I was playing 10 play super aces sunday and was dealt 3 to the royal on the draw. I held them and hit 2 royals. I was shocked. What are the odds of that. Later on the same game I was dealt 3 aces on the draw and hit 4 aces 3 times. Needless to say I had a good day. Rick
long shot draw
rkenner_76098 wrote:
I was playing 10 play super aces sunday and was dealt 3 to the royal
on the draw. I held them and hit 2 royals. I was shocked. What are
the odds of that.
This will occur much more frequently than being dealt a pat royal, or
for that matter, more frequently than hitting a single-line royal in
general. The frequency of hitting on exactly two lines out of 10 this
way is about 1 in 26000 attempts.
Now, I suspect this seem suspiciously often, but keep in mind that it
compares to a 10-play overall royal frequency of around 1 in 4000 to
5000 hands dealt (depending on the game).
···
------
The calculation, if you're interested, is as follows:
In a single line game, the odds of filling a royal on a two card draw
is (2/47 x 1/46) - you're shooting for one of two cards on the first
drawn card and, if successful, the other one for the second drawn card.
When looking to fill two specific lines (say the first and second) in
10-play, the odds of hitting on both of those is the square of the
single line probability above - similar to the probability of hitting
two single line royals in a row, both on 2 card draws.
(2/47 x 1/46) ^ 2
In 10-play you've got several ways in which you can fill exactly two
lines. If the first line is filled then there are 9 other lines that
can complete the pair. Similarly, if it's the second line that's
filled, but not the first, there are 8 remaining. When everything is
said and done, there are 45 ways in which you can complete a royal on
two lines.
So, the previous product must be multiplied by 45 to determine our
probability.
(2/47 x 1/46)^2 * 45 = 1/25968
The odds of filling two or more lines becomes even stronger which is
what makes 10-play a truly exciting game.
- Harry
I wrote that the odds of hitting a royal in 10-play on exactly 2
lines, when holding 3 to the royal, is 1 in 25968 attempts.
I slipped up and left out a part of that calculation. The effect
isn't monumental, but the corrected result is 1 in 26121.
···
------
To correct my earlier explanation of the calculation, I wrote that the
odds of filling two specific lines was (2/47 x 1/46) ^ 2. That's
correct, but in looking to fill exactly 2 lines we're also asking that
none of the remaining lines fill. That probability is a little more
complex. It's: (2/47 x 1/46)^2 x [1 - (2/47x1/46)]^8
The second half that's been added expresses the probability that none
of the remaining 8 lines fill. For a single line that probability is
simply 1 - the probability that it filled (thus the stuff in the
square brackets). Raise that amount to the 8th power and you've got
the joint probability that 8 lines don't fill at the same time.
So, as before, take that equation and multiply by the 45 ways in which
you can fill 2 lines (and none of the other 8) and you're home free.
Since the probability of not filling a single line is very close to 1,
the overall effect of this adjustment is relatively small and for all
practical purposes we're still talking 1 in 26000.
Nonetheless, it doesn't hurt to be accurate. I'm just hoping that
someone doesn't find cause to correct this 
- H.
Harry Porter wrote:
rkenner_76098 wrote:
> I was playing 10 play super aces sunday and was dealt 3 to the
> royal on the draw. I held them and hit 2 royals. I was shocked.
> What are the odds of that.This will occur much more frequently than being dealt a pat royal,
or for that matter, more frequently than hitting a single-line royal
in general. The frequency of hitting on exactly two lines out of 10
this way is about 1 in 26000 attempts.Now, I suspect this seem suspiciously often, but keep in mind that
it compares to a 10-play overall royal frequency of around 1 in 4000
to 5000 hands dealt (depending on the game).------
The calculation, if you're interested, is as follows:
In a single line game, the odds of filling a royal on a two card
draw is (2/47 x 1/46) - you're shooting for one of two cards on the
first drawn card and, if successful, the other one for the second
drawn card.When looking to fill two specific lines (say the first and second)
in 10-play, the odds of hitting on both of those is the square of
the single line probability above - similar to the probability of
hitting two single line royals in a row, both on 2 card draws.
(2/47 x 1/46) ^ 2In 10-play you've got several ways in which you can fill exactly two
lines. If the first line is filled then there are 9 other lines
that can complete the pair. Similarly, if it's the second line
that's filled, but not the first, there are 8 remaining. When
everything is said and done, there are 45 ways in which you can
complete a royal on two lines.So, the previous product must be multiplied by 45 to determine our
probability.
(2/47 x 1/46)^2 * 45 = 1/25968The odds of filling two or more lines becomes even stronger which is
what makes 10-play a truly exciting game.- Harry
rkenner_76098 wrote:
I was playing 10 play super aces sunday and was dealt 3 to the royal
on the draw. I held them and hit 2 royals. I was shocked. What are the
odds of that.
It was pointed out to me that this question might be interpreted
differently than I did.
I read it as asking "What are the odds of completing exactly 2 royals
when 3 to the royal are held for the draw?"
It could also be read (and perhaps this is what was intended) "What
are the odds of being dealt 3 to the royal and then completing exactly
2 royals on the draw?"
The answer to the second question will be equal to the first
question's response times the odds of being dealt 3 to the royal.
- Harry