I've uploaded a pic to the photos section of vpFREE. A friend of mine
held 3 to the Royal on triple play and made identical Royals on the
bottom two lines.
At first glance it looks like a 4-to-it draw. Getting two Royals on
triple play holding <<3>> is pretty dang tough. I don't expect to do
this in my lifetime. I know people who play 3p regularly and haven't
done it holding 4.
It's picture # 58 in the photos section.
dcc1079 wrote:
I've uploaded a pic to the photos section of vpFREE. A friend of mine
held 3 to the Royal on triple play and made identical Royals on the
bottom two lines.
It's picture # 58 in the photos section.
Fantastic!
Of course, I'm driven to run the probabilities 
...
The odds of completing 2 royals out of 3 lines on a 3 card hold are
approx. 1 in 500208 shots. Pretty damn impressive achievement! (A
little more probable, of course, than a dealt royal.)
By comparison, the odds of achieving that "phenomenal" feat of
completing a royal on all 3 lines on a 4 card hold are only 1 in
110592, making your friend's hit all the remarkable.
But the relative improbability of starting the draw with 4 cards to
the royal rather than just 3 turn the odds a bit in just how
frequently you'll see either of these in play.
You'll see the 2 royals/3 lines/3-cards held completion about once in
300 mil. deals. (So, how close is your friend to that lifetime play?
For triple royals/3 lines/4-cards held the expectation is that it'll
pop once every 1.6 billion deals! (Of course, you'll see the triple
royal achievement more frequently than this, since those odds include
starting with 0 to 3 cards held in addition to the once in 649,740
dealt royal probability.
(All probabilities here assume a non-wild 52-card deck.)
- Harry
Harry,
how did you come up with those numbers ?
I get 3/1081/1081 or 1/389520.333... for the 2 royals from 3 cards and
1/47/47/47 or 1/103823 for three royals from 4 cards.
Regards,
Heppel
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...> wrote:
The odds of completing 2 royals out of 3 lines on a 3 card hold are
approx. 1 in 500208 shots. Pretty damn impressive achievement! (A
little more probable, of course, than a dealt royal.)By comparison, the odds of achieving that "phenomenal" feat of
completing a royal on all 3 lines on a 4 card hold are only 1 in
110592, making your friend's hit all the remarkable.
heppel wrote:
Harry, how did you come up with those numbers ?
I get 3/1081/1081 or 1/389520.333... for the 2 royals from 3 cards
and 1/47/47/47 or 1/103823 for three royals from 4 cards.
You're dead on guy. I rushed my calculations in between performing
other work this mroning, and was apparently seriously challenged in
counting how many cards were in the draw deck (not to mention
reversing a multiplication) ... leaving my other work seriously in
question
btw, I'll note that we both calculated (well, I attempted it the
probability of "AT LEAST 2 royals from a 3 card hold" ... which
includes the result of 3 royals. FWIW, the probability of exactly 2
royals is modestly different.
Thanks!
- Harry
Well, statistics is more complicated than I thought. I counted that
single occurance of three royals three times. So the probability for
exactly 2 royals is 1/(3/1081**2-3/1081**3) or approx. 1/389.881,
the probability for 2 or 3 royals is 1/(3/1081**2-2/1081**3) or
approx. 1/389.761 and for good measure the probability for 3 royals is
1/1081**3 or 1/1.263.214.441 .
-- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...> wrote:
heppel wrote:
> Harry, how did you come up with those numbers ?
>
> I get 3/1081/1081 or 1/389520.333... for the 2 royals from 3 cards
> and 1/47/47/47 or 1/103823 for three royals from 4 cards.You're dead on guy. I rushed my calculations in between performing
other work this mroning, and was apparently seriously challenged in
counting how many cards were in the draw deck (not to mention
reversing a multiplication) ... leaving my other work seriously in
questionbtw, I'll note that we both calculated (well, I attempted it
probability of "AT LEAST 2 royals from a 3 card hold" ... which
includes the result of 3 royals. FWIW, the probability of exactly 2
royals is modestly different.
I remember playing a triple play machine and drew 4 to the royal. I
started to salivate, and was mentally counting my money from at least
one royal. Much to my horror, I drew the same two junk cards on two of
the lines. I guess the math is the same, but the results certainly are
not. By the way, I cashed out and moved, as I thought something was
fishy with that machine.
--- In vpFREE@yahoogroups.com, "dcc1079" <dcc1079@y...> wrote:
I've uploaded a pic to the photos section of vpFREE. A friend of mine
held 3 to the Royal on triple play and made identical Royals on the
bottom two lines.At first glance it looks like a 4-to-it draw. Getting two Royals on
triple play holding <<3>> is pretty dang tough. I don't expect to do
this in my lifetime. I know people who play 3p regularly and haven't
done it holding 4.It's picture # 58 in the photos section.
The double royal was mine. And no, I haven't hit 300 mil deals yet.
I just checked my stats and I'm sitting at about 6 million dealt
hands lifetime now (feels closer to 300 mil though).
I used to follow these forums all the time, but I've really gotten out
of the habit in the last few years. I see a lot of the major players
are posting here now. I'll have to start monitoring here a little
more often.
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...> wrote:
You'll see the 2 royals/3 lines/3-cards held completion about once in
300 mil. deals. (So, how close is your friend to that lifetime play?