Gambling Math
by
Frank Scoblete
Gambling Math can tell us quite clearly what our
average expected loss (or
win) will be at each and every game by plugging our betting levels into
a very
simple formula: Average Bet x Speed of Game (or Number of decisions per
hour) x
Hours Played x House Edge = Expected Win/Loss.
So if you wanted to play
blackjack
for one hour at $10 a
hand playing perfect Basic Strategy at a one-half percent disadvantage,
you
could expect to lose on average
four
dollars ($10 average bet x 80 decisions per hour x 1 hour x .005 house
edge =
$4).
You can plug in any game and find this average amount.
Unfortunately,
owing to the streaky, freaky nature of chance, the above formula really
wouldn’t tell you if you were going to lose all, some, most, or none of
your
money in that hour or the next -- or whether you would win a bundle, or
a
single bet, because averages are, well, averages.
Therefore, winning and losing at casino games rarely match
the average expectation on a given evening because wild, weird, and
wonderful
things can happen, as the following true-life examples demonstrate:
1. At the Maxim Casino in Las Vegas in July of 1995, a $5
player won 23 straight hands -- some with doubles, splits, and splits
with doubles
-- in blackjack playing heads up against a dealer in a six-deck game.
At the
fourth hand, he started to escalate his bets and he won several
thousand
dollars in that run. I saw this.
2. At Caesars Palace on July 14, 2000,
gaming writer Barney Vinson witnessed the
number 7 come up at roulette six times in a row -- a billion to one
shot!
3. At the Desert Inn in February 1998, slot Expert John
Robison went 93 spins on a slot machine without one hit.
4. In August of 2000, Joan Cartwright played Let It Ride at
Bally’s in Atlantic City
and lost
$300 at $10 per hand -- without winning a single hand!
5. In roulette, Morris Guttermann lost 11 times in a row on
red when black came up 12 times in a row at the Imperial
Palace
in Las
Vegas in August of 1994. Somewhere
in that awful run,
Morris decided to start increasing his bet figuring that red had to
come up
sooner or later -- as indeed it did. After he lost all his money!
Outlandish wins, or horrendous losses, and a given evening
sees your bankroll skyrocketing to the heavens, or skidding down the
storm
drain. To protect yourself against the latter happening, here is a
simple
formula to help you determine what you need to bring to the casino for
one hour
of play at your favorite game to insure that you will not go broke: Ps
= (q/p)a
- (q/p)s / (q/p)a - 1 x Pi x e=mc2.
Just kidding.
Just bring enough to last
one hour
under the assumption that
you’re going to lose every single bet! It doesn’t get simpler than
that.
The only figuring you
have to do is
how many decisions the
game you are playing has in a given hour and multiply that by your
betting unit
($5, $10, $15, $25 or more) and you will arrive at the absolute
foolproof way
to assure that you can last for one hour if the goddess of chance
decides to treat
you the way the pigeons treat the statues in the park.
Bring
half that much if
you figure you can handle it if the worst possible scenario occurs and
you lose
it all, as half of the suggested bankroll will, for all intents and
purposes,
be very difficult (but not impossible) to lose in one hour’s time.
Gambling
Math: Blackjack
A crowded table at blackjack will have about 60 decisions an hour. So
bring 70
units. Why 70? Because on some hands you’ll have to split and/or double
down.
A
$5 player should have $350; a $25 player should have $1,750. Bring this
much
and you’ll probably be delighted to discover that as a Basic Strategy
Player
you can probably play two or three hours (not just one) without any
serious
threat of going belly up.
Gambling Math:
Craps
How much you need to guarantee that you’ll not be wiped out is tricky
as craps
has many different kinds of bets. If you make the Crazy Crapper bets
with high
house edges and low hit frequencies (for example, the 12), then you
would need
a LOT of money as craps can have 120 or more rolls per hour.
However,
if you
play a very conservative game -- in other words a smart game -- of
Pass/Come
with odds, place the six and/or eight, then you should bring 10 times
the
amount of your spread when you are up on the total number of numbers
you want
to be up on.
Here’s an example: If you
want to bet
$5 on the Pass Line
and back it with $10 in odds and then go up on two Come numbers $5/$10
and
$5/$10, you’d need $450 as $45 is your spread. If you just wanted to go
with
one Pass or Come number, then you would need $150 as $15 was your
spread.
Gambling Math:
Roulette
On the outside even-money bets (Red/Black, Odd/Even, High/Low); you’d
need 40
times your unit bet to assure that you can’t possibly go broke.
Roulette will
have approximately 40 decisions per hour so a $5 player would need
$200.
However, a more realistic figure would be 23 times your bet. Why 23?
Because
that is the most any outside bet ever came up in a row (if memory
serves me
well, it was black) and I doubt if the next time you play roulette
you’ll see
such a record broken.
So $5 bettors could be reasonably
assured that they could
last one hour with $115. The inside bets are another thing entirely as
38
numbers make it hard to guarantee that you’ll win even one bet in an
hour of
play. In fact, it is not unusual for someone to lose 40 decisions in a
row
betting one inside number.
So here you’d have to go with 40
units and pray that
the dealer doesn’t spin any more decisions than that!
Gambling
Math: Let It Ride
Here’s
a game with a low house edge that can be wonderful or
awful depending on how your luck is running. Generally, it is awful
until it
becomes wonderful. Here’s why: The win frequency is approximately 25
percent.
That’s right -- you win only one in four decisions, and you can gallop
a long,
long, long time on the losing end of this pony.
So how much is
enough? About 60 times your minimum bet.
Since Let It Ride allows you to take down two of your three
initial bets, you
tend to lose only on the third bet -- the “$” bet -- when you lose.
With some
exceptions, you will not let that first bet (“1”) or the second bet
(“2”) ride
unless you are assured a winner (10s or better). So if you play for $5
bring
$300 with you and you shouldn’t have any fear of being stampeded.
Gambling
Math: Caribbean
Stud
This game can be fast or
slow or in-between depending on how
fast the dealer deals and how fast (or slow) the players make their
decisions.
On average 40-50 decisions an hour are common so bring 50 times your
minimum
bet and you should be able to last one hour if a hurricane of bad
fortune slams
your way.
Gambling
Math: Baccarat and
Mini-Baccarat
Baccarat is a slow game and
mini-baccarat is a fast game.
The former will have 30-50 decisions an hour at a full table,
the latter will
have upwards of a 150 decisions an hour. If you can afford it, play
baccarat
(even if you have to play for slightly more money) as the speed of
mini-baccarat.
can really rip through a bankroll.
Gambling
Math: Three Card
Poker
This is a very fast game so bring about 80
times your bet
and you should have no fear of being wiped out. Learn the correct
strategy so
you keep the house edge as low as possible.
Recall that the purpose
of these
articles was not
necessarily to tell you the best ways to play the above games, or which
games
to play and which to avoid. It just explained what you need to bring to
assure
yourself of not being wiped out if Lady Luck wipes her feet on you.
Remember this too. Learn
from my
mistake. I know what it’s
like to come home with empty pockets. It’s one of the worst feelings in
the
world.
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