John Robison's Midwest Gaming and Travel article:
http://makeashorterlink.com/?A49025D72
<a href=" http://makeashorterlink.com/?A49025D72">
http://makeashorterlink.com/?A49025D72</a>
1,000,000 hands = "long run" for DB ?
Quoting the Robinson article:
"The range for the 10/7 player is 100.3% to 102.1% and for the 9/7
player it's 98.2% to 99.9%."
Very impressive to have a 90% chance of exceeding the ER of the
machine. I think this only applies to Video poker in Lake
Woebegone<sp?>, where all the players are above average, although I
didn't see Garrison Keeler quoted as a source.
"After 1,000,000 hands, the 10/7 player has pulled ahead of the 9/7
player."
That's one way of looking at it. Maybe I'm a simpleton. I know it's
not precise due to some strategy changes, but the way I look at it
the 10/7 player has pulled ahead by almost one coin as soon as he
hits a full house.
AJ
Using a normal distribution approximation, seems to me that you are
still only about a third of a standard deviation above breakeven
after one million perfectly played 10/7 DB hands. If true, I think
most people would consider it quite a stretch to define this as
reaching the elusive "long run". You'd barely be getting warmed up.
I should have said one unit (5 coins) instead of one coin in the last
sentence of my prior post. See below. Sorry.
AJ
snip
I know it's
not precise due to some strategy changes, but the way I look at it
the 10/7 player has pulled ahead by almost one unit (not one coin)
as soon as he hits a full house.
···
AJ
--- In vpFREE@y..., "AJ" <mile_5280@y...> wrote:
Quoting the Robinson article:
"The range for the 10/7 player is 100.3% to 102.1% and for the 9/7
player it's 98.2% to 99.9%."Very impressive to have a 90% chance of exceeding the ER of the
machine. I think this only applies to Video poker in Lake
Woebegone<sp?>, where all the players are above average, although
I
didn't see Garrison Keeler quoted as a source.
"After 1,000,000 hands, the 10/7 player has pulled ahead of the
9/7
player."
That's one way of looking at it. Maybe I'm a simpleton. I know
it's
not precise due to some strategy changes, but the way I look at it
the 10/7 player has pulled ahead by almost one coin as soon as he
hits a full house.AJ
Has anyone else checked this math. I get a different number but am
not sure I am doing it correctly.
DWK
I think that after 1M hands you are 90% confident to be within about
+/-0.9% of the ER of the machine. Robinson seems to have added a
percent to his range for 10/7 by mistake? I get more like 99.3% to
101.0%. So using his logic, the 10/7 player still hasn't "pulled
ahead" of 9/7 player.
Looking for the point at which the confidence intervals have very
little overlap seems like a crazy way to compare machines. Why make
it hard? IMHO you have lost about 1% of a unit every time you deal a
hand. If you play 600 hands per hour at 9/7DB dollars, you should
ask if you will get $30/hour in (comp+cb+entertainment) value.
btw, the best way I know to compare confidence intervals is to ask
Effen Dolts; he has a written a calculator that doesn't use
approximations. The normal distribution assumption doesn't work very
well until you get through many royal cycles.
AJ
--- In vpFREE@y..., "deuceswild1000" <deuceswild1000@y...> wrote:
--- In vpFREE@y..., "AJ" <mile_5280@y...> wrote:
> Quoting the Robinson article:
>
>
> "The range for the 10/7 player is 100.3% to 102.1% and for the
9/7
···
> player it's 98.2% to 99.9%."
>Has anyone else checked this math. I get a different number but am
not sure I am doing it correctly.DWK
That is the exact same values I got, but was reluctant to publish
them until checked by someone else.
Who is Mr. Dolts and how does one get the program you mention?
BTW thanks for confirming my calculations.
DWK
--- In vpFREE@y..., "AJ" <mile_5280@y...> wrote:
I think that after 1M hands you are 90% confident to be within
about
+/-0.9% of the ER of the machine. Robinson seems to have added a
percent to his range for 10/7 by mistake? I get more like 99.3%
to
101.0%. So using his logic, the 10/7 player still hasn't "pulled
ahead" of 9/7 player.Looking for the point at which the confidence intervals have very
little overlap seems like a crazy way to compare machines. Why
make
it hard? IMHO you have lost about 1% of a unit every time you
deal a
hand. If you play 600 hands per hour at 9/7DB dollars, you should
ask if you will get $30/hour in (comp+cb+entertainment) value.btw, the best way I know to compare confidence intervals is to ask
Effen Dolts; he has a written a calculator that doesn't use
approximations. The normal distribution assumption doesn't work
very
well until you get through many royal cycles.
AJ
--- In vpFREE@y..., "deuceswild1000" <deuceswild1000@y...> wrote:
> --- In vpFREE@y..., "AJ" <mile_5280@y...> wrote:
> > Quoting the Robinson article:
> >
> >
> > "The range for the 10/7 player is 100.3% to 102.1% and for the
9/7
> > player it's 98.2% to 99.9%."
> >
>
> Has anyone else checked this math. I get a different number but
am
···
> not sure I am doing it correctly.
>
> DWK
I agree with AJ and DWK. Robison had typo in his article that
overstated the number by about 1%.
For 90% 10-7 DB, range I got was 99.3 to 101.05
Formula is 100*(1.645*SQRT(Variance)/SQRT(#hands))+Return % for HI
side, and Return % - 100*(1.645*SQRT(Variance)/SQRT(#hands)) for LOW
side. Where variance in this case is 28.2559, # hands is 1 million,
and Return % is 100.1725.
As a side note, for a 90% chance to be a winner (over 100% return) on
10-7, one would need to play about 26 million hands. (assumes no cash
back)
Good luck. TomSki
ps for 99% confidence, use 2.575 for multipler instead of 1.645, and
for 95% confidence, use 1.96.
--- In vpFREE@y..., "deuceswild1000" <deuceswild1000@y...> wrote:
···
That is the exact same values I got, but was reluctant to publish
them until checked by someone else.
DWK
--- In vpFREE@y..., "AJ" <mile_5280@y...> wrote:
> I think that after 1M hands you are 90% confident to be within
about
> +/-0.9% of the ER of the machine. Robinson seems to have added a
> percent to his range for 10/7 by mistake? I get more like 99.3%
to
> 101.0%.
I don't know what the original question was, but AJ asked me to
provide some results on 10/7 vs. 9/7 DB using my distribution
calculator. Below I have results for a fair coin toss, and for
the two DB games after 1,048,576 hands. The coin toss distribution
is symmetrical about zero. I.e., you have a 1% chance of losing
2382 bet units and the 1% chance of winning 2382 bet units.
The median result is in the 50% column. The median is zero for the
coin toss. The median equals the EV for normal distributions. For VP,
the median approaches the EV only after a large numbers of hands.
The distributions are asymmetric for DB, even after a million hands.
The 84% and 16% results correspond to plus and minus one standard
deviation on a normal distribution (VP is not normally distributed).
Note that a lucky player at the 84th percentile loses 4502 units on
9/7 DB. This is worse than an unluck 10/7 player at the
16th percentile, who loses only 3592 units.
Effen Dolts Video Poker Distribution Calculator
COIN TOSS, 0, 2
+------- +-------------------------------------------+
Hands | 1% 5% 16% 50% 84% 95% 99% |
+------- +-------------------------------------------+
1048576 | -2382 -1684 -1018 0 1018 1684 2382 |
+------- +-------------------------------------------+
DOUBLE BONUS POKER, 0, 1, 3, 5, 7, 9, 50, 80, 160, 800
+------- +-------------------------------------------+
Hands | 1% 5% 16% 50% 84% 95% 99% |
+------- +-------------------------------------------+
1048576 |-22224-18714-15308 -9984 -4502 -750 4040 |
+------- +-------------------------------------------+
DOUBLE BONUS POKER, 0, 1, 3, 5, 7, 10, 50, 80, 160, 800
+------- +-------------------------------------------+
Hands | 1% 5% 16% 50% 84% 95% 99% |
+------- +-------------------------------------------+
1048576 |-10536 -7012 -3592 1750 7252 11030 16012 |
+------- +-------------------------------------------+
The one percentile point for a fair coin toss game is a loss of
-0.227%.
This means that 99% of players will do better than this. For 10/7 DB,
the 1 percentile point is a loss of 1.005% vs. a 2.119% loss for 9/7.
This point out how much longer it takes to get within one percent
of the EV for a high-variance game like DB compared to even-money
wagers.
I have played more than a million hands of VP with rather poor
results, so far. After more than 900,000 hands of VP, I was about 1.2%
below expectation. This was mostly due to catching 11 Royals fewer
than the expected number. I have played another quarter million
hands since that low point. I have gotten two more Royals than
expected, and my overall return is now only 0.8% below expectation.
I am living proof that a million hands is not the long run unless
your advantage is more than 1%.
Effen
Effen Dolts was kind enough to run his distribution calculator and
post the results (message 9402). If I interpret his numbers
correctly, they are consistent with the 90% confidence numbers
reported here, 99.3% to 101.05%. However, the tails of the real
distribution are starting to differ significantly from the normal
distribution approximation at 98% confidence at 1 million hands. The
99% confidence error will be worse. So, I wouldn't count on the
using the 2.575 multiplier as suggested below to get a 99% confidence
interval.
If you attempt to size your bankroll for a trip (<100,000 hands)
based on the the formula below, your calculations will be grossly
inaccurate. Unfortunately, Effen's program is not currently
commercially available.
AJ
--- In vpFREE@y..., "tomskilv" <tomskilv@y...> wrote:
I agree with AJ and DWK. Robison had typo in his article that
overstated the number by about 1%.For 90% 10-7 DB, range I got was 99.3 to 101.05
Formula is 100*(1.645*SQRT(Variance)/SQRT(#hands))+Return % for HI
side, and Return % - 100*(1.645*SQRT(Variance)/SQRT(#hands)) for
LOW
side. Where variance in this case is 28.2559, # hands is 1 million,
and Return % is 100.1725.
As a side note, for a 90% chance to be a winner (over 100% return)
on
10-7, one would need to play about 26 million hands. (assumes no
cash
back)
Good luck. TomSkips for 99% confidence, use 2.575 for multipler instead of 1.645,
and
···
for 95% confidence, use 1.96.
Please help me out. I am not singling out A.J.'s post, as various
individuals have been using this/these formulae to make
comparisons.
Formula 1: Std dev of 10/7 DB = sqrt28.256 = 5.316 =std dev of
one hand
Formula 2: Std dev of 10/7 DB for 1,000,000 hands =
sqrt1,000,000 * 5.316 = 5,316 = std dev of 1,000,000 hands of 10/7 DB
Formula 3: 100 * sqrt 28,259/ sqrt 1,000,000 = std dev of what?
What is Formula 3?
--- In vpFREE@y..., "deuceswild1000" <deuceswild1000@y...> wrote:
Please help me out. I am not singling out A.J.'s post, as various
individuals have been using this/these formulae to make
comparisons.Formula 1: Std dev of 10/7 DB = sqrt28.256 = 5.316 =std dev
of
one hand
Formula 2: Std dev of 10/7 DB for 1,000,000 hands =
sqrt1,000,000 * 5.316 = 5,316 = std dev of 1,000,000 hands of 10/7
DB
Formula 3: 100 * sqrt 28,259/ sqrt 1,000,000 = std dev of what?
What is Formula 3?
I think I can answer my own question. It is the std dev of 1,000,000
hands expressed as a percent of the number of hands played. I am
trying to get something answered through private e-mail regarding
using or mis-using (that is what I am trying to learn) comparing
distributions of vp against the normal distribution. The above
formula was throwing me because I had seen it expressed in another
format and it had been a long day.
DWK
You are correct that formula 3 is the std dev of 1,000,000 hands of
10/7 DB expressed as a percent of units played. I think a double
typo has crept in however and 28,259 should be 28.256 however.
Corrected (hopefully) Formula 3
Formula 3: 100 * sqrt 28.256/ sqrt 1,000,000 = 0.532
It may look more intuitive when it is expressed as:
as 100*sqrt(28.256)* sqrt(1000000)/1000000 = 0.532
So one standard deviation is 0.532% of total action.
AJ
-- In vpFREE@y..., "deuceswild1000" <deuceswild1000@y...> wrote:
--- In vpFREE@y..., "deuceswild1000" <deuceswild1000@y...> wrote:
> Please help me out. I am not singling out A.J.'s post, as
various
> individuals have been using this/these formulae to make
> comparisons.
>
> Formula 1: Std dev of 10/7 DB = sqrt28.256 = 5.316 =std dev
of
> one hand
>
> Formula 2: Std dev of 10/7 DB for 1,000,000 hands =
> sqrt1,000,000 * 5.316 = 5,316 = std dev of 1,000,000 hands of
10/7
DB
>
> Formula 3: 100 * sqrt 28,259/ sqrt 1,000,000 = std dev of what?
>
> What is Formula 3?I think I can answer my own question. It is the std dev of
1,000,000
···
hands expressed as a percent of the number of hands played. I am
trying to get something answered through private e-mail regarding
using or mis-using (that is what I am trying to learn) comparing
distributions of vp against the normal distribution. The above
formula was throwing me because I had seen it expressed in another
format and it had been a long day.DWK