vpFREE2 Forums

3play vs 5play to Max royal chances

#1

Math question.
Say one wanted to maximize the probability to hit AT LEAST one
royal.
Here are the paramaters;
Play 3000 base hands of 3 Play (15 coins total per play) or 1800
hands of 5 Play (25 coins total per play). The average number of
royals hit will be the same for each: about .222 royals.
Some numbers that may be of use are the number of hands dealt that
involve drawing to a royal (JOB 9/6) and the chances of making it:

Royal # chances 1 in:
Pat 4 1
Draw 1 936 47
Draw 2 27492 1081
Draw 3 204660 16215
Draw 4 390828 178365
Draw 5 84360 1533939

Total Hands
  2598960

Good luck. TomSki

#2

tomskilv@yahoo.com wrote:

Math question.
Say one wanted to maximize the probability to hit AT LEAST one
royal.
Here are the paramaters;
Play 3000 base hands of 3 Play (15 coins total per play) or 1800
hands of 5 Play (25 coins total per play). The average number of
royals hit will be the same for each: about .222 royals.

snip

Good luck. TomSki

Intuitively, without doing any math, I'd say that you have a better chance of hitting AT LEAST ONE Royal by playing 3 play instead of 5 play. This is because you will get to play more base hands, where you get the 'dealt' Royals.

Cheers.

Bill Velek

#3

I did this quickly, so I might have done something wrong, but the
odds should be the same.

Basically, you take the number of hands originally played (1800 or
3000) times the probability of the pre-draw hand occurring and then
multiply the odds of the pre-draw hand turning into a Royal by the
number of result hands (5 or 3). In the end, you're multiplying in
both cases by 9000.

It comes out to about a 22.2371% chance of hitting a Royal.

Kil

···

--- In vpFREE@yahoogroups.com, tomskilv@y... wrote:

Math question.
Say one wanted to maximize the probability to hit AT LEAST one
royal.
Here are the paramaters;
Play 3000 base hands of 3 Play (15 coins total per play) or 1800
hands of 5 Play (25 coins total per play). The average number of
royals hit will be the same for each: about .222 royals.
Some numbers that may be of use are the number of hands dealt that
involve drawing to a royal (JOB 9/6) and the chances of making it:

Royal # chances 1 in:
Pat 4 1
Draw 1 936 47
Draw 2 27492 1081
Draw 3 204660 16215
Draw 4 390828 178365
Draw 5 84360 1533939

Total Hands
  2598960

Good luck. TomSki

#4

I think I have my answer.
For 9/6 JOB 3 play, the probability of hitting at least one royal
in 3000 base hands is 21.1595%.
  For 9/6 JOB 5 play, the probability of hitting at least one royal
in 1800 base hands is 20.8248%.
  For each game, the average number of royals hit is the same:
0.222371 royals. Good luck. TomSki

Math question.
Say one wanted to maximize the probability to hit AT LEAST one
royal.
Here are the paramaters;
Play 3000 base hands of 3 Play (15 coins total per play) or 1800
hands of 5 Play (25 coins total per play). The average number of
royals hit will be the same for each: about .222 royals.
Some numbers that may be of use are the number of hands dealt

that

···

--- In vpFREE@yahoogroups.com, tomskilv@y... wrote:

involve drawing to a royal (JOB 9/6) and the chances of making it:

Royal # chances 1 in:
Pat 4 1
Draw 1 936 47
Draw 2 27492 1081
Draw 3 204660 16215
Draw 4 390828 178365
Draw 5 84360 1533939

Total Hands
  2598960

Good luck. TomSki

#5

seems like it should be the same:
1-(1-2.4758268E-05)^9000=19.9746855%

···

--- In vpFREE@yahoogroups.com, tomskilv@y... wrote:

I think I have my answer.
For 9/6 JOB 3 play, the probability of hitting at least one royal
in 3000 base hands is 21.1595%.
  For 9/6 JOB 5 play, the probability of hitting at least one royal
in 1800 base hands is 20.8248%.
  For each game, the average number of royals hit is the same:
0.222371 royals. Good luck. TomSki

--- In vpFREE@yahoogroups.com, tomskilv@y... wrote:
> Math question.
> Say one wanted to maximize the probability to hit AT LEAST one
> royal.
> Here are the paramaters;
> Play 3000 base hands of 3 Play (15 coins total per play) or 1800
> hands of 5 Play (25 coins total per play). The average number of
> royals hit will be the same for each: about .222 royals.
> Some numbers that may be of use are the number of hands dealt
that
> involve drawing to a royal (JOB 9/6) and the chances of making it:
>
> Royal # chances 1 in:
> Pat 4 1
> Draw 1 936 47
> Draw 2 27492 1081
> Draw 3 204660 16215
> Draw 4 390828 178365
> Draw 5 84360 1533939
>
> Total Hands
> 2598960
>
> Good luck. TomSki

#6

nightoftheiguana2000 wrote:

seems like it should be the same:
1-(1-2.4758268E-05)^9000=19.9746855%

It can't be the same. See my earlier post which doesn't show any math but logically reasons that, because some of the Royals are 'dealt' Royals (about 1 out of 16), then playing playing more base hands MUST increase the likelihood of hitting AT LEAST ONE Royal.

Cheers.

Bill Velek

#7

Yes, the probability of one royal in 9000 hands of single line
(45000 coin in at 5 coins per hand) is 19.97% as you calculated. But
this will be different for 3 play and 5 play since you will get
fewer base hands. (3000 and 1800).
  I wrote a computer program back in 1995 that calculates the
percentage payback on jacks or better VP. At the time VP Tutor and
Stanford Wong's program were the only two widely available. My
program was able to run about 10 times faster than those. I also
added a few housekeeping subroutines that shows the number of times
you draw for the royal. Thus the source of the number of times you
are drawing live to a royal. In the numbers below, I do need to
change one thing, when drawing 5, the chance of hitting a royal is
not 1 in 1533939 but around 1 in 453515. The reason is that you are
drawing live to more than 1 royal during a total 5 card redraw. On
average, you are drawing to about 3.38 royals. (only dead royal
draws are in the suit where you discard a lone ten)
Since the probability of 1 or more royals in single line play of
9000 hands is 19.97%, intuition tells me it must be less than this
for 3 play and 5 play. Thus my 3 play number of 21.15% and five play
of 20.82% are probably incorrect. But on a relative basis, I think 3
play remains a better choice if you want to maximize the chance of
at least 1 royal if your choice was between 3 play and 5 play. Of
course, playing 1 play would be the best choice of all. Good luck.
TomSki

ps the pat 4 refers to number of dealt royals per 2598960 cycle, and
the 1 means the probability of getting the royal when dealt it. The
columns did not line up on that one.

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:

seems like it should be the same:
1-(1-2.4758268E-05)^9000=19.9746855%

> I think I have my answer.
> For 9/6 JOB 3 play, the probability of hitting at least one

royal

> in 3000 base hands is 21.1595%.
> For 9/6 JOB 5 play, the probability of hitting at least one

royal

> in 1800 base hands is 20.8248%.
> For each game, the average number of royals hit is the same:
> 0.222371 royals. Good luck. TomSki
>
> > Math question.
> > Say one wanted to maximize the probability to hit AT LEAST

one

> > royal.
> > Here are the paramaters;
> > Play 3000 base hands of 3 Play (15 coins total per play) or

1800

> > hands of 5 Play (25 coins total per play). The average number

of

> > royals hit will be the same for each: about .222 royals.
> > Some numbers that may be of use are the number of hands dealt
> that
> > involve drawing to a royal (JOB 9/6) and the chances of making

it:

···

--- In vpFREE@yahoogroups.com, tomskilv@y... wrote:
> --- In vpFREE@yahoogroups.com, tomskilv@y... wrote:
> >
> > Royal # chances 1 in:
> > Pat 4 1
> > Draw 1 936 47
> > Draw 2 27492 1081
> > Draw 3 204660 16215
> > Draw 4 390828 178365
> > Draw 5 84360 1533939
> >
> > Total Hands
> > 2598960
> >
> > Good luck. TomSki

#8

hmm, well, let's check your numbers:

single line play, odds of getting a royal:
dealt: 4/2598960=1.5390772E-06
draw 1: 936/2598960 x 1/47=7.6626395E-06
draw 2: 27492/2598960 x 1/1081=9.7854555E-06
draw 3: 204660/2598960 x 1/16215=4.8564220E-06
draw 4: 390828/2598960 x 1/178365=8.4309485E-07
draw 5: 84360/2598960 x 1/453515=7.1572357E-08
total=2.4758261E-05
probability for 9000 base hands:
1-EXP(-9000x2.4758261E-05)=19.9744600%

3play:
drawn odds are now changed, instead of 1/47 it's
1-(46/47)^3=0.062481338, etc:
dealt: 4/2598960=1.5390772E-06
draw 1: 936/2598960 x 1-(46/47)^3=2.2502283E-05
draw 2: 27492/2598960 x 1-(1080/1081)^3=2.9329218E-05
draw 3: 204660/2598960 x 1-(16214/16215)^3=1.4568368E-05
draw 4: 390828/2598960 x 1-(178364/178365)^3=2.5292704E-06
draw 5: 84360/2598960 x 1-(453514/453515)^3=2.1471660E-07
total=7.0682933E-05
probability for 3000 base hands:
1-EXP(-3000x7.0682933E-05)=19.1074777%

5play:
dealt: 4/2598960=1.5390772E-06
draw 1: 936/2598960 x 1-(46/47)^5=3.6717170E-05
draw 2: 27492/2598960 x 1-(1080/1081)^5=4.8836839E-05
draw 3: 204660/2598960 x 1-(16214/16215)^5=2.4279115E-05
draw 4: 390828/2598960 x 1-(178364/178365)^5=4.2154270E-06
draw 5: 84360/2598960 x 1-(453514/453515)^5=3.5786021E-07
total=1.1594549E-04
probability for 1800 base hands:
1-EXP(-1800x1.1594549E-04)=18.8362834%

Yes, the probability of one royal in 9000 hands of single line
(45000 coin in at 5 coins per hand) is 19.97% as you calculated.

But

this will be different for 3 play and 5 play since you will get
fewer base hands. (3000 and 1800).
  I wrote a computer program back in 1995 that calculates the
percentage payback on jacks or better VP. At the time VP Tutor and
Stanford Wong's program were the only two widely available. My
program was able to run about 10 times faster than those. I also
added a few housekeeping subroutines that shows the number of times
you draw for the royal. Thus the source of the number of times you
are drawing live to a royal. In the numbers below, I do need to
change one thing, when drawing 5, the chance of hitting a royal is
not 1 in 1533939 but around 1 in 453515. The reason is that you are
drawing live to more than 1 royal during a total 5 card redraw. On
average, you are drawing to about 3.38 royals. (only dead royal
draws are in the suit where you discard a lone ten)
Since the probability of 1 or more royals in single line play of
9000 hands is 19.97%, intuition tells me it must be less than this
for 3 play and 5 play. Thus my 3 play number of 21.15% and five

play

of 20.82% are probably incorrect. But on a relative basis, I think

3

play remains a better choice if you want to maximize the chance of
at least 1 royal if your choice was between 3 play and 5 play. Of
course, playing 1 play would be the best choice of all. Good luck.
TomSki

ps the pat 4 refers to number of dealt royals per 2598960 cycle,

and

the 1 means the probability of getting the royal when dealt it. The
columns did not line up on that one.

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:
> seems like it should be the same:
> 1-(1-2.4758268E-05)^9000=19.9746855%
>
> > I think I have my answer.
> > For 9/6 JOB 3 play, the probability of hitting at least one
royal
> > in 3000 base hands is 21.1595%.
> > For 9/6 JOB 5 play, the probability of hitting at least one
royal
> > in 1800 base hands is 20.8248%.
> > For each game, the average number of royals hit is the same:
> > 0.222371 royals. Good luck. TomSki
> >
> > > Math question.
> > > Say one wanted to maximize the probability to hit AT LEAST
one
> > > royal.
> > > Here are the paramaters;
> > > Play 3000 base hands of 3 Play (15 coins total per play) or
1800
> > > hands of 5 Play (25 coins total per play). The average number
of
> > > royals hit will be the same for each: about .222 royals.
> > > Some numbers that may be of use are the number of hands

dealt

> > that
> > > involve drawing to a royal (JOB 9/6) and the chances of

making

···

--- In vpFREE@yahoogroups.com, tomskilv@y... wrote:

> --- In vpFREE@yahoogroups.com, tomskilv@y... wrote:
> > --- In vpFREE@yahoogroups.com, tomskilv@y... wrote:
it:
> > >
> > > Royal # chances 1 in:
> > > Pat 4 1
> > > Draw 1 936 47
> > > Draw 2 27492 1081
> > > Draw 3 204660 16215
> > > Draw 4 390828 178365
> > > Draw 5 84360 1533939
> > >
> > > Total Hands
> > > 2598960
> > >
> > > Good luck. TomSki