Roulette at Morty's

[bonanova]

So I flew to Las Vegas and taught the pros
out there a thing or two, boasted Alex last
night at Morty's. His friends came over to
hear the details.

So what did you play? asked Davey, in only
a slightly skeptical tone. Well, it could have
been anything, was the reply. Since I've got
the whole gambling thing down to a science,
it didn't really matter. I passed the roulette
table first, so I played there the whole time.

Ian knew something about that game. For
example, the ball can drop in slots numbered
1-36, but there are two other slots, 0 and 00,
which usually belong to the house. If you bet
$1 on a number - 5 for example - the payoff is
$36, but your odds of winning are 1/38; and
your average loss is $1 - (1/38)x$36 = $1/19,
or about a nickel. You can't win, he said. If you
play all night, the house will always beat you!

Ah, and that would be the case for lesser mortals,
for sure, Alex beamed. Myself, well, I won't say
how I made out, that would spoil things. Instead,
I'll make you a wager. Here, take a look at this.
And he unwrapped the large box that lay at his
feet. A genuine Las Vegas Roulette Wheel now
lay on the table before them!

Here's the deal, boys. I've got a stack of 105
$1 bills - just like I had last week in the casino.
I'll choose a number - say 18 - and bet each of
these dollars on that number, - 105 spins of
the wheel - until they've all been placed into the
hands of chance.

But here's where the fun begins. I'll wager
you $200 - even odds - that at the end of the
105 spins I'll be money ahead. If I'm not,
you win the $200. If I'm ahead, I win the $200.
What do you say? Any takers?

A moment passed, and neither of the two
answered. OK then, and just because I have
a generous nature, I'll give you a bonus.
You'll be the house for the 105 bets. You get
the house odds on all my bets, and if you
come out ahead, you get an extra $200.

Davey began to stroke his beard while Ian
couldn't believe what he'd heard. Alex had
finally lost it. Before Davey could answer,
he called out, I'll take that bet!

Did Ian go home a happy man? or did he
leave poorer but wiser?

Would you have taken the bet?

[kingofpain]

Too tired to do the math, but by playing the 105 dollars one at a time, he is abusing the skew of a binomial distribution at lower discrete success values to his advantage. His skill is in stopping at 105. The house makes money, but over a LOONG run. My interest was peaked enough to use an online binomial calculator and the probability of atleast 3 successes in 105 trials at p = 1/38 is a little over 0.52

Cheers!

--

Vig

[bonanova]

--

Vig

Too tired to do the math, but by playing the 105 dollars one at a time, he is abusing the skew of a binomial distribution at lower discrete success values to his advantage. His skill is in stopping at 105. The house makes money, but over a LOONG run. My interest was peaked enough to use an online binomial calculator and the probability of atleast 3 successes in 105 trials at p = 1/38 is a little over 0.52

Cheers!

Kewl.

But do you take the bet?

[kingofpain]

Kewl.

But do you take the bet?

Depends on how risk averse I am. I have a ~47% chance of winning. If I win, I would win at least $243 and at most $305. If I lose, I lose at least $203 and at most $5450. I would expect the expected value of winning to be higher than my expected loss, but I wouldn't lay because of the utiliy value or the money in my pocket being high. i.e. I am risk averse. I would say that Alex is close to risk neutral. Alex would probably make money in the long run if he placed these side bets with other gamblers in Vegas while not betting his own money on the wheel itself, but on the odds of coming out ahead after a set of 105 turns if he had played (or if he played dollar bills with the side bet running into tens of thousands so that the $105 is covered by the 2% advantage that he holds)

Cheers!

--

Vig

Edited June 8, 2008 by kingofpain