anything from a newscientist.com article. Those articles
are cute, but one learns nothing deep. I say we go directly to the source!
Here is it, Ed Thorp's _The Mathematics of Gambling_ :

<http://www.bjmath.com/bjmath/thorp/tog.htm>

which is the true "bible" of scientific betting. For the mathematically-
inclined, I also recommend:

<http://en.wikipedia.org/wiki/Gambling_and_information_theory>

<http://en.wikipedia.org/wiki/Kelly_criterion>

and if you still have some energy left, try this:

 _A Markov Chain Analysis of Blackjack Strategy_
<http://www.ece.rice.edu/~crozell/courseproj/MCBJ.pdf>

Have fun! And remember: life is too short to read crappy articles!

