Bob Dancer's LVA - 17 JUN 2014
What's the Background of a Quad?
http://www.lasvegasadvisor.com/bob_dancer/2014/0617.cfm
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Bob wrote: “Interestingly, a single pair is dealt exactly 20 times as often as trips
are dealt. Not ABOUT 20 times. EXACTLY. I’m sure there is a simple explanation for this, but I have not yet discovered it.”
They have the same structure so wouldn’t you expect an integer multiple? Trips are 3 cards of the same rank and 2 kickers, a Pair is 2 cards of the same rank and 3 kickers. I would also expect the quad to be an integer multiple since it is 4 cards of the same rank and 1 kicker.
NOTI wrote: Bob wrote: “Interestingly, a single pair is dealt exactly 20 times as often as trips
are dealt. Not ABOUT 20 times. EXACTLY. I’m sure there is a simple explanation for this, but I have not yet discovered it.”
They have the same structure so wouldn’t you expect an integer multiple? Trips are 3 cards of the same rank and 2 kickers, a Pair is 2 cards of the same rank and 3 kickers. I would also expect the quad to be an integer multiple since it is 4 cards of the same rank and 1 kicker.
You are correct. Trips are 88 times as likely as quads, which in turn are 1760 times as likely as a pair.
It’s not at all obvious to me why this is the case. Yes I read what you wrote, but to me full houses are a special category of trips (i.e. those where the two kickers happen to be paired.) If you add the full houses to the trips, they are 94 times as common as quads.
Clearly your mathematical intuition is superior to mine.
Bob
Could you both show the math on this?
JR
On Tuesday, June 17, 2014 10:50 PM, “Bob Dancer bobdance…@…com [vpFREE]” <vpF…@…com> wrote:
NOTI wrote: Bob wrote: “Interestingly, a single pair is dealt exactly 20 times as often as trips
are dealt. Not ABOUT 20 times. EXACTLY. I’m sure there is a simple explanation for this, but I have not yet discovered it.”
They have the same structure so wouldn’t you expect an integer multiple? Trips are 3 cards of the same rank and 2 kickers, a Pair is 2 cards of the same rank and 3 kickers. I would also expect the quad to be an integer multiple since it is 4 cards of the same rank and 1 kicker.
You are correct. Trips are 88 times as likely as quads, which in turn are 1760 times as likely as a pair.
It’s not at all obvious to me why this is the case. Yes I read what you wrote, but to me full houses are a special category of trips (i.e. those where the two kickers happen to be paired.) If you add the full houses to the trips, they are 94 times as common as quads.
Clearly your mathematical intuition is superior to mine.
Bob
JR asked: “Could you both show the math on this?”
Quads with one kicker:
13 ranks of quads x 12 ranks of kickers x 4 suits
Trips with two kickers:
13 ranks of trips x combin(4,3) suits x combin(12,2) ranks of kickers x 4^2 suits
Pair with three kickers:
13 ranks of pairs x combin(4,2) suits x combin(12,3) ranks of kickers x 4^3 suits
Trips with any other two cards (includes a full boat):
13 ranks of trips x combin(4,3) suits x combin(48,2) other two cards
Thanks for the help.
JR
On Wednesday, June 18, 2014 2:06 PM, “nightoftheiguana2…@…com [vpFREE]” <vpF…@…com> wrote:
JR asked: “Could you both show the math on this?”
Quads with one kicker:
13 ranks of quads x 12 ranks of kickers x 4 suits
Trips with two kickers:
13 ranks of trips x combin(4,3) suits x combin(12,2) ranks of kickers x 4^2 suits
Pair with three kickers:
13 ranks of pairs x combin(4,2) suits x combin(12,3) ranks of kickers x 4^3 suits
Trips with any other two cards (includes a full boat):
13 ranks of trips x combin(4,3) suits x combin(48,2) other two cards