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November 11, 2000
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[ Click here to Ask the Wizard of Odds a question ]
Has anyone done work on the optimal betting strategies
in "Let It Ride" w/ additional information? I know the
casinos say players may not look at other players hands, but
in practice, it seems that most players know what at least
two other players are holding. I may want to go for an
inside straight if I know that at least six of the cards on
the table are NOT what I need to pull. -- Brian of
Stafford, Virginia
Yes! In 'Mastering the Game of Let It Ride' by
Stanley Ko a section is devoted to this topic. Ko
explains how the odds change if you have a 4-card
straight or flush and can see extra cards. He does not
indicate such adjustments at the three-card stage of the
game. You can find this booklet at that Gambler's
Book Club.
Hey Wiz, Great Site. I wondered if you knew the House
Odds on a game played at Foxwoods in Connecticut, called
"Catch A Wave." -- Ken Laird of Boston, USA
Thanks for the compliment. I've been requested
to analyze this game quite a few times. However it is
generally my policy to wait until a game goes nationwide
before I cover it on my site.
Is my boyfriend cheating on me? - Melevinna of IA
City, USA
How should I know? However don't make any
accusations unless you have sufficient evidence to back
them up.
My question revolves around the system Norman Leigh
used in the 60s to break the bank in Nice. His team used a
reverse Labouchere system, which involves absorbing a number
of small losses before hitting a big win (based on the idea
that instead of canceling out wins they are added to the
sequence and losses are crossed out ensuring that each game
can only lose a fixed amount but can potentially win the
table limit). Other than Norman's book (and books based on
it) I have not seen any analysis of the system. The book
states that this approach uses the house edge against them
and that in the long run the player will come out ahead. Is
this nonsense or is there something in this idea? -- Billy
from ?
I admit I don't know much about this incident.
However I will say that if indeed they won it was because
of luck and not because it was a winning system. As I have
said a thousand times before no system based on a
negative expectation game wins in the long run.
First, let me congratulate you on your great website.
I tell everyone I know that if they are going to gamble to
make sure that they visit your site first! My question is on
Three Card Poker ante & play. If you know one of the
dealer's three cards how should you change your basic
strategy and could you obtain an advantage over the house
and by how much? -- G.M. from Monmouth County, New Jersey
Are you friends with Brian Widdowson (see
above)? In 'Mastering the Game of Three Card Poker' by
Stanley Ko a section is devoted to this topic. He
explains when to raise and fold on a queen high hand,
based on the cards of other players you are able to see.
According to Ko if you had perfect knowledge of all cards
in a seven-player game and could make perfect use of this
information it would cut the house edge from 3.37% to
2.32%. You can find this booklet at that Gambler's
Book Club. Thanks for the compliment on my site.
Concerning the 5%vig on buy bets and lays how would
the odds change if $1 was charged for $20-$39, $2 for
$40-$59, $3 for $60-$79 and $4 for $80-$99 without round up.
Your information you give is outstanding. -- Bry of
Chesterton, USA
Thanks for the compliment. The formula for the
house edge in buy and lay bets is the commission divided
by the bet plus commission. In this case the best bet is
to bet $39 for the $1 commission. On the buy bet the
house edge would be 1/40 = 2.5%. Assuming you can lay $78
to win $39 on the 4 and 10, and still only pay $1, the
house edge would be 1/79=1.27%. I'll leave the other
situations as an exercise for the reader (I hated it when
my math books would say that).
How do you win money playing solitaire in Vegas? --
Pattie from Arlington, USA
I have never seen solitaire played for money in
Vegas. I understand in the early days of Vegas people
wagered on the standard Klondike variation of solitaire
but I don't anything else about it.
Ever wonder why Three Card Poker is not available
online? ñ Bob from Houston, Texas
It is still not as popular as Let it Ride and
Caribbean Stud. I speculate when the software developers
either don't understand it or don't think it is popular
enough. However I get asked about Three Card Poker online
all the time. The first online casino to offer the game
is going to be very glad they did, I predict. (p.s. Since this question was published Three Card Poker has become available at most Internet casinos)
In general, when betting on anything which pays even
odds, is there any kind of "system" to help improve chances
and or payoffs? -- JJ from Boston, USA
No.
What is the probability of getting three pair in Pai
Gow? Are the chances lesser or greater than three of a kind?
- Alex of Long Beach, Mississippi
Not counting a three of a kind and two pairs the
following are the ways to get a three pair and number of
combinations.
No wild card: combin(13,3)*10*63*4
=2471040
Wild card used to compete pair of aces:
combin(12,2)*10*62*42 = 380160
Wild card used as singleton ace:
combin(12,3)*63 = 47520
The total number of combinations is 2898720. This is
less than half of the 7470676 combinations for a three of
a kind.
Hi, you have a wonderful page for categorizing the
Casinos by the type of software they used. However,
Casino-On-Net was not mentioned in the list. Do you know
what software is Casino-On-Net using? ñ Andrew from
Bangkok, Thailand
Thanks for the compliment. I believe Casino on
Net uses their own software. It is my understanding that
they are one of the three biggest online casinos. Once a
casino starts making tons of money it is more cost
effective to develop their own software than keep paying
somebody else a percentage of the profit to use theirs.
I've noticed some new video slot machines (Money to
burn, High Bid, Money for nothing, Who Dun it, etc) that
differ from the normal 3 reel slots in the following ways -
first they have 5 reels. You can typically bet on 1 to 9
paylines (even though some have as many as 15 different pay
lines), and multiple coins per line; thus, with 9 pay lines
and 5 coins played per line, you would have a total bet of
45 coins (even in nickles, this can start to add up!). Most
payoffs are multiples of the line bet, even though there are
some "bonus" wins that pay multiples of the total amount
bet. My question is - Is it best to always pay all possible
pay lines, or is there an optimum combination of pay lines
to play to achieve the best return. I suspect that getting a
winning combination on any particular pay line is the same
for all, but wondered if you have any better insight to
share. ñ Scott of Leawood, USA
I believe each frame in these video slots are
weighted the same way. Assuming this to be true any given
line is equally likely to produce any given combination.
Thus the return is the same regardless of the number of
coins played. However I am not sure of this, slot makers
are notoriously secretive about such things.
I wonder if you could comment on the Casino's practice
of switching dealers. It always seems to happen that the
table is on a winning streak and then the casino switches
dealers mid-shoe. All of a sudden everyone starts to lose.
Do you think that certain dealers tip the balance more in
the casino's favor? ñ Hobbes from Toronto, Canada
The casino switch dealers when it is time for
someone to go on a break. Switching dealers does not
change the player's odds unless the player is a card
counter and the game is single or double deck where a new
dealer necessitates a fresh shuffle.
How many numbers does the RNG pick for each spin? Is
it 3 numbers (1 for each reel) or is it 1 number that's
mapped to a unique combination of symbols for all 3 reels?
-- Vincent of Chicago, Illinois
The machine picks one number for each reel.
Great site Mike! Often times I hear the word,
"binomial distribution" being used in gambling. Can you
explain to me what it means? Thanks in advance. -- Dennis
from Toronto, Ontario
Thanks for the compliment. Any introductory
probability and statistics book should give good
treatment to the binomial distribution. Briefly the
binomial distribution is the probability that any given
number of events will happen given a specific probability
for each event and a specific number of trials.
Specifically if the probability of each success is p, the
number of success is s, and the number of trials is n
then the probability of s successes is ps *
(1-p)n-s * combin(n,s). The combin function is
explained in my section on probabilities
in poker. For example suppose you want to know the
probability that in 100 spins of a roulette wheel the
number of reds will be exactly 60. According to the
binomial distribution the probability is
(18/38)60 * (20/38)40 *
combin(100,60) = 0.003291.
I just finished reading your section on strategy for
craps with great interest. I understand that better the pass
line and come bets with full odds is a good strategy. My
question is "does the house edge change at all when playing
a strategy of pass line with full odds and making a maximum
of two come bets with maximum odds?" In other words; how
does time (more rolls) and having more money at risk affect
these odds if at all? Or should a person stick with just the
single bet with full odds? This seems to be a favorite
strategy for most knowledgeable players I have met at the
dice tables. -- Jim of Yakima, USA
The house edge is the same regardless of how
many come bets you make assuming you always take the
maximum allowable odds and leave the odds turned on
during a come out roll. How many come bets you make
should be a matter of personal preference.
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