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July 11, 2004
Column
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The
American Mensa Guide to Casino Gambling has the
following "anything but seven" combination of craps bets
that shows a net win on any number except 7. Here's how much
MENSA advises to bet in the "Anything but 7" system:
- 5- place $5
- 6- place $6
- 8- place $6
- field- $5
- total= $22
They claim the house edge is 1.136%. How is that
possible if every individual bet made has a higher house
edge?
Good question. To confirm their math I made the
following table, based on a field bet paying 3 to 1 on a
12. The lower right cell does shows an expected loss of
25 cents over $22 bet. So the house edge is indeed .25/22
= 1.136%.
|
Mensa Anything but Seven Combo
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Number
|
Probability
|
Field
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Place 5
|
Place 6
|
Place 8
|
Win
|
Return
|
|
2
|
0.027778
|
10
|
0
|
0
|
0
|
10
|
0.277778
|
|
3
|
0.055556
|
5
|
0
|
0
|
0
|
5
|
0.277778
|
|
4
|
0.083333
|
5
|
0
|
0
|
0
|
5
|
0.416667
|
|
5
|
0.111111
|
-5
|
7
|
0
|
0
|
2
|
0.222222
|
|
6
|
0.138889
|
-5
|
0
|
7
|
0
|
2
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0.277778
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|
7
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0.166667
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-5
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-5
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-6
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-6
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-22
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-3.666667
|
|
8
|
0.138889
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-5
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0
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0
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7
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2
|
0.277778
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|
9
|
0.111111
|
5
|
0
|
0
|
0
|
5
|
0.555556
|
|
10
|
0.083333
|
5
|
0
|
0
|
0
|
5
|
0.416667
|
|
11
|
0.055556
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5
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0
|
0
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0
|
5
|
0.277778
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|
12
|
0.027778
|
15
|
0
|
0
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0
|
15
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0.416667
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Total
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1
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-0.25
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The reason the overall house edge appears to be less
than the house edge of each individual bet is because the
house edge on place bets is generally measured as
expected player loss per bet resolved.
However in this case the player is only keeping the place
bets up for one roll. This significantly reduces the
house edge on the place bets from 4.00% to 1.11% on the 5
and from 1.52% to 0.46% on the 6 and 8. For you purists
who think I am inconsistent in measuring the house edge
on place bets as per bet resolved (or ignoring ties) then
I invite you to visit my craps
appendix 2 where all craps bets are measured per roll
(including ties).
I noticed that all video blackjack games that I've
played in Vegas pay even money on a blackjack. Is this fair
according to the rules of blackjack? Because in a previous
question (July
4, 2004) you said, "It is a Nevada state law that
an electronic game with representations of cards or dice
must be based on fair odds. So the game should be fair with
odds the same as in a hand dealt game having the same
rules."
What I meant was that images of cards on the
screen had to be statistically fair. For example if you
took a tally of each card observed in the initial hand of
video poker or video blackjack you would see the
distribution approaching a flat line over time, much as
you would in a hand dealt game. However there is no law
that the standard rules of blackjack must be followed.
The machine can legally offer horrible rules like the
player losing on ties. The only caveat is that the
theoretical return must be at least 75%.
First, two columns ago, (May
30, 2004) someone asked about splitting aces and
then doubling. You seemed to answer it as if the question
meant you could double after you received the second card on
top of the ace. I read the question as meaning you could
double on the ace only, as if it were two cards that added
up to 11. I think that would impact your response, but I'm
not sure by how much.
Yes, I interpreted the question that the place
could after the second card was dealt to the split aces.
If the player could double on each ace alone then that
would reduce the house edge by 0.21% (based on infinite
decks). With an ace alone the player should opt to double
against any dealer up card.
In your June
25 column, you seem to say that you've only seen
other counters (I presume, based on them changing their bets
and/or strategy similar to how you might, if you were
counting) twice in many hundreds of hours of playing. At the
same time, if I read you right, you seem to say that you
think half the players in a strip type casino are successful
counters. That seems to be a contradiction. Maybe you meant
one half of one percent....? Assuming you see 10 or 12
players per hour that might be more in line with the
math.
What I meant was half of one person, or one
person for every two casinos. However you were not the
only person I confused so I reworded my original answer
to say half on one person, not half of everyone playing.
I'm a big fan of your site. I was playing some hands
of Pai Gow Poker on my own and came across an unusual
situation. After splitting hands, the Player had a flush:
A,Q,10,8,3. The House also had a flush: A,joker,10,5,4. So
who wins? The rules simply state that the joker can be used
to complete a flush but does it have a rank? Can it be used
as a second Ace of the flush suit?
Thanks. I just asked a dealer and he confirmed
that the house would win that hand because the joker
would be used as a king. The general rule is the joker
can substitute for any specific card not already in the
same hand as long as it completes a straight, flush, or
straight flush. Otherwise it is treated as a fifth-suit
ace, thus allowing for the possibility of five aces.
If I roll three dice, what is the probability of
getting at least two numbers the same?
The probability all numbers will be different is
(5/6)*(4/6)=20/36. So the probability at least two
numbers will be the same is 1-(20/36) = 16/36 = 44.44%.
Recently I was watching an episode of the new
"reality" show, The Casino. In one scene, the show featured
a "high-roller" playing, I believe, blackjack. Apparently
this gentleman hit a rather bad losing streak because as he
started to lose more and more, he would tear up the cards! I
would have thought this a severe breach of etiquette, if not
some actual gaming commission regulation, but when asked to
stop, he was insulted that they would ask him! Is this sort
of thing generally tolerated and I've just never seen it, or
is this guy just used to being allowed to get away with that
sort of thing because he's losing tons of money, or
something else entirely?
Baccarat (at the big tables) is the only casino
game in which players are allowed to damage the cards. An
explanation I heard is that Asian players bend the cards
anyway as they slowly peak at them that they only use
each card once. Therefore as long as the dealer is replacing the cards
after one usage the casino may as well let the players do
anything with them. Being able to identify cards is
of little value to baccarat players anyway because the
dealer doesn't take a hole card (as the dealer does in blackjack) and the
player has no choice as to whether to hit or stand.
However, there are also gaming regulations that stipulate that the tapes
must show all the cards in case of a dispute,
which isn't possible if the player tears them up first.
In the show you mention the player didn't know this and I think both parties
handled it badly, which led to the hard feelings that the
show captured. Had I been the casino manager I would have
explained what I just said and then asked the player to lay the card
face-up on the table before ripping it
into tiny pieces.
On a related note yours truly will be on The
Casino sometime this season. The story is some
college students try to parlay $1000 into $5000 as
quickly as possible. They seek my advice on how to do
achieve this goal.
I've read quotes similar to this on a couple of
different sites: "If the dealer won 40 hands in a shoe and
you won 20, this trend is likely to continue until you are
broke or until the unfavorable bias is removed through many
shuffles". That seems like somewhat "extreme" wording to me
but my question is, is there any validity to that concept?
Might any clumps of generally favorable (high), or
unfavorable, cards make it through one dealer shuffling such
that a non-shuffle tracker might take advantage by varying
his bets to capitalize on short streaks? By the way, your
site kicks ass.
Thanks for the compliment. This theory is called
card clumping and would make for good fertilizer if it
could be bagged. No legitimate blackjack writer puts any
stock in it at all.
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