Ask the Wizard! (No. 54)
October 30, 2001 column
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I have noticed something over the years watching our
Quinto lottery drawing here in Washington State. It is a 52
'card' game that draws 5. I have noticed that the vast
majority of the time, three suits are drawn. From poker
numbers you find that the chance of getting just one suit (a
flush) is 5148 out of about 2.6 million. What are the odds
of 2,3, or all 4 suits coming up? - Kevin from
Tacoma, Washington
Let's define f(x,y) as the probability of
getting x of one suit and y of another. This function is
not limited to two terms.
With two arguments f(x,y)=
combin(13,x)*combin(13,y)*12/combin(52,5).
With three arguments f(x,y,z)=
combin(13,x)*combin(13,y)*combin(13,z)*12/combin(52,5).
With four arguments
f(w,x,y,z)=combin(13,w)*combin(13,x)*combin(13,y)*combin(13,z)*4/combin(52,5).
The probability of all four suits is
COMBIN(13,1)3*COMBIN(13,2)*4/combin(52,5) =
26.37%.
The probability of three suits is
COMBIN(13,3)*COMBIN(13,1)2*12 +
COMBIN(13,1)*COMBIN(13,2)^2*12/combin(52,5) = 58.84%
The probability of two suits is
COMBIN(13,3)*COMBIN(13,2)*12 +
COMBIN(13,4)*COMBIN(13,1)*12/combin(52,5) = 14.59%
The probability of one suit (including straight and
royal flushes ) is 4*combin(13,5)/combin(52,5) =
0.20%.
So three suits are the most frequent outcome.
What is the best game to use a match play coupon on? —
Rob
First let's define a match play coupon for those
who don't know. This is something often found in casino
fun books. If the player accompanies a match play coupon
with a real even money wager then the match play will be
converted to a like amount of cash if the player wins.
For example if the player has a $5 match play and uses it
along with a $5 bet on red in roulette then if the player
wins his $5 will win $5 and his match play will be
converted to $5. Whether the player wins or loses he will
lose the match play coupon. In the event of a push, the player gets to keep
the match play coupon.
If used in blackjack, the Match Play will usually only pay even money. This decreases the value of the Match Play itself by 2.3%, which is way too much. Of the true even money bets, the best game to use a match play on in the Player bet in baccarat. That has a probability of winning of 49.32% of bets resolved. For the don’t pass in craps, that probability is 49.30%. The value of a Match Play on the Player bet is 47.95% of face value, assuming you wouldn't have bet otherwise.
On a CSM blackjack game, 5 deck, what would be the
effect of the dealer not putting discards back into the
machine every hand if 24 of 52 cards in the discard rack
were face cards? What about 48 of 102? What would be the
effect if 44 of 52 cards were non-face cards? Can the odds
be heavily skewed? I have a feeling that the odds skyrocket
in the casino's favor if the dealer leaves face cards in the
discard. - Doug from Vancouver, Canada
The exact numbers would be difficult to
calculate and I won't get into that. However your
speculation is right that the odds favor the dealer if he
leaves a lot of high cards in the discard rack yet will
put back into play a lot of small cards. This would be
the same kind of thing as preferential shuffling, in
which the dealer of a hand held game shuffles when the
count is good but deals another round on a bad count.
Preferential shuffling is something that definitely does
happen here in Las Vegas so what you describe would not
surprise me either.
Can you please explain the "cut card effect" in
Blackjack. Why don't people use this when quoting BS house
edges for various numbers of decks rather than showing BS
house edges that take this into account? - Andrew from
Melbourne, Australia
I explain all about the cut card effect in my
blackjack appendix 10. The
reason house edge statistics are based on a non-cut card
game is likely out of tradition and mathematical
simplicity. However you make a good point that it would
be more accurate to inflate the house edge figures to
account for the cut card. Yet I am still going to stick
to basing my house edge figures on the first hand of a
freshly shuffled deck. Blackjack is hard enough to
analyze without worrying about the cut card effect all
the time.
I have seen several references to ongoing bonus abuses
from people who reside in Denmark. Do you know more details
about what is going on here? What are they doing, and how
can we avoid being bonus abusers? - Rich
I don't know all the details but there is a lot
of bonus abuse going on by players from Denmark. The way
to avoid being labeled a bonus abuser is to always play
much more than required. I hate to give an exact figure
but exceeding requirements by at least 100% is a good
idea. Giving free play to casinos you get repeated
bonuses from is also good camouflage. It doesn't look
like you are a good faith gambler if you only play during
promotions. In general don't be too greedy.
I've got a question about "progressive betting" (e.g.
"Another Experiment", Player 2 on your Betting Strategies
page). Obviously in normal bj play you experience streaks of
wins and loses. Where is the faulty logic in "minimize your
losing streaks by resetting at 1 unit, and increase your
winning streaks by raising 1 unit after each win?" FYI, I
actually play a little variation of that: 15, 30, 45, 50,
75, 100, 125, etc...Thanks for you time. And, please don't
try to humiliate me like Ann {what's-her-name} on The
Weakest Link :-) I really love your site!!! Thanks for all
of the great info. - Chad R. from Memphis, Tennessee
Progressive betting systems, like yours, will
turn a good session into a great one without the risk of
catastrophic loss as with regressive systems like the
Martingale. However progressive systems will turn a
choppy neutral session into a bad one. Consider what
would happen if you alternated between a win and a loss
the entire session. The wins would all be at $15 and the
losses at $30. Funny you should mention the 'Weakest
Link.' I tried out for that show during the summer and
didn't make it. It is probably just as well because I'm
not that witty in real life and doubt I could come up
with a good rejoinder to one of Ann's jabs.
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